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Navigating the EPO’s “problem-solution approach”—Part I

No matter where in the world you would like to file a patent application, the key patentability requirements in all jurisdictions are essentially the same: novelty and inventive step (in some places also referred to as non-obviousness). According to these requirements, the invention must not be identical to something that is already available to the public (novelty) and the invention must not be a mere trivial modification of the prior art (inventive step).

The European Patent Convention (EPC), which provides the legal basis for granting European patents by the European Patent Office (EPO), states that an invention shall be considered as involving an inventive step, if having regard to the state of the art, it is not obvious to a person skilled in the art (Article 56 EPC). At first sight, one might justifiably think that therefore the only relevant question for assessing an inventive step is whether the invention is obvious to the skilled person having regard to the state of the art. This is however not what the EPO does for assessing inventive step. Since its inception in 1977, the EPO has established a rather unique approach to assess the presence of an inventive step, by breaking up the one question of obviousness, which is explicitly stated in the law, into three separate questions.

a) What is the closest prior art?

b) Which technical problem does the invention objectively solve vis-à-vis the closest prior art?

c) Would it have been obvious to the skilled person at the relevant date to solve this objective   technical problem in a way that falls within the terms of the claims?

This approach is generally called the “problem-solution approach” ( EPO Guidelines for Examination, G-VII.5 ). It is often argued that the roots of the “problem-solution approach” can be traced to Rule 42(1)(c) EPC, according to which the description of the European patent application shall disclose the invention in terms of a technical problem and an offered solution to the problem.

Leaving aside the question of where this approach has its statutory footing, it is important to note that the Boards of Appeal of the EPO over the years have developed this approach in an attempt to provide an objective way for assessing inventive step, avoiding hindsight when considering the prior art. The EPO’s approach tries, what otherwise might be difficult to accomplish, namely to force the person making the assessment into the shoes of the notional skilled person at the relevant date—as it were, when the invention did not yet exist, and from this perspective ask the question whether the invention is obvious over the prior art. Of course, this exercise is a difficult one and prone to subjective elements depending on the person carrying out the analysis. Each step along the way of the “problem-solution approach” aims to take out of the equation this subjective element when assessing inventive step.

While the Boards of Appeal have decided that the application of this approach is not mandatory, they have also repeatedly found that it is the best way of avoiding a subjective ex post facto analysis and therefore in principle the approach should be used. The Boards of Appeal even held that if one exceptionally deviates from this established approach, reasons for deviation must be provided. Furthermore, it is simply a fact that both the departments of first instance of the EPO and the Boards of Appeal in practical life insist on a “problem-solution approach”-analysis when arguing inventive step, whether it is as an applicant during examination proceedings, as a patent proprietor during opposition proceedings or as an opponent. Not following the “problem-solution approach” by the letter is often very much to the detriment of the party involved. Therefore, it is important to familiarize oneself with the general way the “problem-solution approach” works and the peculiarities that come with it.

Navigating the intricacies of the “problem-solution approach” can be a challenging task, even for European patent attorneys, for whom the EPO’s “problem-solution approach” is second nature. Therefore, in the next couple of weeks, I will go in detail through each of the three stages of the “problem-solution approach”, in a series of blog posts at this venue, titled “Navigating the EPO’s “problem-solution approach”—Part I-IV”. Next up: How to find the closest prior art? Stay tuned.

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Dr. Markus Grammel

Dr. Markus Grammel

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The Problem and Solution Approach - Basic Case Law and Recent Development (II) epi Information 2/2016." data-html="true">[1]

Michael m. fischer (de), european patent attorney, b. objective technical problem.

As a next step, the distinguishing features between the appropriate starting point and the subject-matter of the claim are determined. Then, the technical effect achieved by these distinguishing features is determined and an objective technical problem is formulated based on the technical effect. It is important to note that the formulated objective technical problem must not provide pointers to the claimed solution. T 641/00 suggests to put all non-technical features into the problem in order to avoid that they provide pointers to the solution." data-html="true">[2] The objective technical problem need not be the subjective technical problem mentioned in the background section of the patent application. Hence, the objective technical problem can be reformulated. If a technical effect cannot be demonstrated, the problem must be reformulated. [3]

Before the EPO, the presence of a technical effect is essential to the acknowledgement of an inventive step. In this context, the decision T 2044/09 should be cited in which the Board noted that "the mere fact that the claimed subject-matter was not novel over the prior art, even when combining document, was not sufficient to render it inventive. In fact in the absence of a proven effect in comparison to the prior art, it was considered that this must be regarded as an arbitrary non-functional modification of the prior art. Even if there was no pointer or suggestion in the prior art towards the addition of a distinguishing feature, if said modification was not linked to a particular functionality, then it could not per se constitute the basis for acknowledging an inventive step".

Hence, when drafting a European patent application, care should be taken to not only mention a technical problem or a technical effect in the background section of the patent application which normally relates to the overall problem addressed in the patent application but also to mention the technical effects associated with features mentioned in the dependent claims and/or in the description. If the technical effect is not mentioned in the application, it may be more difficult to convince the Examining Division that the technical effect (merely alleged in examination proceedings) is actually achieved. Reference is made to GL G-VII, 5.2 which states that "It is also possible to rely on new effects submitted subsequently during the proceedings by the applicant, provided that the skilled person would recognise these effects as implied by or related to the technical problem initially suggested". While it is common practice in the field of pharmacy to file results of clinical studies performed after the filing of the application in order to demonstrate a technical effect, applicants in other technical areas often do not seem to contemplate this option. For example, if the inventor has published - after filing the patent application - an article in which the technical effect is better explained than in the patent application itself, this article can be adduced in order to demonstrate the technical effect before the EPO. "In T 440/91 }} the Board pointed out that R. 27 EPC 1973 did not rule out the possibility of additional advantages - not themselves mentioned in the application as filed but relating to a mentioned field of use - being furnished subsequently in support of patentability for the purposes of Art. 52(1) EPC 1973 , as such advantages did not alter the character of the invention. Thus, the character of the invention was not altered if the technical problem specified in the application as filed was supplemented by such advantages, since the skilled person might consider them on account of their close technical relationship to the original problem (see also T 1062/93 ). The Board made a distinction with regard to the situation in T 386/89 and T 344/89 , where there was no such technical relationship. In T 386/89 the Board had found that the solution to the technical problem derivable from the application as filed was in no way associated with a technical effect subsequently invoked. This additional effect had thus not been taken into consideration. The alleged effect of a described feature could not be taken into account when determining the problem underlying the invention for the purpose of assessing inventive step, if it could not be deduced by the skilled person from the application as filed considered in relation to the closest prior art. Similarly in T 344/89 , the Board had refused to take account of a subsequently invoked technical effect on the grounds that to do so would have altered the character of the invention ( T 532/00 , T 845/02 , T 2179/08 )" th edition, 2013" data-html="true">[4] . If a technical effect is purported that is associated with a range of values, it should be noted that "an effect cannot be retained if the promised result is not attainable throughout the entire range covered by the claimed subject matter. Therefore, the technical problem needed to be redefined in a less ambitious way ( T 626/90 , T 1057/04 , T 824/07 )" th edition, 2013" data-html="true">[5] . Hence, should a first application not include the technical effects associated with individual features, it should be legitimate to incorporate these technical effects - taking into account the restrictions set forth in the decisions above - into the description of a second application to be filed with the EPO and claiming priority from the first application in order to facilitate its prosecution. Since this addition of technical features does not affect the feature combinations recited in the claims, this measure should not jeopardise the validity of the priority claim. A slightly different question is whether the claimed subject-matter solves the problem to be solved. In this context, the Boards held hat "post-published evidence to support that the claimed subject-matter solves the problem to be solved is taken into account if it is already credible from the disclosure in the patent [or patent application] that the problem is indeed solved. In other words, supplementary post-published evidence may not serve as the sole basis to establish that the problem is solved ( T 1329/04 , T 415/11 )" th edition, 2013" data-html="true">[6] .

At this point, it is worthwhile taking a look across the big pond where no other decision has shaken the patent world in recent years more than "Alice Corp. v. CLS Bank International" rendered by the US Supreme Court in 2014. The patents in suit were held to be invalid because the claims were drawn to an abstract idea, and implementing those claims on a computer was not enough to transform that idea into patentable subject matter. In short, this decision may be interpreted in a way that subject-matter (in this case software) is only patentable if it achieves a technical effect. As harsh and consequential http://cdn.theatlantic.com/assets/media/img/posts/2014/11/chart_1-1/5966e14bf.jpg shows that the USPTO issued fewer than half the number after Alice that it had issued per month during the period prior to Alice. At the same time, however, the issuance of other types of software patents rose. ( https://en.wikipedia.org/wiki/Alice_Corp._v._CLS_Bank_International#Lower_courts )" data-html="true">[7] as this decision may (or may not, if overturned) be for the patent world in the USA, it could constitute a harmonisation between the jurisprudence of the USA and the EPO. The author of this article appreciates the EPO's concentration onto a technical effect. Firstly, it makes sure that a patent is granted only for "technical" solutions (which leads, however, to the problem of the meaning of the term "technical"). Secondly, a patent is granted in return to the applicant making the invention public which can then be further developed by others. Hence, if it is not (at least implicitly) clear what the invention achieves because it is nothing but a combination of seemingly arbitrary features, then the description has to be considered to be incomplete and may be of little or no value to the public since the public does not know what the invention is for (see also the requirement of R. 42 (1) (c) EPC).

If the objective technical problem formulated based on the distinguishing features leads to a problem that cannot occur at the selected appropriate starting point, the selected starting point is inappropriate (see T 513/00 ). At least one cannot show in a logical chain of arguments that starting from this document the subject-matter of the claim can be arrived at in an obvious manner. When attempting to show that the subject-matter of a claim is not inventive using the problem and solution approach, it is advisable to countercheck whether the problem formulated is a problem that the selected appropriate starting point actually has. Otherwise the chain of argumentation becomes illogical.

As already mentioned above, if one has chosen a closest prior art document from a different genus, then it is difficult to formulate a reasonable problem which does not point to the solution because the problem would have to be based on the generic difference. If we consider a military helmet having the features a, b and c and the closest prior art is a worker's safety helmet having the same features a, b and c. The problem cannot be formulated as how to modify the safety helmet to also be able in military actions directly points to the solution. How to modify the safety helmet to be usable in a different environment would be too broadly formulated.

This leads to the question on how specific the objective technical problem should be formulated. In T 1019/99 , the Board held that it is established case law that the objective technical problem to be used in the problem and solution approach is to be formulated so that it does not anticipate or contain pointers to the solution. This constrains the specificity of the formulation. However, there is also a constraint on the amount that the formulation can "back off" from this specificity, i.e. a constraint on the generality of the problem. The problem can be no more general than the disclosure of the prior art allows . Otherwise, a problem could be formulated so generally as to circumvent indications in a prior art document towards the claimed solution. Thus the correct procedure for formulating the problem is to choose a problem based on the technical effect of exactly those features distinguishing the claim from the prior art that is as specific as possible without containing elements or pointers to the solution .

A. Obviousness

Following the gedankenexperiment of the problem and solution approach, by determining the appropriate starting point and the objective technical problem, a hypothetical situation is defined in which the fictitious skilled person [8] , a purely fictitious person with a certain knowledge and abilities, could have been.

(Hypothetical) Situation = Appropriate Starting Point + Objective Technical Problem

While the first two steps of the problem and solution approach are made in full knowledge of the invention (i.e. based on hindsight), it is now important to erase the knowledge of the invention from one's mind in order to be able to assess the question of obviousness without hindsight.

In practice, this situation could be compared with a development process in which a development manager gives a development engineer or team of engineers (skilled person(s)) the order to further develop a given product in a certain respect (based on a functional specification). [9] The question is whether the skilled person in the situation above could and would have found the solution to the objective technical problem, for example in a second document from the prior art, or not (could-would approach). Hence, a skilled person may perform the role of a guinea pig by means of which it is tested whether it reaches - in a given situation - the target (the subject-matter of the claim) or not. It is important to note that the skilled person neither selects the closest prior art nor formulates the problem but is presented with both of them.

The assessment of whether the further development of the prior art is obvious or not is not determined by what the skilled person could have done but by what he would have done. It should be noted that it is completely irrelevant in which situation the inventor actually was.

"That it was theoretically possible for the skilled person to arrive at the invention simply means that he could have used the requisite technical means. If, however, it is to be established that he would actually have used them, it must be possible to ascertain a pointer in the prior art which would have prompted him to do so ( T 1317/08 )" th edition, 2013" data-html="true">[10] .

Although the "raising the bar" initiative a few years ago only affected the European Patent Office and not the Boards of Appeal, some Boards of Appeal came to the conclusion that even an implicit prompting or implicitly recognisable incentive is sufficient to show that the skilled person would have combined the elements from the prior art (see  T 257/98 and T 35/04 ). This must have been the case for the skilled person before the filing or priority date valid for the claim under examination.

In T 1014/07 the Board stated that the mere existence of teachings in the prior art is not a conclusive reason for explaining that the skilled person would have combined these teachings in order to solve the problem that he or she is confronted with. As a further reason for denying an inventive step for the claimed subject-matter the examining division indicated that "[t]he mere fact that a known biochemical step has been added to a known chemical process of oxidation cannot be considered in itself inventive in the absence of a special feature or advantage of the combined use of biochemical and chemical processes". However, for the determination of the obviousness or non-obviousness of claimed subject-matter, it is not decisive that teachings are known - it must be decided whether or not the skilled person would have combined the known teachings such as to arrive at the claimed subject-matter when attempting to solve the underlying technical problem. Thus, in contrast to the examining division's view, the combination of known teachings may result in non-obvious subject-matter, namely when the skilled person is not motivated, for example by promptings in the prior art, to make such a combination. Under these circumstances the presence of any special effect arising from the combination is not necessary to establish an inventive step .

While it appears that the "could-would approach" is sometimes only applied to the question whether there was an incentive/prompting to apply the teaching of a secondary document to the teaching of the appropriate starting point, the author of the article suggests the following more comprehensive scheme:

While the question of "could" merely refers to the fact whether something falling under the features of the claimed solution was somewhere available in the prior art, the question of "would" deals with the question whether the skilled person would have found the solution and applied it to the appropriate starting point. In short:

Could : Would = Solution : Context

In other words, "could" refers to the theoretical possibility of finding the solution while "would" denotes whether the skilled person would have practically found the solution in view of the context in which the solution is presented. Typically, the transfer of a known solution in a suitable context to an appropriate starting point is considered to be a further development that the skilled person could and would have achieved. In T 142/84 [12] , the Board argued in a such an archetypal way: "The respondents are of course correct when they state that the mere fact that a skilled person would not encounter insurmountable difficulties in providing a characterising feature of a claim does not lead (necessarily) to the conclusion that there is no inventive step. However, when the feature is known from a document in the same specialised field, and solves the same problem, then the fact that the skilled person would not encounter insurmountable difficulties in applying this known feature to a known apparatus from a second document does demonstrate that the documents are not conflicting (see T 02/81, OJ EPO 10/1982, 401), and that an inventive step is lacking . The problem solved does not have to be stated expressis verbis in the prior art. The respondents refer further to the earlier decision T 39/82 OJ EPO 11/1982, 423. In that case it was decided that the problems to be respectively solved with a known measure in the known case and in the case to be decided must be taken into account. Since the problems differed fundamentally from one another it could not be considered obvious for the skilled person to use this known measure in a different context. Since however the purpose of the features known from US-A-4 100 657 is the same as in the present case, it cannot be denied that the problems do not differ fundamentally and this prior art gave the skilled person an indication for applying these features in the present case."

In yet other words, the could-would approach tests in how far two documents/teachings fit with each other. This is sometimes compared with a jigsaw puzzle [13] with the documents being the pieces of the jigsaw puzzle. As mentioned above, it is crucial that at least one of the documents contains an incentive/prompting so that its teaching will be applied to the teaching of another document which implies that "mosaic-like combinations will normally not be persuasive" http://www.bardehle.com/en/publications/interactive_brochures/inventive_step.html " data-html="true">[14] . However, one must not forget that the prior art can also be represented by a "prior use" which normally - by its nature - does not contain any incentive/prompting.

While the skilled person needs an incentive to apply the teaching of a second prior art item to that of an appropriate starting point, the Guidelines state under G-VII, 6 (iii) that "it would normally be obvious to combine with a prior art document a well-known textbook or standard dictionary; this is only a special case of the general proposition that it is obvious to combine the teaching of one or more documents with the common general knowledge in the art". This obviously means that no incentive/prompting is needed to apply the skilled person's common general knowledge to an appropriate starting point. Thus, according to the Guidelines, the difference between a normal prior art document and the skilled person's common general knowledge appears to be that the common general knowledge as the skilled person's mental furniture is very present in his brain and therefore the hurdle that the skilled person applies it to a teaching of another document is very low or not existing (= no incentive is needed). However, care has to be taken in order to identify what is actually known from the common general knowledge and how the skilled person would apply it to the teaching of a prior art document. It is important to note that the skilled person's common general knowledge may not be applied in a certain (target-oriented, purposeful) direction to arrive at the claimed subject-matter. This would be considered an unallowable ex-post-facto analysis.

In T 1471/11 , the Board held that "the argument of the appellant must fail that neither claim 1 nor the description of the patent in suit define the claimed arrangement for lubrication to such an extent that it can be understood without having recourse to the general technical knowledge and understanding of the skilled person. With that general technical knowledge in mind, in addition to the teaching of the available documents, the examination of inventive step would necessarily lead to the conclusion that the claimed subject-matter does not involve an inventive step. The reason is that even if it is correct that general technical knowledge and practice needs to be taken into account in order to reduce the arrangement for lubricating defined by claim 1 to practice, the decisive direction in which this general technical knowledge is to be applied to arrive at what is claimed, still needs to be derivable from some teaching or knowledge" [15] . The Board set forth a similar argumentation in T 386/12 and T 1426/10 .

This is different from the use of the common general knowledge in the field of "sufficiency of disclosure" (Art. 83 EPC) where the skilled person would use his common general knowledge in a target-oriented way to determine whether the invention is sufficiently disclosed by the application as a whole. He is in the position to use his common general knowledge in a target-oriented way because he knows the prior art and the invention, while the skilled person in the assessment of inventive step only knows the prior art. However, in both assessments, "the same level of skill has to be applied ( T 60/89 and T 373/94 )" th edition, 2013" data-html="true">[16] . In slightly other words: "The skilled person when assessing sufficiency of disclosure of a patent has knowledge of the invention as disclosed, i.e. knowledge of both the prior art, the problem and its solution, and is aware of documents cited in the patent and the common general knowledge in the art" ( T 6/84 , T 171/84 ) st edition, 2013, p.174, section 2.2" data-html="true">[17] . With both decisions being quite old and search engines becoming more and more powerful, it would be interesting to see if e.g. a novel, unusual or special term in a claim of a patent application, the term not being part of the skilled person's common general knowledge (i.e. cannot be found in standard textbooks, etc.) and the patent application neither containing any explanations nor references to other documents, would make the application not meet the requirement of "Sufficiency of Disclosure" even if an explanation of the term could easily be found using a search engine. The decision T 580/88 also appears to be quite harsh in this respect.

In T 1641/11 , the Board held that the assertion that something was part of the common general knowledge therefore needed only to be substantiated if challenged by another party or the EPO. "Where an assertion that something was part of the common general knowledge is challenged, the person making the assertion must provide proof that the alleged subject-matter indeed forms part of the common general knowledge ( T 438/97 , T 329/04, T 941/04 , T 690/06 )" th edition, 2013" data-html="true">[18] .

D. Further Considerations

The following schematic example wants to demonstrate why it does not make sense to focus on one closest prior art document.

(The lowercase letters denote special features that anticipate the features denoted by the corresponding uppercase letters.)

Both documents D1 and D2 qualify as appropriate starting points (same purpose as the claim, etc.). However, since D2 has one more feature in common with the claim, it could be considered to be the (one and only) closest prior art document. Although D2 is per se closer to the claim than D1, it may be that there are incompatibilities (e.g. mechanical incompatibilities, incompatible dimensions) between D2 and D3 and D2 and D4 such that the skilled person would neither apply the teaching of D3 nor the teaching of D4 to that of D2. Hence, the (wrong) conclusion would be that starting from the closest prior art D2, the skilled person would not have arrived at the subject-matter of the claim in an obvious manner. However, there may not be incompatibilities between document D1 and D3 and the skilled person could and would apply the teaching of D3 to that of D1, thereby arriving at the subject-matter of the claim in an obvious manner. Since there exists one way to arrive at the subject-matter of the claims, it has been shown that claim 1 does not involve an inventive step. Since the question whether one arrives at the subject-matter of the claim in an obvious way also depends on how well the primary reference fits together with the secondary reference, documents must not be prematurely disregarded as appropriate starting points.

Applying the problem and solution approach is sometimes compared with mountaineering http://k-slaw.blogspot.de/2012/09/t-5609-so-close.html " data-html="true">[19] . Two hikers A and B, of ordinary skill, not Reinhold Messner, (person of ordinary skill in the art, no Nobel Prize winner) want to hike to the summit (invention/ subject-matter of claim) of Mount Inv. From their starting point, they both see the summit they want to reach (selection of appropriate starting point is made in knowledge of the invention). Hiker A takes a trail (a first appropriate starting) which is very steep and goes very straight into the direction of the summit (same purpose). This trail appears to be very promising since, as far as he can see, it almost reaches the summit (only one feature missing ☺ ). Hiker B takes another trail (a second appropriate starting point) which also goes in the direction of the summit but is less steep. However, he can only see that his trail ends somewhere in the forest at half the height of the summit (some more features missing ☹ ). When hiker A reaches the end of his trail, he notices that the trail abruptly ends and that he would have to climb (perform an inventive step) the last few meters from there to reach the summit. Unfortunately, there is no signpost (pointer, incentive/prompting) showing him how he could alternatively reach the summit by hiking. He also looks into his standard mountain survival guide (common general knowledge - a hiking map would not be a good analogon under the assumption that the common general knowledge must not be used target-oriented) that he always carries with himself. When hiker B reaches the end of his trail, he has only reached half the height of the summit, but he notices a signpost (pointer to another document) that indicates that several other trails (further documents possibly containing a solution) start from a place very close (neighboring technical field) from here. He follows the signpost and arrives at a point where he sees different signposts (incentives/promptings to different documents), one of them (incentive/prompting to the document disclosing the solution) indicating that this hiking trail - ideal for the ordinary hiker, no climbing necessary - leads to the summit of the mountain. The hiker follows this trail (second document) and easily arrives at the summit without any climbing. A trail which appears at first glance less promising than another trail may lead to the summit while the other trail may not. In the language of the problem and solution approach, this means that not any document that appears to come closer to the subject-matter of the claim than all other documents is suitable to show that the subject-matter of the claim is inventive, while a not so close document is ideally complemented by another document which shows that the subject-matter of the claims is indeed inventive.

E. Alternatives

The EPO lives and breathes the problem and solution approach. Hence, the decision T 465/92 received a lot of attention because already its headnote stated that the problem and solution approach is no more than one possible route for the assessment of inventiveness. Accordingly, its use is not the only possibly approach when deciding on inventiveness under Article 56 EPC. In the Case Law Book 6 th edition, this decision has been classified as "a one-off decision". Interestingly, in the 7 th edition, this remark has been replaced with the sentence that the Board "took the view that all of the seven cited documents came equally close to the invention". Possibly, this decision, which has often been categorized as a heretical decision not to be followed, was an early decision to recognize the issue of referring to one closest prior document, which was not possible in the present case, and therefore decided not to apply the problem and solution approach. Possibly, the members of the Board had a (formal) problem with the superlative notion of a one and only "closest prior art document" and therefore declined applying the problem and solution approach. Maybe, the amendment of the Case Law Book is a late and silent rehabilitation of this decision which partly anticipated the decisions T 967/97 , T 558/00 , T 21/08 , T 308/09 and T 1289/09 that have now found their way into the last version of the Guidelines.

In T 939/92 the Board of Appeal referred to the decision T 465/92 . Although it was held in No. 9.1 of the reasons of this decision that the "problem and solution approach" is not a sine qua non for the determination of inventiveness by the EPO, it follows, in the Board's judgment, from the detailed explanations given in the following points 9.2 to 9.6 of the reasons that in that case the Board refrained from identifying a certain document as "closest state of the art" and formulating a "technical problem" on the basis of such a state of the art. In the present case, however, the question of selecting a particular document as "closest state of the art" is not at issue. However, in decision T 465/92 the Board considered the results which had been objectively achieved by the claimed invention, and then proceeded, on that basis, to decide whether or not the cited state of the art, as a whole, would have suggested to the skilled person that these results could be achieved in the way indicated in the patent under consideration.

In T 188/09 the Board stated that the "problem and solution approach" is regularly applied as an auxiliary means by the instances of the European Patent Office in the course of deciding whether or not claimed subject-matter fulfils the requirements of Article 56 EPC. The appellant, referring to decision T 465/92 of 26 November 1993, observed that there are however cases where the "problem and solution approach" hinders, rather than assists answering the question of whether claimed subject-matter is obvious over the prior art.

In decision T 465/92 the Board explicitly decided not to use the "problem and solution approach" (see points 6 to 9.6 of the Reasons). Thus, the Board understands the appellant's reference to this decision as an argument that the present case is one where the "problem and solution approach" should not be used.

The Board notes first that whatever approach is applied as an auxiliary means for the evaluation of inventive step of claimed subject-matter, in a given evidential situation it must provide the same result, be it either in favour of or against inventive step. Therefore, in the present case, even if the "problem and solution approach" was applied, the decision on inventiveness should be the same as if it was not used.

Moreover, according to the reasons of decision T 465/92 , the Board decided to avoid the "problem and solution approach" because it considered that the seven relevant citations were all equally close to the claimed invention and that therefore, the opponent "ought not to be tied down by having to select one or more citations as being closer than others" (see points 9.3 and 9.4 of the Reasons). Consequently, the Board considered them all individually without selecting one as the closest prior art document .

The Board in decision T 465/92 also notes in point 9.5 of the Reasons that there may be situations which "can result in a complicated multi-step reasoning where the facts were clear, either for or against inventiveness. Thus, if an inventions breaks new ground it may suffice to say that there is no close prior art rather than constructing a problem based on what is tenuously regarded as the closest prior art."

None of the circumstances for the avoidance of the classical "problem and solution approach" referred to in decision T 465/92 is present in the case at hand [i.e. **T 188/09**], i.e. neither can the claimed subject-matter be considered as breaking new ground, since document D4 describes a G-protein coupled receptor specifically located in taste cells nor is there a large number of equally close prior art documents (see points 9 to 13 below).

Thus, having considered the rationale in decision T 465/92 the present Board does not see a reason to apply the approach adopted by the Board in that decision rather than the classical "problem and solution approach".

F. Conclusion

The application of the problem and solution approach has evolved over the years. However, the problem and solution approach is still - and more than ever - the one and only prayer before the EPO and has pushed all other approaches into the field of heresy. The problem and solution approach is even applied outside the scope of the EPC since the PCT International Search and Preliminary Examination Guidelines also suggest applying this approach http://www.wipo.int/export/sites/www/pct/en/texts/pdf/ispe.pdf " data-html="true">[20] . Although the problem and solution approach appears to be algorithmic [21] in nature and hundreds of decisions of the Boards of Appeals give advice on how to apply the approach in many cases, its outcome is in the eyes of the author of this article not always predictable. Ultimately, the question of "inventive step" is a legal question and assessing inventive step is an act of judging which involves subjective elements. In patent law and in many other legal fields the roman legal principle "Iudex non calculat." still applies. Nevertheless, the problem and solution approach is a systematic approach and that alone may be the reason for its success and longevity.

Any feedback is welcome and can be sent to [email protected] or [email protected]

  • This is the second part of an article that is based on a talk held by the author on September 8, 2015 at the European Patent Experts' Forum (EuPEX) in Munich. The first part was published in epi Information 2/2016.
  • T 641/00 suggests to put all non-technical features into the problem in order to avoid that they provide pointers to the solution.
  • Handout of presentation "Problem/Solution Approach to Inventive Step and Challenging Cases" held by Graham Ashley, Chairman of a Technical Board of Appeal, at the conference "Boards of Appeal and key decision" on November 26/27, 2015 in Munich
  • Case Law of the Boards of Appeal, section I.D, 4.4.2, 7 th edition, 2013
  • Case Law of the Boards of Appeal, section I.D.4.6, 7 th edition, 2013
  • The graph available at http://cdn.theatlantic.com/assets/media/img/posts/2014/11/chart_1-1/5966e14bf.jpg shows that the USPTO issued fewer than half the number after Alice that it had issued per month during the period prior to Alice. At the same time, however, the issuance of other types of software patents rose. ( https://en.wikipedia.org/wiki/Alice_Corp._v._CLS_Bank_International#Lower_courts )
  • A detailled definition of the skilled person, his abilities and his knowledge in different fields of technology is omitted. Not many decisions on this seem to have been issued any time recently.
  • Hoekstra, J., "Methodology for Paper C - Training for the European Qualifying Examination", Deltapatents, October 2009, p.151
  • Case Law of the Boards of Appeal, section I.D.5, 7 th edition, 2013
  • Of course, the question whether two teachings are compatible with each other is determined based on the concrete disclosure of the two documents and not on the abstraction level of the claims since the skilled person does not know the subject-matter of the claim.
  • Hoekstra, J., "Methodology for Paper C - Training for the European Qualifying Examination", Deltapatents, October 2009, p.154 and cover page
  • section 3.3 of http://www.bardehle.com/en/publications/interactive_brochures/inventive_step.html
  • The Federal Court of Justice of Germany came to a similar (possibly even broader) conclusion in its decision Xa ZR 56/05 "Airbag-Auslösesteuerung": "The mere fact that a teaching belongs to the skilled person's common general knowledge does not yet prove that it was obvious for the skilled person to employ this teaching in order to solve a specific technical problem". A further decision in this context is the decision X ZR 139/10 "Farbversorgungssystem" in which the Federal Court of Justice came to the conclusion that the skilled person would have applied a solution from his common general knowledge "because using its functionality was objectively expedient and there were no special circumstances rendering such use impossible, difficult or otherwise impracticable from a specialist point of view".
  • Case Law of the Boards of Appeal, section I.D.8.3, 7 th edition, 2013
  • Visser, D., "The Annotated European Patent Convention", 21 st edition, 2013, p.174, section 2.2
  • Case Law of the Boards of Appeal, Section I.D.8.3, 7 th edition, 2013
  • see for instance: http://k-slaw.blogspot.de/2012/09/t-5609-so-close.html
  • "One specific method of assessing inventive step might be to apply the so called "problem-solution approach", PCT International Search and Preliminary Examination Guidelines as in force from October 1, 2015, Appendix to Chapter 13, page 117, http://www.wipo.int/export/sites/www/pct/en/texts/pdf/ispe.pdf
  • Not surprising in view of the high number of scientifically educated people in patent law. Not surprising either if the search tools used by the EPO Examiners already supported the problem and solution approach by e.g. suggesting documents from the same, broader or neighbouring technical fields which in combination anticipate all the features of a claim.

the problem solution approach

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Article Contents

I. introduction.

  • II. The role of the closest prior art
  • III. Selecting the closest prior art document
  • IV. The closest prior art dilemma
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The closest prior art in the problem-solution approach: theoretical considerations and a dilemma

Dr., Examiner at the European Patent Office (Munich, Germany) in the field of biotechnology ( [email protected] ). The present article is based on personal considerations and does not necessarily reflect the official position of the European Patent Office on this subject.

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Thomas M. Leber, The closest prior art in the problem-solution approach: theoretical considerations and a dilemma, Journal of Intellectual Property Law & Practice , Volume 11, Issue 6, June 2016, Pages 471–473, https://doi.org/10.1093/jiplp/jpw054

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The European Patent Office evaluates the inventive step under Article 56 of the European Patent Convention (EPC) through the so-called problem-solution approach (PSA), which starts with the identification of the closest prior art. This short article reconsiders the concept of “closest prior art” from a theoretical and legal point of view, arguing that, it is not possible to define with certainty whether a particular document represents the correct closest prior art. Such certainty can only be achieved once the document has actually been used in the PSA, so at its end.

For a patent to be granted under the EPC, the claimed invention must be novel, involve an inventive step and be industrially applicable (Art. 52(1) EPC). The legal requirement of inventive step is specified in Article 56 EPC and is assessed by the EPO using the so-called problem-solution approach. 1 This established approach comprises the following four steps 2 :

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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

the problem solution approach

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

the problem solution approach

  • Identify the Problem
  • Define the Problem
  • Form a Strategy
  • Organize Information
  • Allocate Resources
  • Monitor Progress
  • Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

  • Asking questions about the problem
  • Breaking the problem down into smaller pieces
  • Looking at the problem from different perspectives
  • Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

  • Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
  • Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

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Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

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You can become a better problem solving by:

  • Practicing brainstorming and coming up with multiple potential solutions to problems
  • Being open-minded and considering all possible options before making a decision
  • Breaking down problems into smaller, more manageable pieces
  • Asking for help when needed
  • Researching different problem-solving techniques and trying out new ones
  • Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

35 problem-solving techniques and methods for solving complex problems

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All teams and organizations encounter challenges as they grow. There are problems that might occur for teams when it comes to miscommunication or resolving business-critical issues . You may face challenges around growth , design , user engagement, and even team culture and happiness. In short, problem-solving techniques should be part of every team’s skillset.

Problem-solving methods are primarily designed to help a group or team through a process of first identifying problems and challenges , ideating possible solutions , and then evaluating the most suitable .

Finding effective solutions to complex problems isn’t easy, but by using the right process and techniques, you can help your team be more efficient in the process.

So how do you develop strategies that are engaging, and empower your team to solve problems effectively?

In this blog post, we share a series of problem-solving tools you can use in your next workshop or team meeting. You’ll also find some tips for facilitating the process and how to enable others to solve complex problems.

Let’s get started! 

How do you identify problems?

How do you identify the right solution.

  • Tips for more effective problem-solving

Complete problem-solving methods

  • Problem-solving techniques to identify and analyze problems
  • Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve. 

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward. 

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.  

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

the problem solution approach

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.  

Try different approaches  

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally 

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator 

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

  • Six Thinking Hats
  • Lightning Decision Jam
  • Problem Definition Process
  • Discovery & Action Dialogue
Design Sprint 2.0
  • Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on. 

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages. 

Lightning Decision Jam (LDJ)   #action   #decision making   #problem solving   #issue analysis   #innovation   #design   #remote-friendly   The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design. 

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition   #problem solving   #idea generation   #creativity   #online   #remote-friendly   A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys 

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges. 

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results. 

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys   #hyperisland   #innovation   This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold. 

World Cafe   #hyperisland   #innovation   #issue analysis   World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD)   #idea generation   #liberating structures   #action   #issue analysis   #remote-friendly   DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology   #action plan   #idea generation   #problem solving   #issue analysis   #large group   #online   #remote-friendly   Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

  • The Creativity Dice
  • Fishbone Analysis
  • Problem Tree
  • SWOT Analysis
  • Agreement-Certainty Matrix
  • The Journalistic Six
  • LEGO Challenge
  • What, So What, Now What?
  • Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed. 

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.  

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It!   #gamestorming   #problem solving   #action   Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed. 

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable. 

The Creativity Dice   #creativity   #problem solving   #thiagi   #issue analysis   Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around. 

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish. 

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis   #problem solving   ##root cause analysis   #decision making   #online facilitation   A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree 

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them. 

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree   #define intentions   #create   #design   #issue analysis   A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward. 

SWOT analysis   #gamestorming   #problem solving   #action   #meeting facilitation   The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results. 

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause. 

Agreement-Certainty Matrix   #issue analysis   #liberating structures   #problem solving   You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic .  A problem is simple when it can be solved reliably with practices that are easy to duplicate.  It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably.  A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail.  Chaotic is when the context is too turbulent to identify a path forward.  A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.”  The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process. 

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID   #gamestorming   #project planning   #issue analysis   #problem solving   When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!   

Speed Boat   #gamestorming   #problem solving   #action   Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How   #idea generation   #issue analysis   #problem solving   #online   #creative thinking   #remote-friendly   A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills. 

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO! 

LEGO Challenge   #hyperisland   #team   A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems. 

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken. 

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What?   #issue analysis   #innovation   #liberating structures   You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists  

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists   #vision   #big picture   #issue analysis   #remote-friendly   This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions 

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

  • Improved Solutions
  • Four-Step Sketch
  • 15% Solutions
  • How-Now-Wow matrix
  • Impact Effort Matrix

21. Mindspin  

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly. 

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation. 

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex. 

MindSpin   #teampedia   #idea generation   #problem solving   #action   A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result. 

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution. 

Improved Solutions   #creativity   #thiagi   #problem solving   #action   #team   You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged. 

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch   #design sprint   #innovation   #idea generation   #remote-friendly   The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper,  Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change. 

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.   

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change. 

15% Solutions   #action   #liberating structures   #remote-friendly   You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference.  15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change.  With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process. 

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud. 

How-Now-Wow Matrix   #gamestorming   #idea generation   #remote-friendly   When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice. 

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them. 

Impact and Effort Matrix   #gamestorming   #decision making   #action   #remote-friendly   In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action? 

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus. 

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively. 

Dotmocracy   #action   #decision making   #group prioritization   #hyperisland   #remote-friendly   Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

  • Check-in/Check-out
  • Doodling Together
  • Show and Tell
  • Constellations
  • Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute. 

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out   #team   #opening   #closing   #hyperisland   #remote-friendly   Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together  

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start. 

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems. 

Doodling Together   #collaboration   #creativity   #teamwork   #fun   #team   #visual methods   #energiser   #icebreaker   #remote-friendly   Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team! 

Show and Tell   #gamestorming   #action   #opening   #meeting facilitation   Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible. 

Constellations   #trust   #connection   #opening   #coaching   #patterns   #system   Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic. 

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree   #thiagi   #opening   #perspectives   #remote-friendly   With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

  • One Breath Feedback
  • Who What When Matrix
  • Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space. 

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round. 

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them. 

One breath feedback   #closing   #feedback   #action   This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix 

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward. 

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved. 

Who/What/When Matrix   #gamestorming   #action   #project planning   With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out! 

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised. 

Response Cards   #debriefing   #closing   #structured sharing   #questions and answers   #thiagi   #action   It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks  to build your agenda. When you make changes or update your agenda, your session  timing   adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore  how to use SessionLab  to design effective problem solving workshops or  watch this five minute video  to see the planner in action!

the problem solution approach

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you! 

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thank you very much for these excellent techniques

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Certainly wonderful article, very detailed. Shared!

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the problem solution approach

Facilitation skills can be applied in a variety of contexts, such as meetings, events, or in the classroom. Arguably, the setting in which facilitation skills shine the most is the design and running of workshops.  Workshops are dedicated spaces for interaction and learning. They are generally very hands-on, including activities such as simulations or games designed to practice specific skills. Leading workshops is an exciting, rewarding experience! In this piece we will go through some of the essential elements of workshop facilitation: What are workshops? Workshops are a time set aside for a group of people to learn new skills, come up with the best ideas, and solve problems together.…

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So, you’ve decided to convene a workshop, a special time set aside to work with a team on a certain topic or project. You are looking for brilliant ideas, new solutions and, of course, great participation. To begin the process that will get you to workshop success, you’ll need three ingredients: participants willing to join, someone to facilitate and guide them through the process (aka, you) and a detailed agenda or schedule of the activities you’ve planned. In this article we will focus on that last point: what makes a good agenda design? Having a good agenda is essential to ensure your workshops are well prepared and you can lead…

the problem solution approach

What are facilitation skills and how to improve them?

Facilitation skills are the abilities you need in order to master working with a group. In essence, facilitation is about being aware of what happens when people get together to achieve a common goal, and directing their focus and attention in ways that serve the group itself.  When we work together at our best, we can achieve a lot more than anything we might attempt alone. Working with others is not always easy: teamwork is fraught with risks and pitfalls, but skilled facilitation can help navigate them with confidence. With the right approach, facilitation can be a workplace superpower.  Whatever your position, career path, or life story, you probably have…

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Adopting the right problem-solving approach

May 4, 2023 You’ve defined your problem, ensured stakeholders are aligned, and are ready to bring the right problem-solving approach and focus to the situation to find an optimal solution. But what is the right problem-solving approach? And what if there is no single ideal course of action? In our 2013 classic  from the Quarterly , senior partner Olivier Leclerc  highlights the value of taking a number of different approaches simultaneously to solve difficult problems. Read on to discover the five flexons, or problem-solving languages, that can be applied to the same problem to generate richer insights and more innovative solutions. Then check out more insights on problem-solving approaches, and dive into examples of pressing challenges organizations are contending with now.

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D. Inventive step

2. problem and solution approach.

Art. 56 EPC gives a negative definition of the "inventive step" required under Art. 52(1) EPC , by setting out that an invention shall be considered as involving an inventive step "if, having regard to the state of the art, it is not obvious to a person skilled in the art". In order to assess inventive step in an objective and predictable manner, the so-called "problem-solution approach" was developed, consisting of the following stages:

(a) determining the "closest prior art",

(b) assessing the technical results (or effects) achieved by the claimed invention when compared with the "closest state of the art" determined,

(c) defining the technical problem to be solved, the object of the invention being to achieve said results; and

(d) considering whether or not the claimed solution, starting from the closest prior art and the objective technical problem, would have been obvious to the skilled person ( G 1/19 , OJ 2021, A77 , point 26 of the Reasons; see also e.g. T 939/92 , OJ 1996, 309 ; T 15/93 ; T 433/95 ; T 917/96 ; T 631/00 ; T 423/01 ; T 215/04 ; T 1621/06 ; T 1183/06 ; T 824/07 ; see also Guidelines G‑VII, 5 – March 2022 version).

On application of the problem-solution approach to claims comprising technical and non-technical aspects (especially in the case of computer-implemented inventions), see in this chapter I.D.9.2 ., and for its application to claims directed to chemical inventions, see in this chapter I.D.9.9.1 .

The boards frequently cite R. 42(1)(c) EPC as the basis for the problem- solution approach. R. 42(1)(c) EPC requires that the invention be disclosed in such terms that the technical problem (even if not expressly stated as such) and its solution can be understood. Problem and solution are thus component parts of any technical invention. The problem- solution approach was primarily developed to ensure objective assessment of inventive step and avoid ex post facto analysis of the prior art. As long ago as T 26/81 ( OJ 1982, 211 ), R. 27(1)(d) EPC 1973 (in the version in force until 31 May 1991; the predecessor of current R. 42(1)(c) EPC ) was recognised as clearly binding.

A solution claimed as non-obvious is patentable only if it actually has the alleged effect. According to T 2001/12 , a doubt that the invention as claimed is capable of solving the problem defined in the application may have the following consequences: a) If the claim fails to specify those features which are disclosed in the application as providing the solution to the problem, then an objection under Art. 84 EPC 1973 may properly arise that the claims do not contain all the essential features necessary to specify the invention; b) if this is not the case, but, having regard to the prior art, and irrespective of what may be asserted in the description, it does not appear credible that the invention as claimed would actually be capable of solving the problem, then an objection under Art. 56 EPC 1973 may be raised, possibly requiring a reformulation of the problem. See also T 862/11 which also dealt with the distinction between the requirements of sufficiency of disclosure ( Art. 83 EPC ), clarity of the claims ( Art. 84 EPC ), and inventive step ( Art. 56 EPC ).

Very early in its case law, the boards emphasised the obligation of objectivity when assessing inventive step; it is the objective rather than subjective achievement of the inventor which has to be assessed (see T 1/80 , OJ 1981, 206 ; T 20/81 , OJ 1982, 217 ; T 24/81 , OJ 1983, 133 ; T 248/85 , OJ 1986, 261 ). Starting out from the objectively prevailing state of the art, the technical problem is to be determined on the basis of objective criteria and consideration given to whether or not the disclosed solution is obvious to the skilled person. Although the problem and solution approach is not mandatory, its correct application facilitates the objective assessment of inventive step. The correct use of the problem and solution approach rules out an ex post facto analysis which inadmissibly makes use of knowledge of the invention ( T 564/89 , T 645/92 , T 795/93 , T 730/96 , T 631/00 ). In principle, therefore, the problem and solution approach is to be used; however, if exceptionally some other method is adopted, the reasons for departing from this generally approved approach should be stated.

In T 967/97 the board stated that the problem and solution approach was essentially based on actual knowledge of technical problems and ways to solve them technically that the skilled person would, at the priority date, be expected to possess objectively, i.e. without being aware of the patent application and the invention that it concerned (see also T 970/00 , T 172/03 ).

In T 2517/11 the board held that the fact that a technical feature of a known method was "hidden" – i.e. implicit in a prior-art document and not identifiable on a mere reading of that document – and could be detected only by way of a mathematical analysis did not mean that it could not be taken into account as a disclosed feature. If an analysis revealed such a "hidden" feature, that showed it was publicly available; whether there had been any objective reason to carry out the analysis was irrelevant (with reference to G 1/92 , OJ 1993, 277 ). This followed from the objective nature of the problem and solution approach developed in the boards' case law, which entailed consideration of all technical features comprised in the closest prior art, regardless of whether they were directly identifiable or hidden, since even hidden features were publicly available.

The board in T 1761/12 held that the problem and solution approach involved analysing the steps the skilled person would have taken to solve the predefined objective technical problem, and nothing else. Any further reflection on whether the associated changes to the closest prior art identified in this analysis made sense had the effect, in practice, of adding the related aspects of other problems to the objective technical problem initially defined.

In T 320/15 the board held that the problem and solution approach did not consist of a forum in which the appellant (opponent) could freely develop various attacks based on diverse prior-art documents in the hope that one of them would succeed.

Instructive summaries of the case law on the problem and solution approach can be found in a number of decisions; see e.g. R 9/14 , T 519/07 , T 698/10 .

According to the board in T 270/11 , the problem and solution approach does not require that the application specify what feature is responsible for producing precisely what advantage or technical effect. All that is required for inventive step is that the claimed subject-matter is not obvious to the skilled person in the light of the prior art ( Art. 56 EPC ). It is common practice to take features from dependent claims or the description and insert them into an independent claim with a view to rendering the subject-matter patentable and to cite the effects and advantages associated with those features as a basis for (re-)formulating the technical problem. To determine the objective technical problem, the technical results and effects achieved by the claimed invention as compared with the closest prior art must be assessed.

In T 465/92 ( OJ 1996, 32 ) the board did not take the problem and solution approach when assessing inventive step, and said this was merely one possible approach, with advantages and drawbacks. It took the view that all of the seven relevant citations came equally close to the invention. See also T 967/97 in the chapter I.D.3.1 . "Determination of closest prior art in general".

In T 188/09 the board noted first that whatever approach was applied as an auxiliary means for the evaluation of inventive step of claimed subject-matter, in a given evidential situation it had to provide the same result, be it either in favour of or against inventive step. Therefore, even if the problem and solution approach was applied, the decision on inventiveness should be the same as if it had not been used. Citing T 465/92 ( OJ 1996, 32 ), the board observed: "if an invention breaks new ground it may suffice to say that there is no close prior art rather than constructing a problem based on what is tenuously regarded as the closest prior art."

In case R 5/13 (as well as R 9/13 , R 10/13 , R 11/13 , R 12/13 and R 13/13 which were all directed against T 1760/11 of 16 November 2012 date: 2012-11-16 ), the petitioners argued that they should have been allowed to discuss all the issues of inventive step of any stage of the problem and solution approach in respect of all possible starting points that they wished to rely on, despite the fact that the board had structured the discussion by first establishing which document or documents constituted the most promising starting point. The Enlarged Board in R 5/13 held that the board had not only followed the sequence for the debate announced in its communication annexed to the summons to oral proceedings, but by doing so it had also systematically applied the standard method of the problem and solution approach. The examination whether or not the subject-matter of a patent claim involved an inventive step according to the well-established problem and solution approach was a matter of substantive law. That was equally true for the determination of the closest prior art as the first step of the problem and solution approach, whether one document alone or a plurality of documents was taken as the starting point or most promising springboard aiming at the invention.

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the problem solution approach

Key Skills for Solution-Focused Problem-Solving

Imagine that you just received an unexpected complex problem and need to find a solution fast. You have never experienced this situation before. What is your approach? Most of us focus on the problem by asking questions such as: “Why do I have this problem? What shall I do to get rid of this problem? Are you sure this is my problem?” Before you know it, the challenge becomes bigger by the minute. Your attention and effort are fully focused on overcoming the problem and you begin to feel less resourceful to find an acceptable solution.

When you   focus on the problem   instead of the desired outcome, you get stuck in the depths of the problem, as if you are in quicksand. Some people walk into the quicksand with lead boots on. One of the most powerful frames you can use to achieve results is to shift from a problem approach (I don’t want X) to an outcome approach (What I want is Y). This immediately shifts your thinking and the way you feel.

Only when your frame of mind is changed to focusing on the desired result can you begin to move forward toward the desired outcome. Using the Solution-Focused approach, you will be surprised how competently you can tackle even the thorniest of problems and turn them into opportunities. 

Interested in becoming a coach? Discover how Solution-Focused coaching skills enable you to create transformational change in yourself and others. 

Solution-Focused communication magnetizes our attention toward getting the desired outcome, and so the outcome is held in mind as   the vision for the future . Others naturally tend to respond positively to our leadership because we hold the vision that serves everyone. Rather than dwelling on the difficulties or the setbacks, the idea of the solution becomes the road to results, and people feel cheered when they can see a strong pathway toward the solution and are inspired by the plan.    

Imagine running a race where there are hurdles every 100 yards. With problem framing, you are focused on the hurdles, “Oh my, how high they are! How hard will I have to work to jump them?” Such a focus, with little or no attention on the finish line, will not make you a champion—guaranteed! The hurdles symbolically (and in reality) stand in your way. When you are focused on the hurdles, you cannot see past them to the finish line that is your true aim. The hurdles loom large in your mind, and the race seems difficult (if not impossible) to run.

With a Solution-Focused approach to communication, your mind is galvanized by your purpose and you are able to see past the hurdles before you. Your purpose always leads you to the finish line, and the hurdles become less important and less of an obstacle. In fact, they may seem so unimportant that they become nonexistent and are just part of the journey. They are still the same height and you’ll still have to jump as high. Yet with the focus on the value of the goal and what is working to move forward towards it, jumping hurdles seems natural and easy. The end of the race is always drawing you onward. The race itself becomes a means to achieve the vision, and it’s the vision—who you are becoming and who you are contributing to—that looms large in your mind. This difference in your focus is the power that leads you to success.

Notice how efficient this approach is – Solution-Focused thinking is far more useful than problem-focused thinking because the focus is on getting the desired outcome, rather than dwelling on the difficulties or setbacks. Constantly operating from a solution perspective is a noticeable characteristic of high achievers.

Focusing on who you are becoming

One of the main ways of producing Solution-Focused results that serve the world is to focus the mind and heart on who you are becoming— and not what you are overcoming. Allowing yourself to go into the lower energies of an overcoming focus puts you into a very challenging and unpleasant hurdle race. People can spend most of their lives running such a race. As soon as you put your attention on what doesn’t work as a ‘reality,’ it is hard to explore what really could work. This is one reason why the Erickson   Solution-Focused method   is successful in moving people quickly beyond mindsets and models that ‘realistically’ start by focusing on the problem as the necessary aspects to deal with.

As a transformational communicator using the coaching approach, once you are secure in this skill for yourself, you will quickly discover the value of using it consistently in coaching conversations with others. This simple and subtle skill of flipping a problem or conflict into a Solution-Focused orientation may be the single most powerful characteristic of transformational coaches who become known as integral change maestros.

Declaring and visualizing outcomes

When outcomes are declared and visualized carefully, people move toward them naturally, almost effortlessly. What was once considered a problem is now little more than a pebble on the road! Having a strong, inspiring, value-based vision for the future cuts all other concerns down to size. We grow and our ‘problems’ diminish.

Once you, the transformational communicator, know how to consciously assist people to orient toward their larger purpose and goals, your clients will move consistently and more easily toward their desired outcomes. They will achieve their outcomes by choice, not by chance.

Creating a compelling future

Developing, holding, and feeling a vision of a compelling future is the single most important task for a person, in order to   achieve their goals   and dreams.

Without this vision and the process of consistently visualizing potential action steps to accomplish it, people move in a random, scattered fashion. They are likely to struggle and get frustrated and stuck.

When people make the choice to hold a specific outcome securely on the movie screen of their minds, they naturally begin to move toward making their vision a reality—no matter how large or small it is. Their chosen outcome becomes their future.

Who you are is the future you are moving into! What is in your mind becomes your reality. You have two choices. You can visualize how your problems continue, which will move you towards having even more problems. Or, you can visualize your outcome becoming real and move toward having it. Which do you prefer?

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Title: randomness is all you need: semantic traversal of problem-solution spaces with large language models.

Abstract: We present a novel approach to exploring innovation problem and solution domains using LLM fine-tuning with a custom idea database. By semantically traversing the bi-directional problem and solution tree at different temperature levels we achieve high diversity in solution edit distance while still remaining close to the original problem statement semantically. In addition to finding a variety of solutions to a given problem, this method can also be used to refine and clarify the original problem statement. As further validation of the approach, we implemented a proof-of-concept Slack bot to serve as an innovation assistant.

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Find the AI Approach That Fits the Problem You’re Trying to Solve

  • George Westerman,
  • Sam Ransbotham,
  • Chiara Farronato

the problem solution approach

Five questions to help leaders discover the right analytics tool for the job.

AI moves quickly, but organizations change much more slowly. What works in a lab may be wrong for your company right now. If you know the right questions to ask, you can make better decisions, regardless of how fast technology changes. You can work with your technical experts to use the right tool for the right job. Then each solution today becomes a foundation to build further innovations tomorrow. But without the right questions, you’ll be starting your journey in the wrong place.

Leaders everywhere are rightly asking about how Generative AI can benefit their businesses. However, as impressive as generative AI is, it’s only one of many advanced data science and analytics techniques. While the world is focusing on generative AI, a better approach is to understand how to use the range of available analytics tools to address your company’s needs. Which analytics tool fits the problem you’re trying to solve? And how do you avoid choosing the wrong one? You don’t need to know deep details about each analytics tool at your disposal, but you do need to know enough to envision what’s possible and to ask technical experts the right questions.

  • George Westerman is a Senior Lecturer in MIT Sloan School of Management and founder of the Global Opportunity Forum  in MIT’s Office of Open Learning.
  • SR Sam Ransbotham is a Professor of Business Analytics at the Boston College Carroll School of Management. He co-hosts the “Me, Myself, and AI” podcast.
  • Chiara Farronato is the Glenn and Mary Jane Creamer Associate Professor of Business Administration at Harvard Business School and co-principal investigator at the Platform Lab at Harvard’s Digital Design Institute (D^3). She is also a fellow at the National Bureau of Economic Research (NBER) and the Center for Economic Policy Research (CEPR).

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Family-based heart health

UCI research program weighs benefits of new approach to cardiac fitness in local communities

Steve Anticona, an agroecological farmer and community outreach coordinator at CRECE Urban Farms, provides a farm tour to participants at the SERVE OC Autumn Family Wellness Festival.

  • SERVE OC takes a family-based approach to optimizing heart health
  • The program aims to scale up intervention over next five years
  • Community partners expand the reach of the project

In the U.S., stroke and cardiovascular disease are significant contributors to mortality, but heart disease and hypertension are of particular concern in Latino communities, where 1 in 4 deaths can be attributed to one or the other. Heart disease ranks as the second-leading cause of death overall for Latinos, while the Vietnamese American population also faces persistently high rates of hypertension, leading to elevated stroke risk.

With that in mind, the UCI Program in Public Health’s Skills-based Educational Strategies to Reduce Vascular Events in Orange County program aims to combat this alarming trend. Led by principal investigator Bernadette Boden-Albala, SERVE OC uses a community-centered, participatory research methodology to engage households in Garden Grove, Santa Ana, Westminster and Anaheim.

Specifically, the program is evaluating the benefits of a family-based approach to optimizing heart health compared to the current medical practice of individual risk factor management. It has so far enrolled 449 people within Orange County’s Latino and Vietnamese American populations, including children as young as 5, with 178 families participating.

For the SERVE OC intervention, Boden-Albala and her team seek to understand and address structural challenges in improving heart fitness. These include health insurance coverage, education and neighborhood resources. Over the last year, families were evaluated for cardiac health using the American Heart Association’s Life’s Essential 8 assessment. This spring, SERVE OC will begin the first of three years of follow-up, and over the next two years, the team will determine whether a family-engaged strategy significantly improves overall family heart health.

“We collect the same metrics from everyone: blood pressure, heart rate, cholesterol, diet, blood sugar levels, exercise and sleeping habits,” says Desiree Gutierrez, one of the SERVE OC project managers and an alumna of UCI’s Program in Public Health. “Every family gets a digital blood pressure device for remote study team monitoring. Community health workers support families in working together to decrease risks and improve health.”

According to Boden-Albala, SERVE OC aims to scale up its intervention over the next five years based on positive data outcomes. Findings will be disseminated to various stakeholders, including government agencies, nongovernmental organizations and schools, emphasizing the importance of a collaborative, community-driven approach to cardiovascular fitness.

“We are working in disadvantaged communities, which is a big part of the impetus in trying to work with the whole family to achieve ideal heart health,” says Boden-Albala, who is director of UCI’s Program in Public Health and founding dean of the planned School of Population and Public Health. She adds that a major goal of the study is to see how working with community groups can help address structural factors that negatively affect the heart health of residents.

“The problem with many health studies is that they don’t look at structural conditions that impact the families,” Boden-Albala says. “If you’re in a house located right next to nonstop traffic and noise pollution, it’s a challenge to get proper sleep – and that’s not the family’s fault. We’re working with community stakeholders to come up with solutions to these challenges and others, like lack of access to fresh fruits and vegetables or to a quiet zone, that people need to overcome to improve their health.”

SERVE OC partners with organizations such as Latino Health Access and operates an office at El Centro Cultural de Mexico in Santa Ana. A local consulting firm, Radiate Consulting, helps with recruitment and trust building in that city, while in Westminster and Garden Grove, the Vietnamese American Cancer Foundation provides community health workers and translation services.

Two chefs demonstrate how to make a meal in a test kitchen.

Continuous engagement with community groups has been crucial to the success of the intervention, and so far, the response has been quite positive.

“SERVE OC helped open my eyes to taking care of my heart,” shared one participant.

“Thanks to my community health worker, Maria, I have the motivation to check my blood pressure weekly,” echoed another.

“We partner with community organizers and stakeholders because at the end of the day, this is everyone’s problem,” Boden-Albala says. “Our guiding principle is that it takes a community to move forward toward better health.”

SERVE OC is one of two projects under a larger community health initiative called UC End Disparities , which is working to prevent cardiometabolic disease across Los Angeles and Orange counties. UC End Disparities is supported through grants from the National Institute on Minority Health and Health Disparities.

If you want to learn more about supporting this or other activities at UCI, please visit the Brilliant Future website at   https://brilliantfuture.uci.edu . Publicly launched on Oct. 4, 2019, the Brilliant Future campaign aims to raise awareness and support for UCI. By engaging 75,000 alumni and garnering $2 billion in philanthropic investment, UCI seeks to reach new heights of excellence in student success,   health and wellness, research and more. The planned School of Population and Public Health plays a vital role in the success of the campaign. Learn more by visiting  https://brilliantfuture.uci.edu/school-of-population-and-public-health .

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The 2024‑25 Budget

Crafting climate, resources, and environmental budget solutions, executive summary, introduction, discussion of governor’s overall approach, zero‑emission vehicles, wildfire and forest resilience, nature‑based activities, other recent augmentations.

Overview of This Report. In response to the multibillion‑dollar budget problem the state is facing, the Governor’s budget proposal identifies significant solutions from recent augmentations made to climate, resources, and environmental programs. This report describes the Governor’s proposals and provides the Legislature with suggestions for how it might modify the spending plan to better reflect its priorities and prepare to address a potentially larger budget problem. The report begins with a discussion of the Governor’s overall approach, including background on recent funding augmentations and the state’s budget problem; a high‑level overview of the Governor’s proposals; our overarching assessment of the proposed approach; and recommendations for how the Legislature could proceed. We then walk through the Governor’s proposed solutions in each of 11 thematic areas, including examples of alternative or additional budget solutions the Legislature could consider.

Recent Budgets Included Significant General Fund Augmentations. Combined, the 2021‑22 and 2022‑23 budget agreements included notable amounts of new spending for a wide variety of activities related to mitigating and responding to climate change, as well as for protecting and restoring natural resources and the environment. In most cases, these augmentations represented unprecedented levels of General Fund for these types of programs, many of which historically have been supported primarily with special funds or bond funds. These budget packages also included agreements to provide additional funding in future years for a six‑year total of about $39 billion (2020‑21 through 2025‑26). To help address the General Fund shortfall that began materializing last year, the 2023‑24 spending plan made a number of revisions—including reductions, delays, and fund shifts—to the thematic packages agreed to in earlier budget deals. On net, the revised budget agreement intended to maintain $36 billion from a combination of funding sources (93 percent of the original total) from 2020‑21 through 2026‑27 for these activities. (In some budget documents the administration cites higher climate spending amounts because it includes several large programs in its totals that we exclude from ours, such as related to transportation and housing.)

Governor Proposes $4.1   Billion in General Fund Solutions for 2024‑25 Budget Problem. Similar to last year, the Governor relies on three strategies to achieve additional General Fund savings from climate, resources, and environmental programs across the budget window (2022‑23 through 2024‑25)—$2 billion from spending reductions, $1.1 billion from delaying spending to a future year, and $1 billion from reducing General Fund and backfilling with a different fund source (primarily using the Greenhouse Gas Reduction Fund, [GGRF]). The amount of multiyear savings proposed across the combined budget window and forecast period (2023‑24 through 2027‑28) is somewhat less—$3.6 billion. This is the net result of some additional out‑year reductions which are more than offset by the costs associated with the resumption of delayed expenditures.

Given State Budget Shortfall, Overall Proposed Approach Has Several Merits. The magnitude of the General Fund problem means that the Legislature faces difficult choices in developing its budget this year. Within this context, we find a number of redeeming qualities in the Governor’s proposal. Specifically, it: (1) continues to fulfill most state objectives by sustaining the vast majority of planned multiyear funding and activities; (2) focuses reductions on recent one‑time augmentations, which is less disruptive than reducing ongoing base programs; (3) does not reduce funding that has already been committed to specific projects or grantees; (4) utilizes GGRF to sustain numerous programs while also achieving General Fund savings; and (5) eliminates most unappropriated General Fund planned for the budget year and future.

Governor’s Proposal Reflects Administration’s Priorities, Maintains Significant Amount of Unspent Funds. The administration’s choices regarding which programs to preserve and which to reduce largely reflect the Governor’s priorities. Specifically, many of the proposed cuts are to programs for which the Legislature advocated during budget negotiations, rather than those that were initially proposed by the Governor. To the extent the Legislature’s priorities differ from the Governor’s, we recommend it select a different mix of programs for funding reductions. Moreover, our review of expenditure data suggests the Governor’s proposal maintains over $1 billion in uncommitted prior‑ and current‑year appropriated funds. The Legislature could reduce some of this funding and achieve General Fund savings as additions or alternatives to the Governor’s proposals, in most cases without major disruptions to specific programs or projects. However, should it wish to capture these savings, we recommend the Legislature consider taking early action ahead of the June budget deadline as in many cases departments have plans to make additional grant awards this spring.

Proposed Delays and Out‑Year Commitments Complicate Future Budget Situation. While the Governor eliminates most of the unappropriated planned General Fund, some of this funding is only temporarily reduced—$1.7 billion in General Fund expenditures are delayed to future years. While these delays provide short‑term savings and might preserve intended activities over the longer term, they also exacerbate future budget problems by increasing out‑year General Fund spending commitments. The proposal also would maintain over $900 million in General Fund spending that previous budget agreements planned for 2025‑26. Building a multiyear spending plan that incorporates this funding sets expectations for potential projects and grantees that may be hard to keep given projected out‑year budget deficits. Moreover, the Governor’s proposal includes plans to dedicate a notable share of out‑year discretionary GGRF revenues for specific purposes (primarily for spending related to zero‑emission vehicles) rather than deferring those spending decisions to future budget negotiations. The Legislature might benefit from preserving additional flexibility around how it wants to use future GGRF resources. Overall, we recommend the Legislature minimize out‑year commitments for both the General Fund and GGRF.

Recommend Legislature Identify Alternative and Additional Budget Solutions Depending on Its Priorities and the Evolving General Fund Condition. We think that generating at least the same magnitude of General Fund solutions from climate, resources, and environmental programs as the Governor will be important in solving the budget problem. Maximizing spending reductions from one‑time funds will allow the Legislature to minimize the use of other budget  tools—like   reserves—that  likely will be needed to address deficits in future years. To the degree some of the Governor’s proposed program reductions represent important efforts for the Legislature, however, it could opt to sustain that funding and instead find a like amount of savings by making alternative reductions, such as to programs with uncommitted funds. Besides alternative reductions, we recommend the Legislature also begin identifying options for potential additional budget solutions from these programs. Further reductions to this one‑time spending could prove helpful in a number of potential scenarios, such as if (1) the budget condition worsens (current LAO revenue projections suggest this is likely), (2) the Legislature wants to reject some of the Governor’s proposed General Fund budget solutions in other policy areas, (3) the Legislature wants to “make room” to fund some of its key priorities, and/or (4) the Legislature determines that some of the solutions included in the Governor’s proposal may not yield anticipated savings. While this process will be challenging, taking the time to consider potential options over the spring will better prepare the Legislature to make decisions in June when it will not have much time to gather information before the budget deadline.

In response to the multibillion‑dollar budget problem the state is facing, the Governor’s budget proposes reducing net General Fund spending by $3.6 billion across six years from climate, resources, and environmental programs. The proposal saves $4.1 billion in General Fund affecting the 2024‑25 budget from a combination of spending reductions, shifting spending to different fund sources, and delaying funding for certain programs to a future year, but over the multiyear period some of these savings are offset by the resumption of the delayed spending. This report describes the Governor’s proposals and provides the Legislature with suggestions for how it might modify the spending plan to better reflect its priorities and prepare to address a potentially larger budget problem.

The report begins with a discussion of the Governor’s overall approach, including background on recent funding augmentations and the state’s budget problem; a high‑level overview of the Governor’s proposals for climate, resources, and environmental programs; our overarching assessment of the proposed approach; and recommendations for how the Legislature could proceed.

We then walk through each of the Governor’s proposed solutions by thematic area, including examples of alternative or additional solutions the Legislature could consider. These thematic areas include:

  • Zero‑Emission Vehicles (ZEVs).
  • Water and Drought.
  • Wildfire and Forest Resilience.
  • Nature‑Based Activities.
  • Community Resilience.
  • Coastal Resilience.
  • Sustainable Agriculture.
  • Circular Economy.
  • Extreme Heat.
  • Other Recent Augmentations.

Recent Budgets Included Significant General Fund Augmentations for Climate, Natural Resources, and Environmental Protection. Combined, the 2021‑22 and 2022‑23 budget agreements included notable amounts of new spending for a wide variety of activities related to mitigating and responding to climate change, as well as for protecting and restoring natural resources and the environment. These budget packages also included agreements to provide additional funding in future years for a six‑year total of about $39 billion (2020‑21 through 2025‑26). Most of this funding was grouped into thematic packages, such as for ZEVs, wildfire and forest resilience, and water and drought‑related activities. (Recent budgets also provided some additional augmentations for natural resources and environmental protection departments that we do not include in these totals. Additionally, as we describe in the box below, this amount does not include some additional non‑environmental funding that the administration sometimes includes in its “Climate Budget” totals.) The funding was spread across numerous departments and was primarily from the General Fund, but did include about $6 billion from other funds, mostly the Greenhouse Gas Reduction Fund (GGRF) and Proposition 98 (dedicated school funding for kindergarten through community college, used here for zero‑emission school buses). In general, these augmentations were all for activities that were one time or limited term in nature, such as providing grants for local entities to construct infrastructure or carry out habitat restoration projects. Some of the augmentations provided funding for activities to be undertaken by state agencies, such as to secure additional electricity resources intended to ensure summer electric reliability.

Clarifying Different “Climate Budget” Spending Totals

Budget documents released by the administration cite higher totals for spending on climate programs than we discuss in this report. Specifically, the administration states that intended multiyear spending for the administration’s “California Climate Commitment” originally totaled $54 billion (as compared to our $39 billion). That document also cites higher numbers for the proposed 2024‑25 budget solutions from climate‑related programs ($6.7 billion as compared to our $4.1 billion) and the revised proposed multiyear total maintained ($48 billion compared to our $34 billion). This discrepancy stems from the administration counting several additional programs in its totals that we exclude from ours. These include multiyear spending plans related to transportation infrastructure ($13.8 billion, which includes $4.2 billion in bond funding for the high‑speed rail project), housing development ($975 million), and various research initiatives and infrastructure projects at the University of California and California State University systems ($722 million), as well as a number of programs in both the health and workforce policy areas.

Presumably, the administration includes this wider array of programs in its climate spending totals because it finds that they have some nexus to addressing or responding to climate change causes and impacts. We have two primary rationales for omitting these programs from our content in this and previous reports related to spending on climate and environmental programs.

First, while many of the programs included in the administration’s totals may have some nexus with climate change, in most cases that is not their primary focus. For example, while developing infill housing could help the state meet its climate goals by reducing driving and associated emissions, the primary goal of the Infill Infrastructure Grant, Adaptive Reuse, and State Excess Site Development programs (all of which are included in the Governor’s Climate Budget totals) is to expand the state’s housing inventory. Indeed, given how widespread climate change impacts are becoming, one might be able to draw some relation between addressing or responding to climate change and an increasingly wide array of state expenditures, meaning grouping and tracking them comprehensively would become progressively more unwieldy and impractical.

Second, to help avoid confusion, we have aligned our summaries with the way the Legislature has approached discussing and adopting its decisions. That is, the thematic “packages” and the handful of other environmental program augmentations we present in this report match the content discussed and voted on in the budget subcommittees that are directly charged with considering fiscal and policy issues related to climate change, natural resources, and environmental protection. The programs we exclude from our totals were deliberated upon in other legislative budget subcommittees and were not considered together in an overarching “legislative climate budget.”

This slight divergence in how the administration and our office summarize climate spending is not new—we each have been largely consistent in our approaches since 2022‑23. (We have adjusted our totals slightly in this report to incorporate some additional “non‑package” augmentations which the Governor is now proposing to modify, as we describe in the text.) Moreover, these distinctions do not represent a true difference in spending estimates, but rather alternative choices in how to frame the discussion of state spending for climate programs.

General Fund Augmentations Represent Significant Departure From Historical Funding Trends. In most cases, the recent augmentations represent unprecedented levels of General Fund for these types of programs, many of which historically have been supported with special funds or bond funds. This anomalous General Fund spending was enabled by the significant tax revenue surpluses the state received (and expected to receive) over the past couple of years. Figure 1 highlights these trends. The figure shows total annual funding (including both the recent one‑time augmentations as well as baseline funds) for the California Department of Food and Agriculture and the departments within the California Natural Resources Agency and California Environmental Protection Agency, along with just the climate‑specific funding provided to some additional departments through the thematic packages. As shown, in the years prior to 2021‑22, spending on climate, natural resources, and environmental programs averaged around $10 billion annually, and General Fund typically made up roughly one‑third of the totals. In contrast, from 2021‑22 through 2023‑24, average annual funding levels for these departments more than doubled, with the General Fund contributing more than half of the funding. In some cases, this short‑term infusion of new funding has allowed the state to expand previous programs or initiate new activities, while in others the state is providing General Fund support to continue existing activities that previously were supported with other fund sources.

Figure 1 - General Fund Spending on Climate, Resources, and Environment Programs Surged in Recent Years

Fiscal Downturn Led to Some Reductions and Modifications to Packages in 2023‑24 Budget Agreement. To help address the General Fund shortfall that began materializing last year, the 2023‑24 spending plan made a number of revisions—including reductions and delays—to the thematic packages agreed to in earlier budget deals. Specifically, the budget included General Fund reductions to the climate funding packages totaling $8.7 billion across 2021‑22 through 2023‑24, although it backfilled about $2 billion of that amount by shifting costs to other fund sources (particularly GGRF). Because the spending plan achieved some of those General Fund savings by delaying funding to future years and also anticipated additional out‑year GGRF backfills, the planned net programmatic reduction from these packages across the multiyear period was only $2.8 billion. That is, the budget agreement intended to maintain $36 billion from a combination of funding sources (93 percent of the original total) from 2020‑21 through 2026‑27 for specified climate‑related and natural resources activities. Figure 2 displays the multiyear funding totals for each package as revised by the 2023‑24 budget agreement. The figure also includes $2.3 billion for certain other significant climate and environmental spending not adopted as part of the thematic packages, including $1 billion to implement the Clean Energy Reliability Investment Plan (CERIP), $500 million to clean up contaminated brownfield sites, and $477 million for a Climate Innovation Program.

Revised Recent and Planned Augmentations to Climate, Resources, and Environmental Programs

(In Millions) a

State Faces a Multiyear, Multibillion‑Dollar Budget Problem.   Due to a deteriorating revenue picture relative to expectations from June 2023, both our office and the administration anticipate that the state faces a significant multiyear budget problem. A budget  problem—also  called a  deficit—occurs  when funding for the current or upcoming budget is insufficient to cover the costs of currently authorized services. Estimates of the magnitude of this shortfall differ based on how “baseline” spending is  defined—the  administration estimates a $38 billion problem whereas in January our office estimated that the Governor’s budget addresses a $58 billion problem—as well as somewhat different revenue projections. Regardless of these distinctions, it is clear that the state faces the task of “solving” a substantial budget problem. Moreover, both our office and the administration estimate that, based on current revenue forecasts, the state will face significant operating deficits in subsequent fiscal years. The Governor proposes to address the 2024‑25 budget problem through a combination of strategies, including relying on reserves and reducing recent one‑time spending commitments. Given that the climate, resources, and environmental policy areas were the largest categories for recent one‑time investments, the Governor targets these programs for a notable share of these spending solutions. Under the administration’s projections, even after adopting the Governor’s proposals, the state still would face operating deficits of $37 billion in 2025‑26, $30 billion in 2026‑27, and $28 billion in 2027‑28. (We discuss the overall budget condition in our January 2024 report,  The 2024‑25 Budget: Overview of the Governor’s Budget .)  

Governor’s Proposals

Uses Three Strategies to Generate $4.1   Billion in General Fund Solutions for 2024‑25 Budget Problem. Similar to last year, the Governor relies on three strategies to achieve additional General Fund savings from climate, resources, and environmental programs: reductions, funding delays, and fund shifts. This generates approximately $4.1 billion in General Fund savings across the budget window (2022‑23 through 2024‑25)—$2 billion from spending reductions, $1.1 billion from delaying spending to a future year, and $1 billion from reducing General Fund and backfilling it with a different fund source. In some cases, the Governor proposes a combination of strategies, such as delaying spending to a future year and shifting the fund source. The amount of multiyear savings proposed across the combined budget window and forecast period (2023‑24 through 2027‑28) is somewhat less—$3.6 billion. This is the net result of some additional out‑year reductions which are more than offset by the costs associated with the resumption of delayed expenditures.

  • Reductions.  The Governor reduces $2 billion in General Fund support for selected programs across the budget window. In some of these cases, the proposal is to rescind funding that was provided in the current or prior year that departments have not yet expended. In others, the Governor proposes not providing funding in 2024‑25 that was pledged as part of a recent budget agreement. For some programs, the Governor partially reduces the intended funding levels and for others the proposal completely eliminates the funding. Besides the $2 billion in reductions affecting the 2024‑25 budget, the proposal reduces an additional $543 million from General Fund expenditures that recent budget agreements had planned for the out‑years (2025‑26 through 2027‑28).
  • Funding Delays.  The Governor proposes delaying $1.1 billion in intended General Fund for certain programs, with the intent to provide it in a future year rather than within the budget window as originally planned. This would achieve near‑term General Fund savings, but shift the associated costs to a future year. In addition to the $1.1 billion originally planned for the current or budget year, the Governor also proposes delaying $635 million in General Fund expenditures that had been planned for 2025‑26.
  • Fund Shifts.  The Governor achieves an additional $1 billion in savings affecting the budget window by reducing or eliminating the intended General Fund for a program but then backfilling it with GGRF.

Relies on GGRF to Maintain Funding for Certain Programs. Of the $2.3 billion in GGRF that the administration estimates is available for discretionary expenditures in 2024‑25, the Governor proposes using more than three‑quarters to backfill proposed General Fund reductions, including the $1 billion in fund shifts for climate and environmental programs. This includes $557 million in current‑year expenditures (primary within the ZEV package) for which the Governor is requesting that the Legislature take early action to reduce General Fund and backfill it with GGRF. (The administration has requested that administering departments pause their spending of authorized General Fund for these programs to avoid eroding these potential current‑year savings.)

The Governor also proposes delaying $600 million in planned GGRF spending for ZEV programs from 2024‑25 to 2027‑28. While this does not directly result in General Fund savings, it has the effect of freeing up additional GGRF resources in 2024‑25 which can then be redirected for alternative purposes (such as the proposed fund shifts, which do generate budget solutions). The Governor also would sustain previous plans to provide $600 million from GGRF for the ZEV package in 2025‑26 and 2026‑27. Please see our companion publication, The 2024‑25 Budget: Cap‑and‑Trade Expenditure Plan , for a more detailed discussion of the Governor’s GGRF proposals.

Vast Majority of Intended Multiyear Funding Would be Maintained. Responding to the causes and impacts of climate change presents significant challenges for California and has therefore been a clear priority of both the administration and the Legislature in recent years. Indeed, the resources and environmental policy areas received the largest proportional share of discretionary one‑time General Fund spending from recent budget surpluses. The Governor’s budget largely sustains this commitment. As shown in Figure 3 , even with the Governor’s proposed budget adjustments, the majority of the spending and activities included in recent budget agreements would continue. Specifically, the proposal would sustain $33.7 billion, or 86 percent of the total original intended amounts. Even these reduced amounts still would represent significant augmentations compared to historical levels for most of these programs. Moreover, as shown earlier in Figure   1, even with the Governor’s proposed reductions, funding levels for climate and resources‑related activities would remain at levels that are roughly comparable to those that were in place in 2019‑20, before the unprecedented increases that have occurred over the last couple of years. This can give the Legislature confidence that even at moderately reduced spending levels such as those proposed by the Governor, the state can continue to make significant progress on its climate and environmental goals. However, as shown in the figure, the proportion of funding proposed to be maintained—and therefore the relative magnitude of the activities that could continue being implemented—does vary by thematic package. For example, the Governor proposes maintaining essentially all of the total intended funding for ZEV programs, but only about half for coastal resilience activities.

Figure 3 - Governor's Proposal Would Retain Majority of Planned Multiyear Climate Funding

Given State Budget Shortfall, Overall Proposed Approach Has Several Merits. The magnitude of the General Fund problem means that the Legislature faces difficult choices in developing its budget this year. Within this context, we find a number of redeeming qualities in the Governor’s proposal. Specifically, it:

  • Continues to Fulfill Most State Objectives. As noted, even with the Governor’s proposed reductions, the vast majority of multiyear funding and activities included in recent budget agreements would be sustained.
  • Focuses Reductions on Recent One‑Time Augmentations. Pulling back one‑time expenditures is less disruptive than making reductions to ongoing base programs.
  • Does Not Reduce Funding That Has Already Been Committed to Specific Projects or Grantees. Sustaining committed funding avoids creating challenges for local grantees and project sponsors that may already have entered into contracts, attained other financing, or initiated construction.
  • Utilizes Other Available Funds to Sustain Numerous Programs. The strategy of using GGRF to backfill many General Fund reductions allows the state to both achieve savings and maintain planned activities.
  • Eliminates Most Unappropriated General Fund Planned for Budget Year and Future. Pulling back on plans to provide funding that had been scheduled for 2024‑25 or future years is among the least disruptive reductions the state can make, in that administering departments should not yet have proceeded in making grant solicitations or initiating projects.

Reducing Remaining General Fund From 2024‑25 and Out‑Years Could Be Less Disruptive Than Some Other Alternatives. While the Governor’s proposal eliminates most of the General Fund that past budget agreements had planned for but not yet provided, it leaves some in place. Specifically, the proposal would maintain about $380 million of General Fund spending planned for 2024‑25 (including $200 million for drinking and wastewater infrastructure projects and about $160 million for several energy programs). Moreover, the Governor sustains plans to provide about $930 million from the General Fund in 2025‑26 (including $500 million for water storage projects, over $300 million for energy programs, and $100 million to implement portions of CERIP). Because these funds have not yet been appropriated and departments do not have the legal authority to spend them, the Legislature should have some certainty that they have not yet been awarded or committed for specific projects. As such, avoiding appropriating this budget‑year and out‑year funding in the first place could be less disruptive for departments and other entities than retracting existing funding. Moreover, avoiding incorporating one‑time expenditures into out‑year spending plans would help address the projected future budget deficit and avoid setting spending expectations that may be hard to keep.

Proposed Delays Complicate Future Budget Situation. While the Governor eliminates most of the unappropriated General Fund planned for 2024‑25, some of this funding is only temporarily reduced. Specifically, as noted above, the Governor proposes delaying a total of $1.7 billion in General Fund expenditures to future years. (This consists of $1.1 billion affecting the 2024‑25 budget window and an additional $635 million from 2025‑26.) While these delays provide short‑term savings and might preserve intended activities over the longer term, they also exacerbate future budget problems by increasing out‑year General Fund spending commitments. Specifically, the delays result in higher planned spending of $315 million in 2025‑26, $665 million in 2026‑27, and $750 million in 2027‑28. As noted above with regard to the out‑year planned funding the Governor proposes to maintain, building a multiyear spending plan that incorporates this delayed funding sets expectations for potential projects and grantees that may be hard to keep given projected out‑year budget deficits. We estimate that state revenues in the out‑years would need to exceed the administration’s forecast by roughly $50 billion per year in order to sustain the total amounts of spending proposed by the Governor’s budget across all policy areas.   Moreover, state priorities may shift in the coming years—based both on the revenue picture but also evolving circumstances such as potential floods or droughts, policy changes at the federal level, or other unforeseen events—and avoiding overcommitting out‑year funds would help preserve legislative flexibility to respond.

Legislature Could Pursue Alternative Approach for Prioritizing GGRF in Current and Budget Years. While the Governor’s approach of using GGRF to backfill General Fund reductions and sustain certain activities has merit, the Legislature could adopt this same strategy in a somewhat different way to align with its priorities. Specifically, it could achieve the same amount of savings as the Governor through directing GGRF funds to backfill a different mix of General Fund reductions. For example, the Governor proposes directing a total of $1.3 billion from GGRF to backfill all the proposed General Fund reductions to the ZEV package, but only $37 million to sustain a mere 8 percent of the proposed reductions to coastal resilience activities. Based on its highest priorities, the Legislature could choose a different allocation. The Legislature has flexibility around how it is able to direct GGRF revenues because the program was authorized in a way that is akin to a tax, meaning the funds can legally be used for broad purposes. Historically, the state has used GGRF for a wide range of environmental programs (along with programs in other policy areas such as transportation and housing).

Extensive Reliance on Out‑Year GGRF Makes Assumptions About Future State Priorities and Revenues. While the state dedicates a share of annual GGRF revenues to recurring ongoing activities (such as the high‑speed rail project, sustainable housing and transit programs, and forest health activities), it generally has maintained about 35 percent for discretionary spending decisions agreed upon by the Legislature and Governor as part of each year’s budget negotiations. The 2023‑24 budget package broke with historical practice somewhat by including plans to dedicate a notable share of out‑year discretionary GGRF revenues for specific purposes rather than deferring that decision to future legislative and administration negotiations. Specifically, the agreement planned to dedicate $600 million from discretionary GGRF annually for three years beginning in 2024‑25 to backfill General Fund reductions within the ZEV package. As noted above, the Governor’s proposal maintains these plans and adds an additional out‑year GGRF commitment of $600 million in 2027‑28 resulting from a proposed delay of some planned ZEV package spending. This would commit a total of $1.8 billion ($600 million per year) in future GGRF revenues from 2025‑26 through 2027‑28. While this approach allows the state to maintain long‑term intended ZEV spending plans and save General Fund, it does raise two key concerns.

First, the Legislature might benefit from preserving additional flexibility around how it wants to dedicate future GGRF funds. Specifically, given the projected budget deficits in the coming years, the Legislature could face some very difficult choices around its expenditures—including a potential need to reduce General Fund support for core ongoing programs. In such a case, the Legislature could find that it has higher priorities for GGRF revenues than sustaining planned one‑time program expansions. While nothing precludes it from revisiting these spending intentions in a future year, leaving them in its multiyear spending plan for now could set unrealistic expectations and make redirecting the funds in the coming years more challenging. In contrast, holding off on making spending commitments until it has more information about the budget situation it faces in each given fiscal year would preserve more flexibility for the Legislature to target available discretionary GGRF funds to its pressing and emerging priorities.

Second, considerable uncertainty exists around how much GGRF revenue will be available in future years. Historically, GGRF revenues have experienced significant volatility. A precipitous drop in GGRF revenues could jeopardize not only these planned out‑year ZEV expenditures but also other longstanding state priorities for which the state has historically relied upon this funding source—raising further questions about the wisdom of committing these additional funds so many years in advance.

Data Indicate Significant Amount of Appropriated Funding Has Not Yet Been Committed by Administering Departments. Of the General Fund appropriated for the thematic packages from 2021‑22 through 2023‑24, we estimate that over $4 billion remains uncommitted. (This typically means that it has not yet been dedicated to specific projects or activities.) Of this total, we estimate that the Governor is proposing solutions—including reductions, delays, and fund shifts—affecting under $3 billion. This leaves over $1 billion in uncommitted prior‑ and current‑year appropriated funding that has not been proposed for a General Fund solution. The Legislature could reduce some of this funding and achieve General Fund savings as additions or alternatives to the Governor’s proposals, in most cases without major disruptions to specific programs or projects. We discuss various specific examples of programs that the Legislature could consider reducing in the subsequent thematic sections of this report.

Governor Gives Precedence to Administration’s Initiatives Over Legislative Priorities . The administration’s choices regarding which programs to preserve and which to propose for reductions largely reflect the Governor’s priorities. Specifically, many of the proposed cuts are to programs for which the Legislature advocated during budget negotiations, rather than those that were initially proposed by the Governor. For example, the Governor proposes cutting $452 million from the multiyear budget agreement for coastal resilience activities—proportionally more than any other of the thematic packages—much of which was originally added by the Legislature. The Governor also proposes cutting several other programs that the Legislature augmented as priorities during previous budget negotiations, such as watershed climate resilience projects ($126 million proposed reduction), addressing per‑ and polyfluoroalkyl substances ($102 million proposed reduction), the Outdoor Equity Grant Program ($25 million proposed reduction), and the Urban Waterfront Program ($12.3 million proposed reduction). Notably, at the same time, the Governor proposes to maintain uncommitted funding for a number of the administration’s priorities, such as for water storage projects ($500 million proposed to retain), water resilience projects ($228 million), and coastal acquisitions ($49 million). To the extent the Legislature’s priorities differ from the Governor’s, it could select a different mix of programs for funding reductions.

We also note that the administration has considerable control over the pace at which programs are administered. For example, we understand that the administration has suspended grant solicitations for certain programs due to funding uncertainty—thus likely contributing to higher uncommitted amounts available for potential reduction—whereas others proceeded in their solicitations without interruption.

Administration Plans to Commit More Funding to Specific Projects in Coming Months. Departments in charge of administering the funding provided through recent budgets indicate that some programs expect to commit additional funds soon by making further grant awards within the next few months. For example, the administration indicates it expects to make some grant awards in spring 2024 for water resilience projects ($228 million currently uncommitted), transmission financing ($200 million currently uncommitted), the Wildlife Conservation Board’s various nature‑based solutions programs (affecting $73 million of the $100 million currently uncommitted), and funding to protect salmon (affecting $30 million of the $35 million currently uncommitted). After those grant awards are made, grantees will reasonably expect that funding is forthcoming and take steps such as entering into contracts and initiating construction activities. At that point, the Legislature will lose the option of reverting the associated funding and capturing savings without causing significant disruptions. As such, for some programs, the Legislature may want to consider taking early action to make funding reductions ahead of the June budget deadline to ensure departments do not proceed with their current plans to commit unspent funds (and erode potential savings). As noted above, we think these amounts could total over $1 billion.

Entities in California Are Receiving Significant Federal Funds for Climate‑ and Environmental‑Related Activities. Recent federal legislation, including the Infrastructure Investment and Jobs Act (IIJA) and Inflation Reduction Act (IRA), have provided large increases in funding for various climate‑ and environmental‑related activities. As shown in Figure 4 , we estimate that, thus far, entities in California—including state agencies and departments, local governments, tribes, private companies, and nongovernmental organizations—have received commitments totaling roughly $9.7 billion from IIJA and IRA to support a wide range of climate‑ and environmental‑related activities. Some of the program areas slated to receive the most funding include drought and water resilience (much of which is for drinking water‑related projects), clean energy, ZEVs, and wildfire and forest resilience. Additionally, many federal agencies have not yet allocated all of their IIJA and IRA funding, so entities in California will have the opportunity to compete for—and potentially secure—additional funding in the near future.

Figure 4 - California Estimated to REceive Billions in Climate and Resources-Related Funds from IRA and IIJA

Notably, many of the federally funded activities are broadly similar to those supported by the state’s programs. However, typically they do not provide an identical dollar‑for‑dollar replacement for state funds, as they may have different eligibility criteria or allowable uses. For example, in some cases, federal programs also require a local funding contribution, which can result in higher barriers to access than some state programs. Despite these program differences, the availability of billions of dollars of federal funds to support climate‑ and environmental‑related activities will ensure that even with recent and proposed reductions to state funding, significant support still is available for many of the same broad purposes planned for in recent state budgets. This consideration may be particularly important if the Legislature finds it needs to make additional reductions to General Fund‑supported programs. For example, it could identify program areas where state entities are receiving significant infusions of federal funds (such as drinking water and ZEVs) and evaluate whether it could make additional reductions to proposed state funds and still make notable progress toward achieving its priorities.

Information on Program Effectiveness Is Limited. Ideally, the Legislature’s decisions around which programs to sustain or reduce could be informed by evidence regarding which activities are most effective at limiting the magnitude and impacts of climate change. Unfortunately, such data are not widely available. In some cases, this is because activities funded by recent budgets are being attempted for the first time. Even for most previously funded programs, however, such outcome data are not regularly collected or tracked. The lack of such information also impedes the Legislature’s longer‑term decisions, such as regarding which programs should be prioritized for future funding investments.   Moreover, future decisions would benefit from information about the process of implementing the recent unprecedented level of funding, including the design of and demand for specific programs, as well as successes and challenges for both administering departments and project sponsors.

Recommendations

While we have identified some advantages to the Governor’s overall approach, the administration’s proposals do not represent the only set of options for addressing the budget problem. The Legislature could make changes to (1) reflect its priorities (such as by making alternative reductions or fund shifts), (2) avoid growing out‑year budget deficits (such as by limiting the use of funding delays), and (3) include a higher level of budget solutions (such as by making additional reductions to unspent prior‑ or current‑year funds). Below, we discuss our overarching recommendations to the Legislature for crafting climate, resources, and environmental budget solutions, which we also summarize in  Figure 5 .

Summary of Overarching Recommendations for Crafting Climate, Resources, and Environmental Budget Solutions

Maximize General Fund Savings by Reducing Significant One‑Time Spending From Climate Packages. We recommend the Legislature adopt a budget that includes significant General Fund savings from climate, resources, and environmental programs—at least as much as the Governor. While this could entail making reductions to some programs the Legislature believes are important, the vast majority of the unprecedented recent investments still would be sustained. Maximizing spending reductions from one‑time funds will allow the Legislature to minimize the use of other budget  tools—like   reserves—that  likely will be needed to address deficits in future years. Moreover, the Legislature faces some urgency in making these changes, as this strategy will not be as readily available as time passes—once one‑time funds are spent, they no longer are available to pull back, leaving fewer (and often more disruptive) options for balancing the budget, such as making cuts to ongoing programs.

Identify Alternative and/or Additional Budget Solutions Depending on Legislative Priorities and the Evolving General Fund Condition. We think that generating at least the same magnitude of General Fund solutions from climate, resources, and environmental programs as the Governor will be important to solving the budget problem. However, we recommend the Legislature modify the Governor’s proposals to reflect its priorities. To the degree some of the Governor’s proposed program reductions represent important efforts for the Legislature, it could opt to sustain that funding and instead find a like amount of savings by making alternative reductions, such as to programs with uncommitted funds. Besides finding alternative reductions, we recommend the Legislature also begin identifying options for potential additional budget solutions from climate, resources, and environmental programs. Further reductions to this one‑time spending could prove helpful in a number of potential scenarios, such as if (1) the budget condition worsens (current LAO revenue projections suggest this is likely); (2) the Legislature wants to reject some of the Governor’s proposed General Fund budget solutions in other policy areas (such as to human services programs); (3) the Legislature wants to “make room” to fund some of its key priorities, which could include support to implement recently chaptered legislation (which the Governor’s budget does not fund); and/or (4) the Legislature determines that some of the solutions included in the Governor’s proposal may not yield the anticipated savings. While this process will be challenging, taking the time to consider, research, and select potential options over the spring will better prepare the Legislature to make decisions in May and June when it will not have much time to gather information before the budget deadline.

Consider Taking Early Action to Halt Program Spending in the Current Year and Capture Associated Savings. To the degree the Legislature identifies uncommitted funding from prior‑ and current‑year appropriations it feels are good candidates for making reductions, it may want to act on them ahead of the June budget package. This will help ensure that departments do not proceed in making grant awards (eroding the potential savings) and that the funds can be captured without causing undue disruptions. As noted above, we think the total amount of additional prior‑ or current‑year unspent funds could total over $1 billion. The Governor already has proposed a package of early action budget items to which the Legislature could add, but this likely will require identifying and acting upon the target programs within the next month or two. The Legislature also could consider directing the administration to temporarily pause all spending of uncommitted prior‑ and current‑year funding from these packages to preserve its options as it gets a better sense of the revenue picture and deliberates its budget package this spring. However, we note that the administration’s compliance with such direction may be difficult to enforce.

Use GGRF to Help Sustain Highest Legislative Priorities. We recommend the Legislature adopt the Governor’s overall strategy of using GGRF to help backfill General Fund reductions for certain programs. This approach allows the state to achieve necessary budget savings while continuing important activities. However, we recommend the Legislature adopt a GGRF spending package that preserves funding for its highest‑priority activities, which may represent a different mix from that proposed by the Governor. For example, instead of prioritizing GGRF to sustain all of the original intended funding for ZEV activities, the Legislature could redirect some of those funds to sustain some additional funding for other program areas proposed for deeper reductions, especially given the significant amount of federal funds available for ZEVs.

Minimize Out‑Year Commitments for Both General Fund and GGRF. As noted, the Governor proposed delaying about $1.7 billion in General Fund spending for climate, resources, and environmental programs to future years, sustains over $900 million in General Fund planned for 2025‑26, and also commits $1.8 billion in out‑year GGRF for maintaining intended multiyear spending levels in the ZEV package. While this approach might preserve funding over the longer term, it also exacerbates future budget problems. Given the out‑year budget forecast, we recommend that—for now—the Legislature consider both reducing planned out‑year funding that has not yet been appropriated, and reducing rather than delaying expenditures and revisiting them in a future year when it has a better sense of its available fiscal resources and highest spending priorities for both the General Fund and GGRF. This would help avoid both worsening out‑year budget deficits and creating spending expectations the state may not be able to fulfill.

Conduct Robust Oversight of Spending and Outcomes, and Consider Whether Additional Program Evaluations Might Be Worthwhile.   We recommend the Legislature conduct both near‑term and ongoing oversight of how the administration is  implementing—and  local grantees are  utilizing—funding  from the recent budget augmentations. In particular, we recommend the Legislature track: (1) how the administration is prioritizing funding, especially within newly designed programs; (2) the levels of demand and over‑ or under‑subscription for specific programs; (3) any barriers to implementation that departments or grantees encounter; and (4) the impacts and outcomes of funded projects. The Legislature has a number of different options for conducting such oversight, all of which could be helpful to employ given that they would provide differing levels of detail. These include requesting that the administration report at spring budget hearings, requesting reports through supplemental reporting language, and adopting statutory reporting requirements (such as those typically included for general obligation bonds). Additionally, to the degree it might want more intensive external program evaluations for certain high‑priority programs to help assess their effectiveness, the Legislature could consider adopting language that directs the administration to set aside a portion of provided funding to contract with researchers to conduct more in‑depth studies.

Overview of Specific Proposed Adjustments

Recent Budget Agreements Included $10   Billion Over Several Years for ZEV Programs. The 2021‑22 and 2022‑23 budgets included plans to provide a combined $10 billion over several years to different departments for a collection of activities intended to promote statewide adoption of ZEVs. Of this initial funding plan, the majority of support was from the General Fund ($6.3 billion), but also included $1.6 billion from Proposition 98 General Fund, $1.3 billion from GGRF, and about $700 million combined from federal and other special state funds. As shown in Figure 6 , funded activities included programs for both light‑ and heavy‑duty vehicles, such as vehicle purchase incentives and projects to expand the state’s vehicle charging network.

Governor’s Proposed Changes to ZEV Package

General Fund Unless Otherwise Noted (In Millions)

The 2023‑24 budget agreement made some changes to this original package in light of the evolving General Fund condition. Specifically, it reduced multiyear funding for several programs by a total of $845 million. This included reducing $550 million for transit buses and infrastructure, $150 million for school buses and infrastructure, and $85 million for ports. However, the current‑year agreement also added money for a new flexible ZEV transit capital program that provides formula funding to transit agencies which they can use to support zero‑emission buses and related infrastructure and/or to cover their operating expenses. This program is funded with GGRF and intended to provide $910 million over four years, thereby more than offsetting the reductions in terms of total multiyear planned ZEV spending. To achieve General Fund savings, the 2023‑24 budget package also included a number of fund shifts to use GGRF revenues in place of some planned General Fund (including for out‑year expenditures) and delayed certain intended spending to 2026‑27.

Governor’s Proposal: Reduces $38   Million, Delays $600   Million, and Shifts $475   Million to GGRF. As shown in Figure 6, the Governor’s budget proposes to reduce net multiyear spending for ZEV activities by $38 million relative to the 2023‑24 budget package. The proposal also includes delays and fund shifts. Specifically:

  • Modest Reductions to Four Programs ($38   Million). The budget makes reductions to the following programs: California Energy Commission (CEC) ZEV manufacturing grants ($7 million), CEC emerging opportunities ($7 million), and the California Air Resources Board (CARB) and CEC drayage trucks and infrastructure pilot projects ($14 million and $9 million, respectively).
  • Funding Delays ($600   Million). The Governor proposes delaying a total of $600 million in planned expenditures from GGRF for seven programs from 2024‑25 to 2027‑28. (This delay has the net effect of freeing up $600 million in GGRF funds in the budget year, which the Governor then uses to backfill General Fund reductions for other programs. The proposal also would commit a like amount of GGRF in 2027‑28 for the delayed expenditures.) The affected programs are: CEC ZEV fueling infrastructure grants ($120 million); CEC clean trucks, buses, and off‑road equipment ($137 million); Clean Cars 4 All ($45 million); CEC and CARB drayage trucks and infrastructure ($50 million and $48 million, respectively); CARB sustainable community plans and strategies ($100 million); CEC Equitable At‑Home Charging ($80 million); and CARB charter boats compliance ($20 million). The administration notes that prior‑year funding is available for most of these programs to meet applicant demand in the interim.
  • Current‑Year Shift to GGRF ($475   Million, Early Action). The budget proposes shifting $475 million of current‑year ZEV expenditures from General Fund to GGRF for the following programs: ZEV fueling infrastructure grants ($219 million); drayage trucks and infrastructure ($157 million); transit buses and infrastructure ($29 million); and clean trucks, buses, and off‑road equipment ($71 million). This proposed change is enabled by higher‑than‑projected cap‑and‑trade auction revenues materializing in the current year. The Governor is requesting that the Legislature take early action to effectuate this fund shift so that programs can proceed with making grant awards this spring.

LAO Comments: Legislature Could Consider Alternative and/or Additional Reductions. While there is significant unspent funding planned for the budget year and out‑years in the ZEV package, most of this funding is from GGRF. Consequently, making reductions would not automatically generate General Fund savings. However, the Legislature could achieve further budget solution if it were to reduce GGRF spending on ZEV activities, make additional General Fund reductions elsewhere, then redirect the freed‑up GGRF to backfill those other priorities. Based on available data on remaining funds, the Legislature could consider reducing the following:

  • School Bus and Infrastructure (About $1   Billion in Proposition   98 General Fund). The 2022‑23 budget package established a new program to fund zero‑emission school buses and related infrastructure administered by CARB and CEC. The Legislature previously approved $500 million of Proposition 98 General Fund to fund the first round of grants and adopted intent language to allocate additional funding in the future. The Governor’s budget provides an additional $500 million of Proposition 98 General Fund for a second round of grants in 2024‑25. The administration has indicated it is in the process of, but has not yet allocated, the original grant funding. With this in mind, we recommend the Legislature: (1) consider reverting the prior funding (about $500 million) to achieve General Fund savings, and (2) reject the new $500 million proposed in the budget year. For more information about the school bus spending, please see our report, The 2024‑25 Budget: Proposition   98 K‑12 Education Analysis .
  • Buses and Off‑Road Equipment (At Least $249   Million). CARB has used its appropriations for this category of activities to fund its Hybrid and Zero‑Emission Truck and Bus Voucher Incentive Program. Expenditure data suggest $249 million of the GGRF previously appropriated for this program is unspent and could be reverted and redirected to achieve General Fund savings elsewhere. CEC also received funding in this category but the administration had not provided data on CEC’s expenditures as of this writing.
  • Charter Boats Compliance ($60   Million). CARB closed its grant solicitations for this program in December 2023 and currently is reviewing applications. Approximately $40 million of General Fund plus $20 million of GGRF remains in the balance. The Legislature could consider reverting this $60 million but likely would have to take early action in order to capture the savings as CARB is in the process of preparing to award the funds.
  • Emerging Opportunities ($47   Million). CARB is using this funding for ZEV technology demonstration projects. Of the $53 million General Fund originally allocated, $47 million remains in the program’s balance and could be reverted for General Fund savings.
  • CEC ZEV Program Funding (Unknown, Potentially Several Hundreds of Millions of Dollars). Updated information on CEC’s ZEV package expenditures was not available at the time of this writing. Based on historical CEC ZEV spending time lines, we suspect that several hundreds of millions dollars of unspent funding could be available. We will provide more information to the Legislature after we receive these data from the administration.

Recent Budget Agreements Included $8.8   Billion Over Several Years for Water and Drought‑Related Activities. As shown in Figure 7 , the 2022‑23 budget appropriated and intended to provide a combined $8.8 billion ($8.3 billion from the General Fund and about $450 million from other funds) over several years to various departments for emergency drought response and water resilience activities. Nearly half of the funding ($4 billion) was to support activities related to drinking water quality and availability, water recycling and groundwater cleanup, water supply, and flood management. About $1.4 billion was intended for immediate drought response activities, such as for the State Water Resources Control Board (SWRCB) to respond to drinking water emergencies. The remaining funding ($3.3 billion) was to support habitat restoration, water quality, and conservation activities. The 2023‑24 budget agreement reduced total multiyear funding by $632 million General Fund (7 percent). Major reductions included $278 million for water recycling, $119 million for Salton Sea restoration activities, and $60 million for local assistance grants related to implementation of the Sustainable Groundwater Management Act.

Governor’s Proposed Changes to Water and Drought Resilience Package

General Fund Unless Otherwise Noted a (In Millions)

Governor’s Proposal: Reduces $810   Million, Delays $100   Million, and Delays and Shifts $21   Million. Also shown in Figure 7, the Governor’s budget proposes to reduce multiyear General Fund spending for water and drought resilience, relative to the 2023‑24 budget agreement, by $810 million. (The $7.3 billion the Governor proposes to retain represents 84 percent of the original 2022‑23 package.) The proposal would revert $100 million appropriated in earlier years for water recycling projects administered by SWRCB and delay providing it until 2025‑26. Similarly, for the California Department of Food and Agriculture’s (CDFA’s) State Water Efficiency and Enhancement Program, the proposal would revert $21 million General Fund appropriated in earlier years and instead provide the same amount of funding from GGRF in 2024‑25. Proposed reductions include:

  • Watershed Climate Resilience. The budget proposes to reduce funding by $438 million ($126 million to the Department of Water Resources [DWR] and $312 million to the Wildlife Conservation Board [WCB]), retaining just 11 percent ($56 million) of the original amount. DWR indicates that the proposed reduction would affect the number of long‑term projects it can fund but not its near‑term program plan, which includes six pilot studies and a subsequent set of grants. While the reduction will lead to WCB awarding fewer grants, it has other funding sources available for these types of projects, including $43 million from Proposition 68 (2018) and annual support of $21 million from the Habitat Conservation Fund.
  • Water Recycling and Groundwater Cleanup: The proposal would reduce funding for groundwater cleanup by $55 million and for water recycling by $119 million (the 2023‑24 budget already reduced funding by $278 million). (As noted above, the budget also would delay $100 million until 2025‑26 for water recycling.) Relative to the original package, the budget would retain $348 million, or 43 percent for these two programs. SWRCB indicates it would prioritize providing low‑cost financing for water recycling projects through its State Revolving Fund (SRF) programs and providing grants for water recycling and clean water projects in disadvantaged communities. In addition, the federal IIJA is providing more federal funding than normal for SRF programs between 2022 and 2026 ($1.16 billion for the Drinking Water SRF and $790 million for the Clean Water SRF), which can be used for water recycling and groundwater cleanup projects.
  • Per‑ and Polyfluoroalkyl Substances (PFAs) Support. The proposal would reduce funding for addressing PFAs by $102 million (retaining $53 million, or 27 percent, of the original total, after accounting for additional reductions made in 2023‑24). PFAs are long‑lasting chemicals which are hard to break down and have been used in a variety of consumer and industrial products. Reduced funding would result in fewer and/or smaller state‑funded grants. However, SWRCB will receive approximately $460 million in federal funds through its SRF programs from 2022 through 2026 to address “emerging contaminants,” which include PFAs.
  • Dam Safety. The budget would halve funding—from $100 million to $50  million—for dam safety pilot projects administered through a competitive grant program by DWR. The reduction would result in DWR funding fewer projects.
  • Agricultural Programs. The budget would reduce funding for drought relief for small farmers by $13 million and for on‑farm technical assistance by $6 million. (Relative to the original package, the budget would retain $21 million, or 53 percent, for these two programs.) CDFA indicates that demand for drought relief grants was lower than anticipated (it awarded about $12 million of the available $25 million), perhaps in part due to a similar program being offered through the Governor’s Office of Business and Economic Development (GO‑Biz). The on‑farm technical assistance program was similarly undersubscribed, although CDFA indicates this could reflect the limited capacity of technical assistance providers, rather than the needs of farmers.
  • Forecasting Activities. The budget would reduce an ongoing appropriation for DWR—from $17 million to $10 million annually—that supports water supply/runoff forecasting. Specifically, the reduction would result in conducting fewer aerial snow surveys and conducting them (and associated modeling) in fewer watersheds.

LAO Comments: Legislature Could Consider Alternative and/or Additional Reductions. In light of the state budget condition, the Legislature has several options for additional and/or alternative reductions from the water and drought resilience package.

  • Water Storage Projects ($500   Million in 2025‑26). The administration’s original proposal for this funding noted that it would build on the $2.7 billion provided by Proposition 1 (2014) for water storage projects, yet specific details on how the funds would be used have not been provided. Given this funding has not yet been appropriated, eliminating it likely would be less disruptive compared to certain other options before the Legislature.
  • Drinking Water Project Grants ($200   Million). While these programs are important, the state currently has an unprecedented amount of federal funding available for these purposes through the federal SRFs. In addition, state statute requires an annual GGRF appropriation of $130 million (through 2030) to SWRCB for the same types of drinking water projects. As such, the state could continue to pursue its goals and focus on the drinking water needs of disadvantaged communities even with a reduction in General Fund support.
  • Water Recycling (Reduce Rather Than Delay $100   Million). Although eliminating this funding—rather than delaying it, as proposed by the Governor—would reduce the number of projects SWRCB could support with state funding (which is more flexible than federal funding), other funding sources are available for these projects. Specifically, SWRCB can use federal funds provided through the SRF for water recycling projects.
  • Revert Unspent Funding Provided in Earlier Budgets. Of the $6.5 billion General Fund already appropriated for water and drought resilience packages across 2021‑22, 2022‑23, and 2023‑24, the Governor proposes reducing about $524 million of uncommitted funds (as discussed above). Based on our review of other uncommitted funds, the Legislature could consider additional reductions of close to $775 million. For example, SWRCB has about $300 million in uncommitted funds for drinking water/wastewater programs. SWRCB expects to commit a good portion of this funding between April and June, with an estimated $65 million remaining by the end of the 2023‑24 fiscal year. Consequently, depending on how much of this funding the Legislature wished to pull back, it may have to act quickly to capture the potential savings that currently are available. While these programs remain important, particularly among disadvantaged communities, SWRCB could partially offset reductions with federal SRF funding and its annual GGRF appropriation. Additionally, the California Natural Resources Agency (CNRA) has approximately $228 million in uncommitted funds for water resilience grants. The administration indicates it will select awardees in the March/April time frame, meaning the Legislature would have a short window to act and reduce these funds to solve the budget problem. Other examples include $50 million for dam safety (given the Governor already proposes a reduction of the other $50 million, an additional reduction would eliminate the pilot program) and $104 million for WCB’s streamflow enhancement program.

Recent Budget Agreements Included $7.9   Billion Over Several Years for Energy Programs. The 2021‑22 and 2022‑23 budgets included plans to provide a combined $7.9 billion ($6.9 billion from the General Fund and about $1 billion from other funds) over several years to different departments for an energy package. As shown in Figure 8 , funded activities focused primarily on three categories—reliability , clean energy, and ratepayer relief. (In addition to programs shown in the figure, the recent agreements included $1 billion for CERIP implementation and a Climate Innovation program, both of which are discussed in the “Other Recent Augmentations” section of this report.) On net, the 2023‑24 budget agreement reduced total multiyear funding by $944 million. Major reductions included $549 million from the California Arrearage Payment Program at the Department of Community Services and Development, $270 million from the Residential Solar and Storage Program at the California Public Utilities Commission (CPUC), $105 million from the Distributed Energy Backup Assets (DEBA) program at CEC ($100 million of which was redirected to the Investments in Strategic Reliability Assets program at DWR for no net budget savings), and $50 million from the program providing incentives for long‑duration storage. In addition, the 2023‑24 adjustments to the energy package included numerous funding delays as well as shifts totaling about $1 billion from the General Fund to GGRF.

Governor’s Proposed Changes to Energy Package

Governor’s Proposal: Reduces $419   Million, Delays $505   Million, and Shifts $144   Million to GGRF. Also shown in Figure 8, the Governor’s budget proposes to reduce net multiyear spending for energy activities by $419 million relative to the 2023‑24 budget package. (This would retain 83 percent of the original intended amount.) The proposal also includes funding delays for four programs totaling $505 million. Finally, the Governor shifts $144 million for two programs from the General Fund to GGRF (Equitable Building Decarbonization and incentives for long‑duration storage). Major proposed program changes include:

  • Funding Delays for Four Programs. The  proposal delays funding for (1) Residential Solar and Storage (instead of $75 million in 2024‑25 and $125 million in 2025‑26, it would provide $100 million in both 2026‑27 and 2027‑28), (2) a pump storage project at the Oroville Dam complex (instead of $90 million in 2024‑25 and $110 million in 2025‑26, it would provide $100 million in both 2026‑27 and 2027‑28), (3) Investments in Strategic Reliability Assets (delays $55 million from 2024‑25 to 2025‑26), and (4) DEBA (reverts $50 million from 2023‑24 and instead provides $25 million in both 2025‑26 and 2026‑27).
  • Equitable Building Decarbonization. The budget proposes reducing overall funding for this CEC program by $283 million, retaining $639 million, or 69 percent, of the original allocation. This program is intended to support energy upgrades for low‑ and middle‑income households and still is being developed by CEC. The reduction would result in fewer direct install incentives. (The Governor also proposes to shift $87 million for this program from General Fund to GGRF in 2024‑25, which would have no programmatic effect.)
  • Carbon Removal Innovation Program. This proposal would reduce this program by $40 million, adding to the $25 million reduction that was adopted in 2023‑24. There is no further funding proposed for this program beyond the $35 million retained in 2022‑23 (representing 35 percent of the original allocation).
  • Industrial Decarbonization. The budget would reduce funding for this new CEC program that provides incentives for technologies that reduce emissions at industrial operations by $22 million, retaining $68 million from its original planned allocation of $100 million. The proposal would reduce the number of state‑funded projects, but the program plans to leverage $90 million in federal Department of Energy (DOE) funds, which would help offset the reduction.
  • Hydrogen Grants. The proposed reduction of $35 million would retain $65 million of the original amount for CEC to provide these grants. The administration noted this program is a good candidate for reductions due to more than $1 billion newly coming to California from DOE to support hydrogen energy development through the Alliance for Renewable Clean Hydrogen Energy Systems (ARCHES) initiative.
  • Food Production Investment Program. This proposed reduction of $19 million would be in addition to $10 million reduced from the program in 2023‑24. Relative to the original package, the budget would retain $46 million, or 62 percent, for this program. CEC expects it would support 10 to 14 fewer projects as a result of the proposed reduction.
  • Capacity Building Grants. The original package provided $30 million across 2021‑22 and 2022‑23 to provide capacity grants to tribes and community‑based organizations to participate in CPUC decision‑making processes. CPUC has not yet spent this funding and the Governor proposes to reduce it by $20 million. To accommodate this reduction, CPUC would decrease its grant funding allocations by approximately 70 percent and forgo a planned technical assistance contract.

LAO Comments: Legislature Could Consider Alternative and/or Additional Reductions. In light of the state budget condition, the Legislature has several options for generating General Fund savings through making additional and/or alternative reductions from the energy package. Based on the best available data on remaining funds, the Legislature could consider reducing the following programs (all amounts from the General Fund unless otherwise noted).

  • Hydrogen Grants (Additional $65   Million). The Legislature could consider a further reduction or elimination of the program’s funding—beyond the $35 million proposed by the Governor—due to the significant federal funding (more than $1 billion) newly available for hydrogen development in California through ARCHES. None of this funding has yet been committed.
  • Industrial Decarbonization (Additional $60   Million). The Legislature could consider a further reduction or elimination of the program’s funding beyond the $22 million proposed by the Governor. As noted above, federal funds are also available to support the goals of this program. This program has not yet begun dispersing funding.
  • Food Production (Additional $35   Million). The Legislature could consider further reductions beyond the $19 million the Governor proposes for this program, which has only committed a small portion of its funding. However, if the Legislature wants to make additional reductions, it may have to take early action, as the administration plans to collect proposals later this spring. The funds the Governor proposes retaining for the program are from GGRF, not General Fund, but the Legislature could instead eliminate General Fund for a different program and redirect this GGRF to offset those reductions in order to achieve additional savings.
  • Transmission Financing ($225   Million). Previous budgets appropriated $225 million to the California Infrastructure and Economic Development Bank to boost new electricity transmission in the state. The administration has not yet dispersed these funds, though it plans to do so later this spring. The Legislature could consider making reductions or eliminating this funding, but it may have to take early action. Additionally, federal energy funds the state is receiving to support grid reliability may be able to help offset reductions to this program.
  • DEBA ($543   Million). As of this writing, data from the administration indicate this program (which is intended to provide incentive funding to promote more efficient backup energy resources) has $543 million from previously appropriated funds remaining in its balance. CEC indicates that it expects to release additional solicitations this spring. Given the large size of this allocation and that CEC has only spent a total of $2 million (on administrative costs) thus far, it seems a reasonable candidate for capturing additional savings. Depending on the level of savings needed, the Legislature could prioritize equity by making reductions to the portion of program funding not explicitly directed to disadvantaged communities (roughly half of the funding). Given CEC’s plans to proceed with new grant solicitations this spring, the Legislature may have to consider early action if it wants to make reductions.

Recent Budget Agreements Included $2.8   Billion for Wildfire Resilience‑Related Activities. Recent budget packages included a total of $2.8 billion over a four‑year period—2020 ‑21 through 2023‑ 24—to support wildfire and forest resilience. Roughly 40 percent of the funding over the four years—$1.1  billion—was for programs designed to promote healthy forests and landscapes, generally by removing hazardous fuels. Just over one‑quarter of the funding—$766  million—was  to support the installation and maintenance of wildfire fuel breaks. The remaining  funds—totaling  $909  million—was  for projects to increase regional capacity for conducting forest health projects, as well as to encourage forest‑sector economic stimulus, science‑based forest management, and community hardening. Of the $2.8 billion total, $2 billion was from the General Fund and the remaining $755 million was from GGRF.

The 2023‑24 budget agreement reduced net funding for various wildfire and forest‑resilience activities by $47 million and shifted $14 million from the General Fund to Proposition 98. The largest reduction—$25  million—was  for efforts to steward state lands, intended to help CNRA departments bring buildings in high‑fire‑risk zones into compliance with new defensible space regulations that are under development pursuant to Chapter 259 of 2020 (A B 3074 , Friedman). As shown in Figure 9 , after these reductions, the budget retained a multiyear total of $2.8 billion for wildfire and forest resilience activities (98 percent of the original planned amount).

Governor’s Proposed Changes to Wildfire and Forest Resilience Package

Governor’s Proposal: Reduces $101   Million and Shifts $163   Million. The Governor’s 2024‑25 budget proposes some additional General Fund reductions to the wildfire and forest resilience funding that was included in recent budget agreements. Cumulatively, the reductions would lower General Fund spending by $101 million across the following seven programs, while retaining a total of $2.7 billion for wildfire and forest resilience (95 percent of the original funding provided). In general, the proposed reductions will result in fewer projects being undertaken by each program. The affected programs consist of:

  • Forest Legacy Program. This program funds conservation grants and easements with private landowners to protect forest land from conversion to non‑forest uses and to support good management practices. The budget proposes to reduce funding by $4 million, retaining $45 million.
  • Prescribed Fire and Hand Crews. This funding supports the California Department of Forestry and Fire Protection (CalFire) fuels reduction crews, as well as a CalFire contract with the California National Guard to perform vegetation management work. The costs of the National Guard crews ultimately were paid by the federal government, resulting in savings. The budget proposes to reduce funding by $5 million, retaining $129 million.
  • Conservancy Projects. This funding was provided for multiple state conservancies to support projects aimed at improving resilience to wildfires. The budget proposes to reduce funding by $28 million ($9.4 million from the San Diego River Conservancy, $9 million from the Coachella Valley Mountains Conservancy, $5.7 million from the Sacramento‑San Joaquin Delta Conservancy, $2.3 million from the State Coastal Conservancy, and $1.3 million from the San Gabriel and Lower Los Angeles Rivers and Mountains Conservancy). While these reductions would lessen the number of projects that conservancies can undertake, it still would leave significant funding—$350  million—for conservancy‑led wildfire resilience efforts.
  • Biomass to Hydrogen/Biofuels Pilot. This funding was for a pilot administered by the Department of Conservation (DOC) aimed at creating hydrogen and/or liquid fuel from forest biomass. The budget proposes to reduce funding by $44 million (retaining $6.5 million). The retained funding has already been used for a first round of planning grants for project developers and DOC’s administrative activities. The proposed reduction will mean that DOC will not move forward with an originally planned second round of grant funding, which had been expected to support the implementation of pilot projects.
  • Monitoring and Research. This funding was to support various efforts—including by CalFire as well as universities and other researchers—to improve knowledge of forest conditions and the effectiveness of different practices to reduce the risk of wildfire spread or damage. The budget proposes to reduce funding by $6 million, retaining $32 million.
  • Interagency Forest Data Hub. This funding was to create an Interagency Forest Data Hub. The budget proposes to reduce funding by $3 million, retaining $7 million.
  • Home Hardening. This funding was provided to implement the wildfire mitigation assistance pilot program authorized by Chapter 391 of 2019 (A B 38 , Wood), providing grants to homeowners in certain vulnerable communities for retrofits aimed at improving resilience to wildfires. The budget proposes to reduce funding by $12 million, retaining $38 million. The proposed reduction would mean fewer homes and communities would be included in the pilot.

In addition to the reductions discussed above, the budget shifts $163 million across four programs to GGRF, including (1) stewardship of state‑owned lands ($34.5 million), (2) fire prevention grants ($82 million, proposed for early action), (3) Regional Forest and Fire Capacity Program ($20 million), and (4) unit fire prevention projects ($26 million). Notably, the Governor does not propose to make any changes to the $200 million continuous appropriation from GGRF for forest health and wildfire prevention that was authorized as part of the 2021‑22 budget but is not fully reflected in the budget packages. Accordingly, in addition to the amounts in Figure 9, under the Governor’s plan, an additional annual $200 million from GGRF would be provided for these purposes in 2024‑25 through 2028‑29.

LAO Comments: Legislature Still Has a Few Potential Alternative and/or Additional Reductions It Could Make to Unspent Current‑ and Prior‑Year Funds. The Legislature has a few other options that it could consider in addition to or in place of the Governor’s proposed solutions. For example, the Legislature could replace some or all of the proposed fund shifts with reductions, which would make additional GGRF available for other critical legislative priorities.

Additionally, the Legislature could consider (1) making reductions to programs that have significant uncommitted balances but are not included in the Governor’s proposed solutions and/or (2) increasing the size of the reductions to certain programs beyond what the Governor proposes to capture the full uncommitted balance. Some potential options for these types of additional solutions include:

  • Tribal Engagement ($22   Million). This program supports tribes in the planning and implementation of projects that advance wildfire resilience, forest health, and cultural use of fire. It has an uncommitted balance of $22 million General Fund, almost all of which is currently anticipated to be awarded sometime in summer 2024.
  • Forest Improvement Program ($22   Million). This program provides financial assistance to private, nonindustrial forestland owners under cost‑share agreements. This program has an uncommitted balance of roughly $22 million ($20 million of which is General Fund and $2 million of which is GGRF). Of this total, CalFire plans to award an $8 million block grant by April 2024 to allow partner organizations to offer similar assistance outside of the Forest Improvement Program. CalFire expects to award the remaining funding through its typical rolling solicitation process, which provides awards of a couple of million dollars every two months. The Legislature could consider reducing funding for this program, with the amount available for generating savings dependent on when the Legislature acts.
  • Prescribed Fire and Hand Crews ($31   Million GGRF). In addition to the $5 million in uncommitted General Fund that the Governor proposes reducing, the program currently has roughly $31 million of uncommitted GGRF from prior appropriations. The Legislature could consider also reducing these funds and redirecting them to offset other General Fund costs. If it were to reduce funds for this program, CalFire would have less funding for fuel reduction work and research grants. We note that if the Legislature is interested in reducing the portion of this funding that CalFire uses for research grants ($4.5 million), taking early action would be important to reduce disruptions given the department plans to make those awards in May 2024.
  • Home Hardening Program ($13   Million). This program has faced various implementation challenges and as such has roughly $25 million of General Fund that has not yet been committed. Accordingly, in addition to the Governor’s proposed $12 million reduction, the Legislature could consider capturing an additional $13 million in General Fund savings. A reduction to the funding for the program would result in fewer homes and communities being included in the pilot.

Recent Budget Agreements Included $1.6   Billion for Nature‑Based Activities. Recent budget agreements included $1.6 billion on a one‑time basis over three years—from 2021‑22 through 2023‑ 24—from  the General Fund for various departments to implement a variety of nature‑based activities. As shown in Figure 10 , about one‑third of the total funding—$495  million—was to support programs focused on acquiring and managing land for conservation and habitat restoration‑related purposes. Just over one‑quarter of the funding—$403  million—was  to support wildlife protection programs. The remaining  funding—totaling  $667  million—was  for regionally focused programs, youth and tribal programs, wetland‑focused projects, and other types of activities. Many of the funded programs are related to helping the state achieve various goals and plans established by the administration over the past few years, such as the objective of conserving 30 percent of the state’s lands and coastal waters by 2030 (“ 30x30 ”) as established by the  Governor’s Executive Order N‑82‑20  and the  Natural and Working Lands Climate Smart Strategies .

Governor’s Proposed Changes to Nature‑Based Activities Package

General Fund (In Millions)

The 2023‑24 budget agreement made General Fund reductions to planned nature‑based activities totaling $155 million across five programs. The largest reduction—$100  million—was  to funds provided to various conservancies across the state. Some other notable changes included reducing: $35 million for a WCB program to mitigate the impacts of climate change on wildlife, $10 million for the State Coastal Conservancy’s (SCC’s) San Francisco Bay wetlands support, and $6 million for the California Department of Fish and Wildlife’s (CDFW’s) Natural Community Conservation Program Planning and Land Acquisition program. After accounting for these reductions, the budget retained $1.4 billion for nature‑based activities (90 percent of the original planned amount).

Governor’s Proposal: Reduces $15   Million. As shown in Figure 10, the Governor’s 2024‑25 budget proposes to achieve $15 million in General Fund savings by eliminating funding for the following two nature‑based activity‑related programs:

  • Wetlands Restoration at Redondo Beach. The original package provided $10 million for CNRA to provide funding to the City of Redondo Beach to purchase a former power plant site on which the city would like to develop a regional park and restore historic wetlands. CNRA indicates that the city intended to use the funds to bid on the property at auction after the resolution of legal matters that are still pending. If the funding is eliminated as proposed, the city may not have sufficient funds to acquire the property, however, the timing of when the city might need the funds still is uncertain.
  • Regional Conservation Strategies. The original package provided $5 million for a WCB program created by Chapter 455 of 2016 (A B 2087 , Levine) that supports the development of voluntary, nonregulatory regional planning processes. This program also previously received $5 million in Proposition 68 funding in 2018. WCB expects the impact of the proposed General Fund elimination would be minimal because it still has remaining Proposition 68 funding for this same purpose.

After accounting for these reductions, the budget proposes to retain a total of $1.4 billion for nature‑based activities (89 percent of the original planned amount).

LAO Comments: Legislature Could Consider Alternative and/or Additional Reductions From Unspent Current‑ and Prior‑Year Funds. Based on our review of expenditure data, we estimate that about $400 million remains uncommitted from various prior‑ and current‑year nature‑based activity‑related program appropriations that the Governor does not propose reducing. Given the significant amount of uncommitted funding in this area, to the extent the Legislature needs to identify alternative and/or additional solutions, it has multiple options to consider. Some examples include:

  • Various WCB Programs ($102   Million). These WCB programs support planning, acquisition, and restoration projects on natural and working lands . Currently, about $102   million of the $245   million originally provided for these programs remains uncommitted and could be considered for reduction. Such a reduction would mean fewer projects are completed. However, a significant amount of funding still would be retained, both in these programs as well as in other programs that support activities with similar objectives, such as CDFW’s program to mitigate climate change impacts on wildlife and WCB’s other programs. We note that WCB indicates that it plans to make additional awards for these programs in the coming months. Thus, if the Legislature would like to reduce funding for these programs, taking early action would maximize the amount of savings available.
  • WCB’s Program to Protect Wildlife From Changing Conditions ($100   Million). WCB originally received $353 million to protect wildlife from changing conditions. Of this amount, $218 million has been committed to projects and the 2023‑24 budget package reduced $35 million. However, nearly $100 million remains uncommitted and thus could be considered as a potential solution. As with WCB’s other programs discussed above, additional reductions would result in fewer projects, but the board still would maintain significant funding for similar activities from other sources. WCB indicates that it plans to make additional awards totaling roughly $30 million in the coming months, making this program another potential candidate for early action.
  • CNRA’s Tribal Nature‑Based Solutions Program ($97 Million).  This is a new program aimed at helping facilitate access, co‑management, and ancestral land return. While providing funding to support tribes has merit in light of historical injustices, only about $3   million of the $100   million provided in 2022‑23 or 2023‑24 has been committed. Thus, the remaining $97   million could potentially be considered for reduction given the severity of the state’s budget problem. We note, however, that the administration indicates that it expects to make awards as soon as April 2024, so should the Legislature want to consider reducing the funding, it would be advisable to take early action. (We note that the budget also proposes to convert a temporary staff position that supports this program to permanent status. Should the program be eliminated, that position would no longer be needed, resulting in a small amount of ongoing savings.)
  • SCC’s Coastal Acquisitions ($49   Million).  This funding has been set aside for SCC to undertake acquisitions that help protect natural resources and provide for public access. Currently, roughly $49 million of the $50 million that was originally provided for this purpose remains uncommitted. SCC reports that it anticipates it ultimately would use the funding for a complex, significant acquisition opportunity which currently is in the appraisal phase.
  • Wetlands Restoration Program ($13   Million). The original package provided $54 million for this CDFW program, which funds wetland and meadow restorations, and also supports a recently created Beaver Restoration Program. Of the $54 million, roughly $34 million remains uncommitted. CDFW anticipates awarding roughly $21 million early this spring, leaving $13 million the Legislature could reduce.
  • Wildlife Corridors ($20   Million). Of the $42 million originally provided to CDFW for wildlife corridors, roughly $20 million remains uncommitted and therefore could be considered for a budget solution. CDFW notes that it is reviewing proposals on a continuous basis, so the amount available for reduction would be dependent on when the Legislature takes action.
  • Climate Smart Land Management Program ($7.5   Million). This is a new program administered by DOC that aims to increase the capacity of state partners to support natural working lands and 30x30 goals. Roughly $7.5   million of the $16   million originally provided for this program remains uncommitted and DOC does not anticipate making awards until June or July 2024. Given the condition of the General Fund, the Legislature could make further reductions and use the first round of funding as a more limited pilot. It could then evaluate the outcomes of that funding before deciding whether it is worthy of future support.

Recent Budget Agreements Provided $2.2   Billion for Community Resilience. As shown in Figure 11 , recent budgets included $2.2 billion for programs focused on helping communities address the causes and impacts of climate change. Funding was provided across 2021‑22 through 2024‑25. The funds support both previously existing and newly established programs. For example, the largest share of the funding is for a program established in  2017—through  Chapter 136 (A B 617 , C. Garcia)—that supports efforts to reduce pollution and improve air quality in highly impacted communities. The same is true for the Transformative Climate Communities Program, which began in 2018 and funds community‑led development and infrastructure projects. The remaining programs displayed in Figure 11 were initiated with funding provided in the recent budget packages.

Governor’s Proposed Changes to Community Resilience Package

The 2023‑24 budget revised the funding for several of these programs to save $765 million General Fund through a combination of reductions and fund shifts. Specifically, the 2023‑24 budget package included $515 million in reductions (24 percent), delayed $50 million from 2023‑24 to 2024‑25, and shifted $250 million for the A B 617 program from the General Fund to GGRF. After accounting for the reductions, the budget retained $1.7 billion for community resilience activities across the multiyear period (76 percent of the original planned amount)—about $1 billion from GGRF and $607 million from the General Fund. As a separate but related action (not reflected in the figure), the budget doubled funding for the California Climate Action Corps program (from $4.7 million to $9.3 million per year beginning in 2023‑24) and made the funding ongoing rather than ending in 2025‑26 as originally planned.

Governor’s Proposal: Reduces $90   Million General Fund. As shown in the figure, the Governor proposes new General Fund reductions totaling about $90 million across a few programs in the community resilience package. These include $75 million from the regional climate resilience program, $9.8 million from regional climate collaboratives, and $5 million from the Climate Adaptation and Resilience Planning Grants Program. In a separate but related action (not reflected in the figure), the Governor proposes providing $250 million from GGRF for an additional year of support for the A B 617 program in 2024‑25.

LAO Comments: Proposal Captures Most Remaining General Fund but Legislature Could Consider Other Possible Solutions. Based on our review of expenditure data, some additional funding in the community resilience package remains uncommitted and could be considered for reductions. These include:

  • Climate Adaptation and Resilience Planning Grants ($10   Million). Only $10 million of the $25 million provided for this program has been committed to date. While the Governor proposes reducing associated funding by $5 million, an additional $10 million would remain uncommitted. The administration currently is finalizing its guidelines for the next round of grants and expects to close applications and begin making awards in late spring or early summer.
  • Environmental Justice Initiatives (Between $5   Million and $15   Million). The administration indicates that it is finalizing awards for the first round of these grants and expects to still have between have between $5 million and $15 million General Fund available for future grant cycles that would be initiated in the second half of 2024 or later. The Legislature could consider reducing the funding for these programs to achieve General Fund savings rather than moving forward with the next rounds of the grants.
  • Climate Action Corps Program (Up to $9.3   Million Ongoing Annually). The 2023‑24 budget package doubled annual funding levels for this program and made it ongoing. The Legislature could consider lowering or eliminating the ongoing commitment. While taking such action ultimately would result in fewer individuals participating in these activities, scaling back a recently initiated program likely would be less disruptive than making reductions to longstanding ongoing programs—which could become necessary if the fiscal situation worsens and the Legislature is unable to identify sufficient budget solutions elsewhere. Additionally, federal funding supports a similar program.

Recent Budget Agreements Included $1.3   Billion for Coastal Resilience Activities. As shown in Figure 12 , recent budgets included $1.3 billion across four years (2021‑22 through 2024‑25) for a variety of activities to increase coastal resilience and adapt to the effects of sea‑level rise. The package included funding for SCC for projects to protect the coast (including coastal watersheds) from the effects of climate change ($500 million), adapt to the effects of sea‑level rise using nature‑based approaches ($420 million), and adapt infrastructure to the effects of sea‑level rise ($144 million). The package also included funding for the Ocean Protection Council (OPC) to support projects to protect and restore marine wildlife and ocean and coastal ecosystems ($117 million) and to implement Chapter 236 of 2021 (S B 1 , Atkins), which aims to support local governments in sea‑level rise planning ($102 million). The enacted 2023‑24 budget reduced this overall funding by $183 million, primarily in SCC’s coastal protection program.

Governor’s Proposed Changes to Coastal Resilience Package

Governor’s Proposal: Reduces $452   Million and Shifts $37   Million. The Governor’s budget proposes to reduce General Fund support for SCC by $392 million across its three programs and for OPC by $60 million across its two programs. In addition, for OPC’s implementation of S B 1 , the proposed budget would delay $27 million from 2023‑24 to 2024‑25 and shift the fund source for both that amount and the original $10 million planned in 2024‑25 from the General Fund to GGRF. Relative to the original package, the proposed changes would result in 51 percent of funding retained, or $660 million of the original $1.3 billion. Reduced funding would limit the number of projects SCC can fund and could affect its ability to draw down future federal funding that requires a state match. SCC indicates it would focus on managing previously authorized projects and advancing recently selected priority projects by completing environmental reviews and permits and potentially securing additional federal funds. SCC recently applied for $150 million in federal funds and would be able to use its existing and retained funds for the required state match, but with the proposed reductions likely would not have sufficient matching funds to apply for future rounds of federal grants.

LAO Comments: Proposal Eliminates Nearly All Unspent Coastal Funding. The Governor’s proposal would reduce a significant share (49 percent) of funding from the coastal resilience package—proportionally more than any other of the thematic packages. One rationale for this approach is that a significant amount of SCC’s funding has not been spent, making it easier to pull back to help solve the state’s significant budget deficit without halting particular projects or reneging on specific spending commitments. We note that a key reason this magnitude of funding still is available is because the Governor had proposed reducing it in the 2023‑24 budget, not because there is a lack of activities to pursue. During budget negotiations—which lasted through June 2023—SCC could not make plans to spend funds that might not materialize. The funds ultimately were restored in the final budget agreement because the Legislature viewed these activities as significant priorities. However, given that the funds have not yet been awarded for specific projects, approving these proposed reductions likely would be less disruptive than other alternatives the Legislature may have to consider. In addition, based on our review of expenditure data, OPC has about $20 million in uncommitted funds that the Legislature also could consider reducing.

Recent Budget Agreements Included $1.2   Billion for Sustainable Agriculture. As shown in Figure 13 , past budgets committed a total of $1.2 billion ($916 million from the General Fund and $268 million from various special funds) for a package of programs related to promoting sustainable agriculture. This funding was provided from 2021‑22 through 2023‑24. Almost half of the funding was provided to CARB to support (1) agricultural equipment upgrades and replacements that reduce greenhouse gas and air pollutant emissions ($363 million) and (2) financial incentives to implement alternative practices to agricultural burning in the San Joaquin Valley ($180 million). The remaining funds—$641  million—were for a wide range of programs, mostly administered by CDFA. For example, $170 million was provided for the Healthy Soils Program, which allocates grants to implement practices that improve soil health, sequester carbon, and reduce greenhouse gas emissions.

Governor’s Proposed Changes to Sustainable Agriculture Package

The 2023‑24 budget made several changes to the package. This included scoring $144 million in General Fund savings across various programs. Major reductions included $25 million from the Climate Catalyst Fund, $22 million from the Conservation Agriculture Planning Grants Program, and $15 million from the Pollinator Habitat Program. The budget package also reduced $65 million in General Fund from the Healthy Soils Program but partially backfilled it with $50 million from GGRF, resulting in a net reduction of $15 million. Overall, these actions resulted in a net reduction of $94 million in total funding—maintaining $1.1 billion, or 92 percent, of the previously approved funding levels.

Governor’s Proposal: Reduces $23   Million and Shifts $24   Million. As shown in Figure 13, the Governor proposes net reductions in General Fund support for two programs totaling $23 million. Additionally, the proposal would revert $24 million in General Fund provided to livestock methane reduction programs in 2022‑23 and backfill the reduction with an equal amount from GGRF in 2024‑25, resulting in no net programmatic funding impact. This will allow the state to both capture budget savings and still meet a matching requirement for federal funding ($77 million) that CDFA recently received. Compared to the original 2022‑23 agreement, the Governor’s budget would retain $1.1 billion, or 90 percent, of the originally approved funding levels for sustainable agriculture activities. The two proposed reductions consist of:

  • Farm to Community Food Hubs Program ($14   Million). The proposal would eliminate most funding provided for this program, apart from $1 million the department has already spent on administrative activities. The remaining funds have not yet been committed.
  • Healthy Refrigeration Grant Program ($9   Million). The Governor reduces funding that has not yet been committed but retains $12 million which CDFA has already awarded. While the proposal would scale back the program, it still would allow the state to gather information on whether the program is effective in achieving its primary goal of improving access to healthy foods in underserved communities.

LAO Comments: Proposal Captures Most—but Not All—Available General Fund Savings From Uncommitted Prior‑Year Funds. Based on our review of program expenditure data, apart from the Governor’s proposals, most remaining sustainable agriculture funds have already been fully awarded to projects or are expected to make final awards in the coming months. However, we have identified one additional option the Legislature could consider for seeking additional or alternative savings:

  • Farm to School Incubator Grant Program ($50   million). This program provides funding to schools to purchase locally grown foods, coordinate educational opportunities, and further collaboration and coordination between schools and producers. Of the $90 million the program was provided from the General Fund, CDFA has not yet solicited grant applications or made awards for roughly $50 million. (The department plans to make grant awards from this funding later this spring.) Given that the program is still relatively new (it began in 2020‑21) and has uncommitted funds, the Legislature could reduce this funding and allow the program to continue operating at a scaled‑down level with fewer grants than originally intended. The Legislature may need to take early action to prevent the department from proceeding with its grant application and award process and eroding these potential savings.

Recent Budget Agreements Included $468   Million for Circular Economy Activities. As shown in Figure 14 , past budgets provided a total of $468 million ($138 million from the General Fund and $330 million from various special funds) for a package of programs related to promoting recycling and waste reduction. Funding was provided from 2021‑22 through 2022‑23. Circular economy funding went to nine programs, all of which are administered by the California Department of Resources Recycling and Recovery (CalRecycle). Roughly half of the funding ($240 million) was to support local jurisdictions in implementing the organic waste requirements established by Chapter 395 of 2016 (S B 1383 , Lara). Significant funding also was provided to support (1) the expansion of organics recycling infrastructure, such as composting facilities ($105 million) and (2) the Recycling Market Development Zone (RMDZ) Loan Program, which provides loans to recycling businesses that prevent, reduce, or recycle recovered waste materials ($50 million).

Governor’s Proposed Changes to Circular Economy Package

The 2023‑24 budget made three changes to the package that resulted in a net reduction of $24 million in total funding—maintaining $444 million or 95 percent of the previously approved funding levels. These reductions—all of which were intended to be supported by the General Fund—included $15 million from recycling feasibility grants, $5 million from community composting opportunities, and $4 million from the RMDZ Loan Program.

Governor’s Proposal: Reduces $7   Million. As shown in Figure 14, the Governor proposes to reduce General Fund for the Compost Permitting Pilot Program by $7 million. This program has yet to announce when funding will be made available for grants. Ultimately, the proposed reduction would mean the program would not be able to provide local grants to support the siting and permitting of composting facilities. However, the remaining amount—about $1  million—will support a research contract that will identify statewide best practices for permitting these types of facilities, which could make potential future program activities even more effective. CalRecycle indicates that it awarded that contract in December 2023. Assuming this reduction, the Governor’s proposal would retain $437 million, or 93 percent of the initially approved funding levels for sustainable agriculture activities.

LAO Comments: Proposal Targets Available Remaining Uncommitted Funds. The Governor’s proposal largely captures the remaining uncommitted funds from the circular economy package. Based on available information, nearly all of the programs within this package have fully awarded funds to projects or are expected to make final awards in the coming months. The Governor’s proposal incorporates the one notable exception, the Compost Permitting Pilot Program.

Recent Budget Agreements Included New Focus on Extreme Heat. The past few years represent the first time the state provided significant funding explicitly to mitigate the impacts of extreme heat—originally planned for a total of $649 million from 2020‑21 through 2023‑24 ($634 million General Fund and $15 million GGRF). Figure 15 highlights these funding allocations. In some cases, the recent budget agreements created new programs such as the Extreme Heat and Community Resilience program within the Governor’s Office of Planning and Research (OPR), which is a program aimed at boosting community‑level preparation. The funding also supported some programs that existed previously but were not explicitly focused on mitigating extreme heat, such as the Urban Greening, Urban Forestry, and Low‑Income Weatherization programs. In addition, funding was included for the Department of Industrial Relations to expand its existing outreach, education, and strategic enforcement efforts to improve worker protections from heat‑related illnesses.

Governor’s Proposed Changes to Extreme Heat Package

The 2023‑24 budget package saved $303 million General Fund through a combination of making $245 million in reductions and shifting $58 million in expenditures from the General Fund to GGRF. The reductions included $175 million from the Urban Greening program, $40 million from the Extreme Heat and Community Resilience program, and $30 million from the Urban Forestry program. The fund shifts from General Fund to GGRF included $33 million for the Green Schoolyards program and $25 million for the Extreme Heat and Community Resilience program.

Governor’s Proposal: Reduces and Shifts Funding. The Governor proposes to save about $150 million General Fund through a combination of $109 million in fund shifts and $40 million in reductions. The proposed solutions include:

  • Extreme Heat and Community Resilience. The proposal reduces the program by $40 million and shifts the remaining $70 million from General Fund to GGRF.
  • Urban Greening. The proposal shifts $24 million from General Fund to GGRF.
  • Protections for Vulnerable Populations. The proposal shifts $16 million from General Fund to the Labor and Workforce Development Fund.

LAO Comments: Legislature Could Capture Additional Savings by Reducing Rather Than Shifting Funds. Through a combination of reductions and fund shifts, the Governor’s proposal eliminates nearly all of the uncommitted General Fund that was included as part of the extreme heat package. However, the Legislature could modify a couple of proposed solutions to further help the General Fund condition.

  • Urban Greening Program ($24   Million). Due to the proposed fund shift, the administration has paused evaluation of grant requests for this program. Because the funding has not yet been committed, the Legislature could consider reducing the funding rather than shifting it to GGRF. Doing so would free up GGRF that the Legislature could then use to backfill additional General Fund reductions elsewhere.
  • Extreme Heat and Community Resilience Program ($95   Million). None of the funding for this program has yet been committed. OPR plans to award $20 million during a first round of grant funding sometime this summer. Given the budget condition, in addition to the Governor’s proposed $40 million reduction and in lieu of the proposal to shift $70 million to GGRF in 2024‑25, the Legislature could consider eliminating all funding for the program. Doing so would save an additional $25 million General Fund and also free up $70 million in GGRF that could be used to backfill additional General Fund reductions elsewhere.

Recent Budget Agreements Also Included One‑Time Funding for Activities That Were Not Captured in the Thematic Packages. Outside of the thematic packages highlighted in this report, recent budgets also provided or planned to provide one‑time funding for a variety of climate and resources‑related activities. Figure 16 shows several of these non‑package augmentations totaling $2.7 billion, all from the General Fund. (The figure does not include a comprehensive list of all funding provided in recent budgets for environmental programs outside of the thematic packages, but rather just those the Governor is now proposing to modify as described below.) The largest of these augmentations include $1 billion planned over three years to implement CERIP, $500 million over three years to clean up brownfield sites, and $477 million mostly over two years for a new Climate Innovation Program intended to support California companies in advancing climate technologies. (The 2023‑24 budget package reduced originally planned funding for the Climate Innovation Program from $525 million to $477 million. That is the only revision that has been made thus far to originally planned funding for the programs reflected in the figure.)

Governor’s Proposed Changes to Other Recent Augmentations

Governor’s Proposal: Reduces $578   Million and Delays $1.1   Billion to Later Years. To achieve General Fund savings, the Governor’s budget proposes an overall spending reduction totaling $578 million across the various activities shown in the figure, thereby retaining $2 billion, or 77 percent, of the revised 2023‑24 amounts. The proposal also includes several significant funding delays, totaling $1.1 billion. This figure displays proposed reductions and resulting multiyear funding levels. Some key changes include:

  • CERIP—Delay . Chapter 239 of 2022 (S B 846 , Dodd) included a plan to provide a total of $1 billion to implement CERIP — $100 million in 2023‑24, $400 million in 2024‑25, and $400 million in 2025‑26. The budget proposes to delay $800 million of this planned funding. Specifically, it would maintain $100 million each in 2023‑24 and 2025‑26, and provide $300 million in 2026‑27 and $500 million in 2027‑28. The overall funding level would stay the same but stretch over a longer period of time.
  • Brownfield Cleanups—Delay . The Department of Toxic Substances Control (DTSC) received $300 million in 2021‑22, $100 million in 2022‑23, and $100 million in 2023‑24 for cleanup activities. The budget proposes to revert $175 million from prior appropriations and delay providing it until 2025‑26 ($85 million) and 2026‑27 ($90 million). The overall funding level would stay the same but stretch over a longer period of time.
  • Climate Innovation Program—Reduction . The 2023‑24 budget provided $2 million in 2022‑23 and planned to provide $475 million over 2024‑25 and 2025‑26 for the Climate Innovation Program. The Governor’s budget proposes to reduce all $475 million in future spending, retaining just $2 million.
  • Diablo Canyon Land Conservation and Economic Development Plan—Delay . Chapter 239 required CNRA to lead planning efforts for how to manage the conservation of Diablo Canyon lands and local economic development as the nearby nuclear power plant is decommissioned. Chapter 239 included intent language to provide $10 million in 2022‑23 and $150 million in 2024‑25 to support the plan. The budget proposes to keep the same overall funding level, but delay the $150 million in 2024‑25 and instead provide $50 million in 2025‑26, $50 million in 2026‑27, and $50 million in 2027‑28.
  • California Nutrition Incentive Program—Reduction . The budget proposes to revert $33 million of CDFA’s $35 million appropriation in 2023‑24 for the California Nutrition Incentive Program. While the reduction would not affect any of CDFA’s existing federal funding awards, it would affect CDFA’s ability to draw down future federal funds through the Gus Schumacher Nutrition Incentive Program, as the department was planning to use these funds to meet its state fund matching requirements.

LAO Comments: Legislature Could Consider Alternative and/or Additional Reductions. To the extent the Legislature needs to find alternative and/or additional solutions to those chosen by the administration, it has some options among the non‑package augmentations. First, the Legislature could consider reducing rather than delaying some or all of the funding the Governor proposes shifting to a future year. Second, the Legislature could look at uncommitted balances in other non‑package augmentations that the Governor has not targeted for solutions. Below we provide examples within both categories.

  • CEC’s CERIP implementation: $800 million.
  • DTSC’s brownfield cleanups program: $175 million.
  • Diablo Canyon Land Conservation and Economic Development Plan implementation: $150 million.
  • California Department of Parks and Recreation’s (Parks’) Outdoor Equity Program: $50 million from previous appropriations remains uncommitted (in addition to the $25 million the Governor proposes reducing from planned 2024‑25 funding). Awards are anticipated to be made in May 2024.
  • Parks’ Natural Resources and Park Preservation Fund: $26 million remains uncommitted of the original $50 million transfer from the General Fund, after $20 million was scored as budget solution last year.
  • OPC’s Intertidal DNA Barcode Library: $9 million remains uncommitted of the $10 million that was provided in 2023‑24.
  • CNRA’s Museum Grant Program: $30 million remains uncommitted of the $50 million that was provided in 2021‑22.
  • DWR—CERIP : $32   million that was provided in 2023‑24 for central procurement remains uncommitted (the Legislature could provide funding at a later date when there is more certainty about what is needed).
  • GO‑ Biz—CERIP : $11 million that was provided in 2023‑24 remains uncommitted and GO‑Biz has not yet solicited proposals.

The unprecedented levels of funding the state provided in recent years represent a significant commitment to addressing the causes and impacts of climate change, as well as pursuing numerous other state environmental goals. These augmentations were enabled by the large General Fund surpluses the state received—and expected to receive—over the past few years. Given the change in the state’s overall fiscal condition, reducing this spending correspondingly is both reasonable and necessary—particularly for expenditures that were planned when the state had a different General Fund outlook but that have not yet been implemented. Scaling back these spending intentions will require the Legislature to make difficult choices, particularly since certain constituencies were anticipating receiving funds for local projects. However, the Legislature can modify the Governor’s proposals to craft a budget package that both achieves required General Fund solutions and sustains its highest‑priority activities. Moreover, the level of funding that already has been expended—and therefore cannot be reduced—still will be exceptional by historical standards. These commitments, combined with the significant amount of new federal funding flowing into the state for similar activities, should provide the Legislature and public with some comfort that the state can continue to make notable progress in pursuing its climate and environmental goals despite the modifications necessitated by the budget downturn.

Emulation-based adaptive differential evolution: fast and auto-tunable approach for moderately expensive optimization problems

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  • Published: 15 February 2024

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  • Kei Nishihara   ORCID: orcid.org/0009-0006-2610-9276 1 &
  • Masaya Nakata   ORCID: orcid.org/0000-0003-3428-7890 1  

In the field of expensive optimization, numerous papers have proposed surrogate-assisted evolutionary algorithms (SAEAs) for a few thousand or even hundreds of function evaluations. However, in reality, low-cost simulations suffice for a lot of real-world problems, in which the number of function evaluations is moderately restricted, e.g., to several thousands. In such moderately restricted scenario, SAEAs become unnecessarily time-consuming and tend to struggle with premature convergence. In addition, tuning the SAEA parameters becomes impractical under the restricted budgets of function evaluations—in some cases, inadequate configuration may degrade performance instead. In this context, this paper presents a fast and auto-tunable evolutionary algorithm for solving moderately restricted expensive optimization problems. The presented algorithm is a variant of adaptive differential evolution (DE) algorithms, and is called emulation-based adaptive DE or EBADE. The primary aim of EBADE is to emulate the principle of sample-efficient optimization, such as that in SAEAs, by adaptively tuning the DE parameter configurations. Specifically, similar to Expected Improvement-based sampling, EBADE identifies parameter configurations that may produce expected-to-improve solutions, without using function evaluations. Further, EBADE incepts a multi-population mechanism and assigns a parameter configuration to each subpopulation to estimate the effectiveness of parameter configurations with multiple samples carefully. This subpopulation-based adaptation can help improve the selection accuracy of promising parameter configurations, even when using an expected-to-improve indicator with high uncertainty, by validating with respect to multiple samples. The experimental results demonstrate that EBADE outperforms modern adaptive DEs and is highly competitive compared to SAEAs with a much shorter runtime.

Avoid common mistakes on your manuscript.

Introduction

Several real-world applications, e.g., neural architecture search [ 64 ] and aerodynamic design [ 17 ], require optimization of expensive-to-evaluate objectives, where the objective values are calculated using computationally expensive simulations [ 44 ]. Considering vehicle structure optimization [ 39 ] as an example, the evaluation of a single design using a crashworthiness simulation takes 20 h [ 39 ]. For such expensive optimization problems (EOPs), the number of function evaluations (FEs) is restricted due to limited budgets of computational and financial resources. Consequently, the main challenge of EOPs is to obtain acceptable solutions under the restricted number of FEs. For this challenge, sample-efficient approaches, such as Bayesian optimization, that reduce the number of FEs are prevalent. Although EOPs are encountered for both single-objective and multi-objective optimization domains, this paper focuses on single-objective EOPs and denotes them as EOPs for simplicity.

Over the last two decades, various sample-efficient approaches have been developed based on evolutionary algorithms (EAs) [ 13 ]. The main motivation behind this pursuit is that typical EAs often assume hundreds of thousands of FEs and thereby become impractical in terms of solving EOPs. Several sample-efficient approaches consider very restricted FE budgets, usually with a few thousand or even hundreds of FEs. In addition to such extreme cases, there exist many EOP instances using low-cost simulations, where budgets are moderately restricted to, e.g., several thousands of FEs. For example, in the automatic calibration of watershed models [ 54 ], a maximum of 10,000 FEs are used, and the corresponding evaluation of one solution using the Soil and Water Assessment Tool takes at least 2 min. However, such EOPs with moderately restricted budgets, referred to as moderately EOPs in this paper, have not undergone adequate systematic research compared to ones with very restricted budgets.

Surrogate-assisted EAs (SAEAs) [ 8 , 16 ] are a popular sample-efficient approach for solving EOPs. Surrogate models of the objective function are constructed using machine learning (ML) techniques, and SAEAs utilize them to identify expected-to-improve solutions. For example, several works have proposed SAEAs using Bayesian optimization, where EAs are used to optimize the Expected Improvement (EI) metric [ 18 ]. SAEAs have been proven to be effective when the number of FEs is a few thousand or in the order of hundreds [ 13 ]. However, application of SAEAs to moderately EOPs in practice experiences the following difficulties.

Other than their excellent performance corresponding to a few thousand of FEs, SAEAs tend to struggle with premature convergence when a higher number of FEs are considered [ 47 , 60 ]. This problem has been highlighted more clearly in complex function landscapes [ 24 ].

Owing to the aforementioned difficulty, tuning the parameter configurations of SAEAs, which govern their performance, is important [ 26 , 32 , 40 ]. However, advance fine-tuning under restricted FE budgets is usually hindered in EOPs.

Most SAEAs are time-consuming as they repeatedly construct and reuse ML models during a run. Their runtimes are often not ascribed much importance, relying on an assumption that they are negligibly smaller than the computational times required by simulations [ 5 , 10 ]. However, reducing the runtime becomes crucial when using low-cost simulations [ 5 ].

Note that the second difficulty is not only applicable to SAEAs but also EA-based algorithms; it is known that EA performances depend significantly on their parameter configurations [ 27 ]. Thus, despite the great success of SAEAs, development of high-performance, auto-tunable, and computationally efficient algorithms is essential.

Incorporating automatic parameter-tuning mechanisms into EAs is an effective approach to improve performance while avoiding manual parameter-tuning [ 20 ]. Adaptive EAs [ 19 ] are a popular paradigm in this regard—their parameter configurations are controlled during a run. For example, jDE [ 3 ] controls two parameters used in the differential evolution (DE) [ 46 ] algorithm—the scaling factor and the mutation rate. In addition to these two parameters, SaDE [ 42 ] controls mutation and crossover strategies of DE. Several works have proposed various adaptive EAs and established that they outperform standard EAs, with comparable runtimes [ 3 , 23 , 61 ].

Accordingly, adaptive EAs can be used to develop computationally efficient and auto-tunable methods for solving moderately EOPs. However, most adaptive EAs are not designed for this purpose as they usually assume hundreds of thousands of FEs [ 23 , 41 ]. In particular, the adaptive EA, in its basic form, is subject to the following limitations when it is extended to an EOP. Most adaptive EAs are designed to update new parameter configurations based on ones that generate good solutions in past generations, and updated parameter settings are employed without validating their effectiveness in advance. This may require extensive trial-and-error to identify good parameter configurations and thereby requires a high number of FEs [ 29 ]. Further, most adaptive EAs are designed to assign different parameter configurations to each solution in a population, i.e., so-called individual-based adaptation. However, this adaptation style may be less effective in reliably identifying a good parameter configuration, because the effectiveness of each configuration is usually validated with respect to only one sample.

This paper presents a novel adaptive EA as a computationally efficient and auto-tunable approach for solving moderately EOPs. The presented algorithm, an emulation-based adaptive DE (EBADE), is based on the DE framework and does not utilize surrogate models. However, to improve sampling efficiency, EBADE is designed to emulate the principle of sample-efficient approaches, such as those in SAEAs, by controlling the parameter configurations. In particular, the following two strategies are involved in EBADE. First, a prior validation process is introduced to pre-screen candidate parameter configurations before use. In this process, as in EI-based sampling, candidates that likely generate “expected-to-improve” solutions are selected without using FEs. This intends to prevent the use of less-effective parameter configurations and thereby reduce the number of FEs. Second, EBADE employs a subpopulation-based adaptation, in which a parameter configuration is assigned to each subpopulation, rather than to each solution. Thus, each parameter configuration is used to produce multiple solutions to update its corresponding subpopulation. This intends to validate the effectiveness of parameter configurations using multiple samples carefully. That is, in EOP, parameter configurations should be evaluated by multiple samples. The main contributions of this work are as follows:

To the best of our knowledge, this is the first attempt to develop an adaptive EA for moderately EOPs. This paper contributes to the development of computationally efficient and auto-tunable approaches for EOPs.

An adaptation mechanism for parameter configurations effective under restricted FE budgets is introduced. Its effectiveness is validated by comparing EBADE with not only popular adaptive DEs but also state-of-the-art SAEAs.

Note that our previous work [ 37 ] presented an early investigation on the prior validation mechanism and integrated it into two popular adaptive DEs—jDE and SaDE. However, the prior validation process was designed to pre-screen candidate parameter configurations based on their ability to reproduce the current best solution, which suffers from premature convergence. Further, it was applicable only to individual-based adaptation frameworks like jDE and SaDE. Consequently, the prior validation-based jDE and SaDE underperform in the case of moderately EOPs compared to state-of-the-art SAEAs. EBADE extends the prior validation process to emulate EI-based sampling on the subpopulation-based adaptation framework.

The remainder of this paper is organized as follows. Section  2 describes the standard DE framework, as well as possible parameters and genetic operators considered as primary options in the present study. The latter half of Sect.  2 presents a literature review. Section  3 presents the detailed mechanism of EBADE. Section  4 reports experiments conducted using the CEC 2013 real-parameter single-objective benchmark function suite [ 25 ]. We compare the performances of EBADE and popular adaptive DEs as well as state-of-the-art SAEAs to investigate their effectiveness for moderately EOPs. Section  5 discusses the EBADE algorithm. Finally, Sect.  6 presents our conclusions and prospective directions of future research.

This section describes the DE algorithm as background information. Subsequently, related works are summarized.

Differential Evolution

DE is a population-based evolutionary algorithm for solving a real-parameter optimization problem using a single-objective function, \(f:\mathbb {R}^D\rightarrow \mathbb {R}\) , where D denotes the problem dimension. In this paper, we consider the minimization of f , where the search space \(\mathcal {X}\) is bounded by \(\mathcal {X} \in [l_j,u_j]_{j=1}^{D}\) .

During initialization, DE produces and then evaluates N initial solutions, forming an initial population \(\mathcal {P}=\{\varvec{x}_{i}\}^{N}_{i=1}\) . Each initial solution is uniformly sampled from the search space \(\mathcal {X}\) . Subsequently, as the main loop, all solutions in \(\mathcal {P}\) are updated via the following procedures. For each solution \(\varvec{x}_{i}\) , a mutant solution \(\varvec{v}_{i}\) is produced using a defined mutation strategy with a scaling factor \(F \in [0,1]\) . Note that the original paper considers \(F \in [0,2]\) [ 46 ], but \(F \in [0,1]\) is typically assumed [ 52 ]. Table  1 summarizes popular mutation strategies, where \(\varvec{x}_{r_{1}}\) , \(\varvec{x}_{r_{2}}\) , \(\varvec{x}_{r_{3}}\) , \(\varvec{x}_{r_{4}}\) , and \(\varvec{x}_{r_{5}}\) denote mutually exclusive solutions randomly selected from \(\mathcal {P}\) and different from \(\varvec{x}_{i}\) ; \(\varvec{x}_{ best }\) denotes the current best solution in \(\mathcal {P}\) ; and \(\varvec{x}_{p best }\) denotes a randomly selected solution from the top \(\lfloor N \times p \rfloor \) solutions in \(\mathcal {P}\) where \(p \in [0,1]\) is a hyperparameter to define greediness [ 63 ]. Next, a trial solution \(\varvec{u}_{i}\) is generated by applying a defined crossover strategy to \(\varvec{x}_{i}\) and \(\varvec{v}_{i}\) with a crossover rate \( CR \in [0,1]\) . Typically, binomial or exponential crossover strategies are used, which are described in Algorithms 1 and 2, respectively, where rand [0, 1] denotes a random value in [0, 1] sampled from a unified distribution. After generating trial solutions for all the solutions, they are evaluated using f . If \(\varvec{u}_{i}\) is not worse than \(\varvec{x}_{i}\) , i.e., \(f(\varvec{u}_{i}) \le f(\varvec{x}_{i})\) , \(\varvec{x}_{i}\) is updated using \(\varvec{u}_{i}\) . These procedures are repeated until the termination criteria are satisfied.

figure a

Binomial crossover

figure b

Exponential crossover

Related works

This subsection first reviews popular adaptive DEs. Then, surrogate-assisted DEs are introduced. Finally, the position of EBADE in this context is discussed.

Table  2 summarizes the related works discussed below. In the “Adaptation style” column, related works are categorized into two classes—Indiv. and Subpop. corresponding to individual-based and subpopulation-based adaptation, respectively. For algorithms without adaptation of any parameter configuration, the entry in this column is set to “–”. The problem dimension and maximum number of FEs adopted in the experiments are listed in the columns “ D ” and “ \( FE _{\max }\) ”, respectively, to indicate the type of problem addressed.

Adaptive DEs

Individual-based adaptation

In the jDE [ 3 ] framework, each solution is paired with specific values of F and \( CR \) , i.e., individual-based adaptation. This may potentially provide suitable parameter configurations for a particular solution. The hyperparameters F and \( CR \) are randomly sampled once again with predefined probabilities \(\tau _F\) and \(\tau _{ CR }\) . They can then be updated based on comparisons between a solution and a trial solution in terms of fitness. This comparison-based adaptation utilizes the algorithm characteristic of the DE framework [ 52 ]. Several branches of jDE have been proposed, including FDSADE [ 53 ] and ISADE [ 15 ], which adaptively control both \(\tau _F\) and \(\tau _{ CR }\) . JADE [ 63 ] explored another paradigm of the sampling method of the hyperparameters utilizing probabilistic distributions determined using previous information concerning superior solutions, which is different from uniform random sampling used in jDE. JADE revealed the impact of the sampling method on adaptive DEs, and several subsequent variants have incorporated the concept of JADE, e.g., MDE_ p BX [ 14 ] and SHADE [ 50 ]. SHADE is a highly popular variant among adaptive DEs that updates probabilistic distributions using success-history memories. This mechanism improves the robustness of JADE by maintaining a diverse set of parameters of probabilistic distributions. Modern approaches, including L-SHADE [ 51 ] and jSO [ 4 ], utilize the SHADE framework to control F and \( CR \) . They also control N using linear population size reduction, which promotes a transition from exploration to exploitation with the progression of the search phase. Additionally, jSO employs fine-tuned scheduling-based adaptation.

Some adaptive DEs control both genetic operators and hyperparameters as parameter configurations to improve the capacity to specialize the framework to a given problem. However, this suffers from the drawback of increased complexity due to the increase in the number of parameter configurations requiring adaptation. One possible approach to address the bottleneck involves predefined sets of parameter configurations, e.g., SaDE [ 42 ] defines a limited number of pairs of mutations and crossovers, e.g., rand/1/bin and rand-to-best/2/bin . Similarly, CoDE [ 55 ] prepares predefined parameter sets \(\{F, CR \}\) as well as pairs of genetic operators. EPSDE [ 35 ] adapts parameter configurations selected from two pools of hyperparameters and genetic operators. Recently, the selection of the best mutation strategy in adaptive DEs from all candidates has been studied. CSDE [ 48 ] and AL-SHADE [ 23 ] are state-of-the-art adaptive DEs that demonstrate that adaptation of mutation strategies remains important while proposing new mutation strategies. DE-DDQN [ 45 ] and FLDE [ 49 ] primarily adapt to mutation strategies via reinforcement learning and random forest, respectively, but these ML-based methods require long computational times.

Subpopulation-based adaptation

Recent studies have integrated a multi-population scheme into the DE framework to utilize the divide-and-conquer strategy. They divide the population into multiple subpopulations, with each searching a different area. When the adaptation mechanism is included in a multi-population scheme, different parameter configurations of DE are assigned to subpopulations. For example, two populations are used for exploitation and exploration in the study [ 31 ]. In MPEDE [ 58 ], three defined parameter configurations are paired with corresponding subpopulations, where each subpopulation size is adaptively controlled depending on the current search dynamics. Moreover, some works allocate different adaptation mechanisms of existing adaptive DEs to subpopulations to further improve performance by combining various adaptation mechanisms. For instance, a hybrid amalgamation of CoDE and JADE was proposed as HMJCDE [ 22 ], and EDEV [ 59 ] incorporates EPSDE, CoDE, and JADE.

Surrogate-assisted DEs

Surrogate-assisted DEs without adaptation of DE parameter configurations

In EOPs, especially under severely restricted FE budgets, SAEAs comprise one of the most popular approaches. We now introduce some surrogate-assisted DEs. CADE [ 30 ] uses a support vector machine (SVM) as the classification model to screen solutions, reducing the number of FEs. CRADE [ 28 ] combines two SVMs to approximate the objective function and classify solutions, compensating for the weaknesses of both models. GPEME [ 26 ] is a standard SAEA, which reduces dimension using the Sammon mapping when the problem dimension exceeds 30. Then, it generates offspring solutions and evaluates only one solution that is “expected-to-improve” using the lower confidence bound metric obtained by the Kriging model constructed using recently evaluated solutions. ESAO [ 57 ] combines the global radial basis function network (RBFN) and the local Kriging model. RBFN is used to roughly select a search region and the elaborate search is conducted using the Kriging model. SAHO [ 40 ] adaptively selects optimizers from DE and TLBO [ 43 ] while screening solutions using RBFN to design diverse searches. Recently, SAEAs that adaptively select RBFNs with different configurations have been proposed, e.g., DSS-DE [ 32 ] and SADE-ATDSC [ 38 ], since the performances of SAEAs depend on parameter configurations of both EAs and MLs.

Surrogate-assisted DEs with individual-based adaptation

Some surrogate-assisted DEs incorporate adaptive DE mechanisms into SAEAs to inherit the advantages of both EAs and SAEAs. However, most of these algorithms use individual-based adaptation—SAEAs with subpopulation-based adaptation have not been developed. For example, DE-AEC [ 62 ] uses RBFN to screen solutions and adapts F and \( CR \) , as in jDE. S-JADE [ 7 ] enhances the performance of JADE using RBFN. Like ESAO, S-JADE [ 7 ] utilizes two types of RBFNs; global and local RBFNs are constructed using all evaluated solutions and neighborhood solutions of the current population, respectively.

Alternatively, DE parameter configurations have also been adapted while screening solutions. This produces various solutions to be screened by varying DE parameter configurations. SMDE [ 21 ] uses four mutation strategies and generates the same number of offspring solutions via mutation strategies for each base solution. Then, the solution with the best predicted fitness is adopted. Thus, SBSM-DE considers four candidate solutions generated in different ways, although FE is conducted only once per base solution. Other examples are as follows. DESSA [ 29 ] is used with CoDE or SaDE. For example, DESSA-CoDE has three sets of parameters and three mutation strategies, i.e., nine pairs of parameter configurations are considered as adaptation candidates. After generating the nine corresponding trial solutions, rank-SVM is used as a surrogate model for screening. SMA-EPSDE [ 33 ] and ESMDE [ 34 ] are derivatives of EPSDE and use two mutation strategies ( rand/1 and current-to-rand/1 ), two crossover strategies ( binomial and exponential ), \(F\in [0.5,1.0]\) , and \( CR \in [0.0,1.0]\) as candidate parameter configurations. They randomly sample parameter configurations and generate solutions until the approximated fitness exceeds the fitness of base solutions. The difference between SMA-EPSDE and ESMDE comprises the dataset selection criteria for the Kriging model. Sa-DE-DPS [ 11 ], SAPDE-ANN [ 1 ], and SAPDE-RSM [ 1 ] conduct a search on the approximation function for a certain number of generations while adapting parameter configurations to accelerate the search.

Position of EBADE in this context

According to Table  2 , most adaptive DEs are tested with \(D \times \) 10,000 FEs, while many surrogate-assisted DEs are designed for FEs not exceeding 1000. Some surrogate-assisted DEs which screen solutions and adapt parameter configurations simultaneously use \(D \times \) 10,000 FEs, but real-world EOPs with more than 10,000 FEs are rarely encountered [ 2 , 9 , 12 , 17 , 21 , 32 , 36 , 56 , 57 ]. Thus, we investigate if EBADE improves performance within 10,000 FEs, i.e., for moderately EOPs.

As noted in the “Adaptation style” column in Table  2 , most existing adaptive DEs use individual-based adaptation, while subpopulation-based adaptation is only being studied recently. In this study, EBADE adapts parameter configurations using subpopulation-based adaptation, without using surrogate models. In the experiments presented in Sect.  4 , we compare EBADE with adaptive DEs and SAEAs. For adaptive DEs, we choose comparison algorithms based on both individual-based and subpopulation-based adaptation to investigate the effectiveness of EBADE compared to both typical and modern categories.

The prior validation mechanism of EBADE introduced in the next section has never been discussed in the existing literature. In contrast, most adaptive EAs update parameter configurations by referring to those that have generated good solutions in past generations.

Proposed algorithm

The proposed algorithm, EBADE, is an adaptive DE for solving EOPs. In contrast to typical adaptive EAs, a prior validation process is utilized to identify good DE parameter configurations before using them. This accelerates the evolutionary search while reducing the number of FEs by avoiding the use of less effective parameter configurations. Here, we first discuss the idea underlying our prior validation process, i.e., the process of estimating the effectiveness of parameter configurations in advance, and subpopulation-based adaptation. Subsequently, the detailed algorithms of EBADE are explained.

Usually, the effectiveness of algorithmic parameter configurations cannot be estimated without using them, because it depends on the current search dynamics and random factors. However, the idea of EBADE is to produce good parameter configurations by emulating the sampling mechanism of SAEA without consuming FEs. Specifically, EBADE comprises the prior validation mechanism and subpopulation-based adaptation. Our idea is based on two insights summarized below.

Generally, SAEAs first generate multiple candidate solutions and estimate the quality of candidate solutions, and then remove undesired ones to reduce FEs. When estimating quality, SAEAs often utilize the improvability of candidate solutions, e.g., the EI metric. However, EBADE cannot estimate the quality of candidate solutions directly due to the lack of surrogates. Instead, EBADE utilizes parameter configurations that directly affect solution generation. By emulating the SAEA mechanism, EBADE generates multiple parameter configurations and estimates their quality. Then, without consuming FEs, EBADE removes less effective parameter configurations before generating solutions for FE. Emulating the idea of the EI metric, EBADE selects a candidate parameter configuration that is likely to generate “expected-to-improve” solutions. Specifically, the superior solution mentioned in the preceding paragraph is set to the solution with the best fitness improvement ratio (FIR). Since FIR represents the degree of improvement in the fitness value, the solution with the best FIR may not necessarily coincide with the solution with the best fitness value, preventing the latter from being chosen even if it is stuck in a local optimum. Also, by selecting the solution with the best FIR, the various solutions that are progressing will continue to be selected even if some solutions in the population stagnate. Thus, our prior validation mechanism is expected to enable EBADE to guide solutions to the “expected-to-improve” area, transcending premature convergence to the local optima.

Although testing or validation data consist of multiple samples in the ML domain, most existing adaptive DEs utilize individual-based adaptation. In other words, a parameter configuration is validated using only one solution in the existing adaptive DEs. Thus, individual-based adaptation may be inefficient in EOPs, because a large number of FEs are consumed over multiple generations to gain a large number of samples for a parameter configuration during its validation. Accordingly, EBADE employs subpopulation-based adaptation, where a parameter configuration is paired with multiple solutions, i.e., all solutions in a subpopulation. This improves the validation accuracy of the effectiveness of parameter configurations, reflecting the results of FE by narrowing down the number of parameter configurations and validating each with respect to multiple samples. Additionally, subpopulation-based adaptation is also vital for the prior validation mechanism as one candidate parameter configuration is validated with respect to multiple samples in the prior validation phase. The subpopulation-based scheme can mitigate the possibility of a sample moving in an unintended direction due to random numbers, resulting in an unjustified evaluation of parameter configurations.

Consequently, EBADE is designed to improve the efficiency of adaptation using the prior validation mechanism and subpopulation-based adaptation, emulating sample-efficient approaches such as SAEAs without using any surrogate.

Parameter configuration vector

In EBADE, four algorithmic parameter configurations, the mutation strategy, the crossover strategy, the scaling factor, and the crossover rate are controlled during a run. Let \(\varvec{\theta } = [\theta _{v}, \theta _{u}, \theta _{F}, \theta _{ CR }]\) be a parameter configuration vector that defines the DE parameter configuration, where each variable in \(\varvec{\theta }\) is defined as follows:

\(\theta _{v} \in \{1, 2, 3, 4\}\) specifies the index of the mutation strategy to be used. EBADE uses four mutation strategies, best/1 , current-to-best/1 , current-to- p best/1 , and rand-to-best/1 , indexed by 1, 2, 3, and 4, respectively.

\(\theta _{u} \in \{1, 2\}\) specifies the index of the crossover strategy to be used. Binomial and exponential crossover strategies are used and indexed by 1 and 2, respectively.

\(\theta _{F} \in [0,1]\) indicates the specific value of the scaling factor F used in the mutation strategy specified by \(\theta _{v}\) .

\(\theta _{ CR } \in [0,1]\) indicates the specific value of the crossover rate \( CR \) used in the crossover strategy specified by \(\theta _{u}\) .

For example, given \(\varvec{\theta } = [1, 2, 0.5, 0.8]\) , a DE algorithm uses best/1 mutation with \(F=0.5\) and exponential crossover with \( CR =0.8\) . As the mutation strategy, we choose those that accelerate convergence of the DE population the most [ 6 ], since the rapid convergence of the population is prioritized during the optimization of EOPs [ 16 ].

In summary, the solution-generation procedure of DE specified with \(\varvec{\theta }\) , i.e., the generation of trial solutions, is described in Algorithm 3.

figure c

Get trial solution

Overall framework

EBADE uses and subsequently optimizes M subpopulations, \(\mathcal {P}_{1}, \mathcal {P}_{2}, \dots , \mathcal {P}_{M}\) , simultaneously, where each subpopulation size is set to a common value N . Each subpopulation \(\mathcal {P}_{m}\) has its own parameter configuration vector \(\varvec{\theta }_{m}\) .

Algorithm 4 describes the overall procedure of EBADE, which consists of the following four components—initialization, a search phase, post hoc validation, and prior validation. To begin with, each subpopulation \(\mathcal {P}_{m}\) and its parameter configuration vector \(\varvec{\theta }_{m}\) are initialized. Next, in the search phase, DE is executed for each subpopulation with its corresponding parameter configuration. Subsequently, post hoc validation is performed to identify ineffective parameter configurations that have failed to produce good solutions during the search phase. Finally, ineffective parameter configurations are modified in the prior validation phase into plausibly good parameter configurations without consuming FEs. Subsequently, EBADE returns to the search phase with the modified parameter configurations and the three latter phases are repeated until the termination criteria are satisfied.

The rest of this section describes the detailed procedure of each phase.

figure d

Initialization

Initially, each subpopulation \(\mathcal {P}_{m}\) is initialized with N initial solutions. The initial solutions are produced using the same method as the standard DE (see Sect. 2.1 ). Accordingly, similar to existing DEs with multi-population mechanisms [ 22 , 31 , 58 , 59 ], EBADE produces different initial subpopulations to boost the performance while preventing premature convergence. Thereafter, all initial solutions are evaluated using the objective function. Subsequently, the parameter configuration vector \(\varvec{\theta }_{m}\) for \(\mathcal {P}_{m}\) is initialized as follows. The values of \(\theta _v\) and \(\theta _u\) are set to random integer values sampled from \(\{1,2,3,4\}\) and \(\{1,2\}\) , respectively. For \(\theta _{F}\) and \(\theta _{ CR }\) , \(\theta _{F}=0.5\) and \(\theta _{ CR }=0.9\) are used as the default configurations of standard DE [ 46 ].

Search phase

This phase conducts evolutionary search to collect multiple validation samples and estimate the effectiveness of parameter configurations during the following post hoc validation phase. To this end, each subpopulation is updated by executing the DE solution-generation process for one generation.

Lines  6 - 16 in Algorithm 4 describe the procedure of this phase. A DE algorithm is executed on each subpopulation for one generation, corresponding to the update of all N solutions in \(\mathcal {P}_{m}\) . First, EBADE constructs the whole population \(\mathcal {P}_{ all }\) by concatenating all subpopulations, \(\mathcal {P}_{1}, \mathcal {P}_{2}, \dots , \mathcal {P}_{M}\) . This population \(\mathcal {P}_{ all }\) is used as the pool of candidate solutions in the mutation strategy. Since this process also influences the discovery of superior solutions, we employ an information-sharing strategy that utilizes all possible solutions. In other words, all possible variables in \(\mathcal {P}_{ all }\) , i.e., \(\varvec{x}_{r_{1, 2, 3}}\) , \(\varvec{x}_{ best }\) , and \(\varvec{x}_{p best }\) , are used while generating a mutant solution \(\varvec{v}\) for \(\varvec{x}\in \mathcal {P}_{m}\) , even if they belong to other subpopulations.

Next, all solutions in all subpopulations are updated following the original DE methodology. Specifically, for each subpopulation \(\mathcal {P}_{m}\) , each trial solution \(\varvec{u}\) of \(\varvec{x}\) is generated using \(\varvec{\theta }_{m}\) and \(\mathcal {P}_{ all }\) . Then, each \(\varvec{u}\) is evaluated using the objective function. If the fitness value \(f(\varvec{u})\) of \(\varvec{u}\) does not exceed that of \(\varvec{x}\) , \(\varvec{x}\) is replaced with \(\varvec{u}\) . During the search phase, \(N \times M\) solutions can be sampled for each \(\varvec{\theta }\) ; thus, exactly \(N \times M\) FEs are consumed.

Post hoc validation phase

This phase identifies good/bad parameter configurations by estimating their effectiveness based on the results of the previous search phase. Good parameter configurations are reused during the next search phase without any modification, whereas bad ones are modified during the next prior validation phase.

A straightforward way to define a good parameter configuration is in terms of its success to generate the current best solution in terms of the objective values. Although this definition was used in our previous work [ 37 ], it may easily induce premature convergence, as it does not consider the improvement of objective values. Here, we define good parameter configurations as “worth-to-continue” ones, which are identified as those generating solutions with high FIR values. Specifically, suppose a solution \(\varvec{x}_{g}\) is generated during the g th generation from its corresponding parent solution \(\varvec{x}_{g-1}\) , and the FIR value for \(\varvec{x}_{g}\) , denoted as \(\delta _f(\varvec{x}_g)\) , is calculated as

where \(\delta _C \ge 0\) denotes a constant value to avoid division by zero. Corresponding to a large value of \(\delta _f(\varvec{x}_g)\) , it is expected that the parameter configuration vector \(\varvec{\theta }\) used to generate \(\varvec{x}_g\) from \(\varvec{x}_{g-1}\) can be effective to identify further good solutions during the next search phase. In contrast, corresponding to a small value of \(\delta _f(\varvec{x}_g)\) , \(\varvec{\theta }\) may be ineffective as it does not contribute to discovering a good search region.

Accordingly, EBADE determines good/bad parameter configurations using the following procedures. They are described by the lines  17 - 21 in Algorithm 4. First, EBADE  reconstructs the whole population \(\mathcal {P}_{ all }\) by combining all subpopulations updated during the search phase. Subsequently, an FIR value for each solution \(\varvec{x}\) in \(\mathcal {P}_{ all }\) is calculated, and the top M solutions having the M highest FIR values, \(\varvec{x}^{*}_{1}, \varvec{x}^{*}_{2}, \dots , \varvec{x}^{*}_{M}\) , are determined. Then, a parameter configuration vector \(\varvec{\theta }_{m}\) is identified as a good one if there is at least one top solution \(\varvec{x}^*\) generated by \(\varvec{\theta }_{m}\) ; otherwise, it is identified as a bad one. Technically, EBADE stores indices of the bad parameter configurations in an index set of ineffective parameter configurations \(\Theta \) , which is mathematically defined as follows:

Note that EBADE utilizes FIR to determine good parameter configurations, but this may be hindered until solutions begin to improve to some extent after several generations. Other possible indicators may be required to detect good configurations even with a small improvement, but we will leave this for future work.

Prior validation phase

This process modifies bad parameter configurations to likely good ones before using them in the next search phase. As defined during post hoc validation, we consider good parameter configurations to be those that have generating good solutions with the top M FIR values. Using this definition, we modify bad parameter configurations to enable them to generate such top solutions.

Lines  22 - 25 in Algorithm 4 correspond to this phase and Algorithm 5 presents the detailed procedure of our prior validation phase. First, EBADE selects the target solution \(\varvec{x}_{ target }\) from the solutions discovered so far. This is commonly set for all bad parameter configurations \(\varvec{\theta }_{i}\) to improve the probability of generating effective parameter configurations using \(\varvec{x}_{ target }\) repeatedly. The solution with the best FIR in \(\mathcal {P}_ all \) is selected as the target solution. Note that the search direction is also guided towards the best solution as mutation strategies with high exploitation ability are utilized. Thus, the modified parameter configuration is expected to consider the directions towards the best solution and the area that remains to be searched, i.e., the best FIR solution.

For each bad parameter configuration indexed by \(i \in \Theta \) , EBADE randomly generates multiple parameter configuration candidates and then removes less effective ones, only retaining one. Then, the remaining candidate is replaced with \(\varvec{\theta }_{i}\) . Technically, K candidate parameter configurations \(\varvec{\theta }_{k}\) , \(k=1,2,\dots ,K\) are generated following the procedure used during initialization, except for \(\theta _{F}\) and \(\theta _{ CR }\) , where \(K\in \mathbb {N}\) is a hyperparameter. For each \(\varvec{\theta }_{k}\) , its \(\theta _{F}\) and \(\theta _{ CR }\) are randomly selected from [0, 1]. Then, EBADE selects one candidate parameter configuration that produces a solution closest to a target solution \(\varvec{x}_{ target }\) . In particular, for each candidate parameter configuration \(\varvec{\theta }_{k}\) , EBADE tests the ability of \(\varvec{\theta }_{k}\) to generate solutions close to a target solution \(\varvec{x}_{ target }\) . More specifically, for each solution \(\varvec{x}\) in its corresponding subpopulation \(\mathcal {P}_{i}\) , its trial solution \(\varvec{u}\) is generated by the DE solution-generation process specified using \(\varvec{\theta }_{k}\) , i.e., \( GetTrialSolution (\varvec{\theta }_{k}, \varvec{x}, \mathcal {P}_{ all })\) . These sample solutions are not evaluated using the objective function. Then, the minimum Euclidean distance between each \(\varvec{u}\) and \(\varvec{x}_{ target }\) is recorded as d ( k ). Finally, the index having the minimum d ( k ), \(k=1,2,\dots ,K\) , is set as \(k^*\) , and \(\varvec{\theta }_{i}\) is replaced with the candidate \(\varvec{\theta }_{k^*}\) .

figure e

Prior validation

Experiments

In this section, the performance of EBADE is evaluated on single-objective benchmark functions with restricted FE budgets. All experiments are conducted using a Intel(R) Core(TM) i7-10700 4.8 GHz CPU and 16 GB RAM.

Experimental configurations

Test problems.

We used 28 bound-constrained benchmark functions, F1, F2, \(\dots \) , and F28, used in the competition on Real-Parameter Single Objective Optimization at the IEEE Congress on Evolutionary Computation 2013 [ 25 ]. Note that F1–F5, F6–F20, and F21–28 are categorized as unimodal, multimodal, and composition functions, respectively (see [ 25 ] for detailed definitions). The problem dimension was set to \(D\in \{10, 20, 30\}\) . The search space of all functions was commonly set to \(\varvec{x} \in [-100, 100]^D\) .

Comparison algorithms

We compared the performances of EBADE and four adaptive DEs, SHADE, jSO, CSDE, and EDEV, and four SAEAs, GPEME, S-JADE, SAHO, and ESMDE. The brief descriptions and parameter configurations of comparison algorithms are summarized below.

SHADE, which has been the basis of modern adaptive DEs, employs the current-to- p best/1 mutation strategy and adapts F and CR based on success history memories, \(M_{F,r}\) and \(M_{CR,r}\) , respectively, using individual-based adaptation. Via comparison with SHADE, the impacts of our prior validation and subpopulation-based adaptation mechanisms are evaluated. We used \(H=100, M_{F,h,init }=0.5, M_{CR,h,init }=0.5, |Archive |=100, p_{\min }=2/N\) , and \(p_{\max }=0.2\) [ 50 ].

jSO, which is an extension of L-SHADE [ 51 ]. Based on a specific schedule for parameter control, jSO adapts F , CR , and N for individual-based adaptation. In particular, N decreases as the number of FEs increases to evolve more generations by the end of the search. We verify if EBADE outperforms local search conducted by jSO at the end of the search in moderately EOPs. We used \(H=5, M_{F,h,init }=0.3, M_{CR,h,init }=0.8, |Archive |=N, N_{init}=25\log {D^{3/2}}, N_{\min }=4, p_{\min }=0.125\) , and \(p_{\max }=0.25\) [ 4 ].

CSDE, which is one of the state-of-the-art adaptive DEs. CSDE adapts F , CR , and the mutation strategy for individual-based adaptation. CSDE shifts between two mutation strategies ( current-to - p best/1 and p best-to-rand/1 ) depending on the degree of stagnation in the search. Comparison with CSDE reveals if EBADE outperforms state-of-the-art adaptive DEs in moderately EOPs. We used \(F_{init }=0.5\) , \(CR_{init }=0.5\) , \(N=100\) , \(FP=200\) , \(\mu =0.5\) , and \(\sigma =0.1\) [ 48 ].

EDEV, which is a state-of-the-art subpopulation-based adaptive DE. EDEV adaptively assigns JADE, CoDE, and EPSDE to subpopulations. Thus, EDEV adapts F , CR , the mutation strategy, and the crossover strategy. Comparison with EDEV is important, because both EDEV and EBADE are subpopulation-based adaptive DEs that adapt four parameter configurations of DE. We used \(\lambda _1=\lambda _2=\lambda _3=0.1\) , \(\lambda _4=0.7\) , \(ng=20\) , (JADE: \(\mu _{F,init}=0.5\) , \(\mu _{CR,init}=0.5\) , \(c=0.1\) , \(p_{\min }=0.05\) , \(p_{\max }=0.2\) ), (CoDE: \(\{F,CR\}\in \{\{1.0,0.1\}\) , \(\{1.0,0.9\}\) , \(\{0.8,0.2\}\}\) , \(\{\) rand/1/bin , rand/2/bin , current-to-rand/1 \(\}\) ), (EPSDE: \(P_{F}\) \(=\{0.4,0.5,\dots ,0.9\}\) , \(P_{CR}\) \(=\{0.1,0.2,\dots ,0.9\}\) , \(P_{v}\) \(=\{\) rand/1 , best/2 , current-to-rand/1 \(\}\) ) [ 59 ].

GPEME, which is one of the most popular and frequently compared SAEAs, employs DE and the Kriging model. Thus, GPEME is the standard of SAEA and comparison with it is essential. We used \(N=100, F=0.8, CR=0.8, \tau =100, \lambda =50, l=4, \omega =2\) , regression \(=\) zero-order, correlation \(=\) Gaussian, \(\theta \in [10^{-5}, 10^2]\) , and \(\theta _{init}=10^{-2}\) [ 26 ].

S-JADE, which is a state-of-the-art SAEA, consists of modified JADE with multiple RBFN models. By comparing with S-JADE, we compare the performances of EBADE and state-of-the-art SAEAs with DE parameter configuration adaptation in moderately EOPs. We used \(N=100\) , \(F_{out}=0.5\) , \(CR_{out}=0.75\) , \(p_{pbest_{out}}=0.05\) , \(F_{in}=0.5\) , \(CR_{out}=0.5\) , \(p_{pbest_{in}}=0.1\) , \(std_F=0.1\) , \(std_{CR}=0.1\) , \(L=10\) , \(\epsilon =0.01\) , \(c=0.1\) , \(FE_{max_{in}}=2,000\) , kernel \(=\) cubic, and \(r=rand(0,\ 1.25)\) [ 7 ].

SAHO, which is also a state-of-the-art SAEA, employs DE and TLBO as optimizers and the RBFN model as a surrogate. In addition to SAHO being one of the state-of-the-art SAEAs, comparison with GPEME and SAHO provides a relative performance comparison of EBADE for different ML models used in these SAEAs. We used \(N=100\) , \(F=0.9\) , \(CR=0.5\) , \(K=30\) , \(neighbor=5D\) , and kernel \(=\) cubic [ 40 ].

ESMDE, which adapts DE configuration during screening of the solution by the Kriging model. The candidate configurations are two mutation strategies ( rand/1 and current-to-rand/1 ), two crossover strategies ( binomial and exponential ), \(F\in [0.5,1.0]\) , and \(CR\in [0.0,1.0]\) . By comparing with ESMDE, we verify if the adaptation mechanism of EBADE outperforms SAEAs with DE parameter adaptation in moderately EOPs. We used \(c=10\) , regression \(=\) zero-order, correlation \(=\) Gaussian, \(\theta \in [10^{-5}, 10^2]\) , and \(\theta _{init}=10^{-2}\) [ 34 ].

Parameter configuration of EBADE

The size of each subpopulation was taken to be \(N=4\) , the number of subpopulations was \(M=25\) , the number of candidate configurations was \(K=6\) , and the parameter in the current-to - p best/1 is \(p=0.5\) . Thus, the size of the whole population \(\mathcal {P}_{ all }\) is \(N \times M = 100\) , and these configurations are identical to those in the compared adaptive DEs above. Note that \(\delta _C\) in Eq. ( 1 ) was not needed, because the objective values except at the global optimum were non-negative. The objective value at the global optimum of each function was 0, but no trial reached the global optimum.

Evaluation scheme

All algorithms were forcibly terminated when the number of FEs reached its maximum budget \( FE _{\max }\) , including FEs used for the initialization phase. The performance of algorithms was evaluated in terms of the best objective value discovered at \( FE _{\max }\) , and their mean values over 21 independent trials were reported. The Wilcoxon signed-rank test was applied to identify significant differences with a significance level of \(p<0.05\) . Additionally, the average runtimes of all algorithms to complete one trial were compared.

We set \( FE _{\max }=6000\) as a default value as moderately restricted budgets of FEs were assumed. However, additional results corresponding to 2000–10,000 FEs are presented in Sect.  4.3 to investigate the scalability of EBADE with respect to the number of FEs.

Tables  3 , 4 , and 5 summarize the performances recorded corresponding to 6000 FEs for problems with \(D\in \{10, 20, 30\}\) , respectively. The best and worst performances are highlighted in bold and italic, respectively. In the tables, “ \(+\) ”, “−”, and “ \(\sim \) ” indicate that the performance of a compared algorithm is statistically better than, statistically worse than, and comparable to that of EBADE, respectively. Further, the average rank and the overall statistical results, i.e., the counts of \(+/-/\sim \) , are summarized at the bottom of each table.

As is evident from Table  3 , EBADE outperformed adaptive DEs (SHADE, jSO, CSDE, and EDEV) and one SAEA (ESMDE) significantly on multiple problem instances with \(D=10\) . In particular, the performance of EBADE was statistically better than those of adaptive DEs on at least 14 problem instances. In addition, EBADE exhibited comparable performance with respect to three SAEAs (GPEME, S-JADE, and SAHO). In particular, the performance of EBADE was statistically better than SAEAs on at least nine problem instances, and there were only a maximum of six statistically worse cases. Consequently, EBADE was assigned the best rank, outperforming the considered SAEAs. This indicates a benefit of auto-tunable approaches in solving EOPs—the performance of EBADE is less problem-dependent owing to adaptive control of parameter configurations during a run. Although the performance of SAEAs could be improved via fine-tuning, it is usually hindered in EOPs.

Even when D is increased to 20 and 30, EBADE remained effective, as evidenced by Tables  4 and 5 . The performance of EBADE was better than those of adaptive DEs and highly competitive with SAEAs on several problem instances. For \(D=30\) , the effectiveness of EBADE was slightly poorer, as GPEME outperformed EBADE on certain problems. However, EBADE was assigned the best rank, indicating that it performed well on average. All four adaptive EAs considered for comparison were assigned worse ranks than the SAEAs, except for ESMDE, as they are not designed for restricted FEs. These observations empirically corroborate the effectiveness of our emulation-based adaptation mechanism.

Table  6 presents the average algorithmic runtimes required to complete one trial corresponding to each problem dimension. EBADE required the second-highest runtime among the five adaptive DEs, but the differences were only a few seconds at most. On the other hand, EBADE outperformed the SAEAs in terms of speed; the runtime of EBADE was smaller than that of the SAEAs by at least an order of two.

In summary, overall results suggest that, without any help of surrogate models, EBADE performs comparably with SAEAs while operating much faster than them. This observation empirically suggests that the proposed emulation-based adaptation enables the adaptive DE mechanism to accelerate its evolutionary search under a restricted number of FEs, demonstrating the possibility to realize computationally efficient and auto-tunable optimizers for solving moderately EOPs.

Additional results

To investigate the scalability of EBADE with respect to the number of FEs, we conducted additional experiments with different values of \( FE _{\max }\) under the same experimental environment as in Sect.  4.1 , except for \( FE _{\max }\) . Specifically, \( FE _{\max }\) was set to \(\{2000, 4000, 8000, 10{,}000\}\) in addition to its default value of 6000. Here, we report the average ranks and the overall statistical results.

Table  7 reports the statistical results summarized as the counts of \(+/-/\sim \) . Figure  1 depicts the average ranks of all nine algorithms. Overall, the performance of EBADE was statistically better than those of all the four adaptive DEs even when \( FE _{\max }\) was decreased/increased from its default value 6000. The superiority of EBADE over the four adaptive DEs is also corroborated by Fig.  1 , since EBADE was assigned the best rank among five adaptive DEs corresponding to all problem dimensions and all \( FE _{\max }\) cases. These results prove that EBADE was successfully adapted to EOPs.

When \( FE _{\max }\) was 2000, three SAEAs—GPEME, S-JADE, and SAHO—outperformed EBADE corresponding to all problem dimensions, as the number of “ \(+\) ” was sufficiently larger than that of “−”. This result clearly demonstrated the effectiveness of surrogate-assisted search on highly restricted FE budgets. However, when \( FE _{\max }\) was increased to 4000, the performance of EBADE became competitive to those of the SAEAs, except in the 30-dimensional cases. When \( FE _{\max }\) was further increased to 8000 and 10,000, the effectiveness of EBADE was highlighted even more. These tendencies can be also observed in Fig.  1 —EBADE was always assigned the second or third rank when \( FE _{\max }\le 4000\) , and its rank improved to first for \( FE _{\max } \ge 6000\) . On the other hand, the ranks of SAEAs gradually decreased with the increase of \( FE _{\max }\) ; this indicates stagnation in SAEA performances. This is because SAEAs tend to struggle with premature convergence with a higher number of FEs. As observed in [ 47 , 60 ], generally, surrogate-assisted searches provide a strong exploitation bias to promote evolutionary search under very restricted budgets of FEs. However, this degrades the diversity of solutions with a higher number of FEs, degrading the search performance and the quality of (global) surrogates. Consequently, as shown in Fig.  1 , SAEAs performed very well for very restricted budgets of FEs; however, their performances gradually degraded with the increase of FEs. EBADE was assigned to the best rank for all dimensions when \( FE _{\max } \ge 6000\) , as shown in Fig.  1 . Thus, this observation indicates that EBADE is well scaled to the increase of the problem dimensions D on moderately EOPs. A possible reason for this is that EBADE can possess a better diversity of solutions than that of SAEAs; after the adaptation of parameter configurations, EBADE generates solutions similar to the standard DEs without any pre-screening process using surrogates.

The following differences were identified between the different algorithmic mechanisms. The relatively simple algorithm of SHADE ensured its scalability with respect to D , since the average rank increased slightly as D increased, as in Fig.  1 . jSO also exhibited improved performance—it ranked second among adaptive DEs and its average rank was slightly higher than those of all SAEAs when \( FE _{\max } \ge 8000\) \((D=10)\) and \( FE _{\max } =\) 10,000 \((D=20)\) , as in Fig.  1 . This was attributed to the mechanism by which jSO reduces the population size towards each set \( FE _{\max }\) to gain the number of solution evolution. If this mechanism were incorporated into EBADE, it may further improve its performance. However, EBADE already outperformed SHADE and jSO based solely on the prior validation mechanism and subpopulation-based adaptation. As depicted in Fig.  1 , the average rank of CSDE increased with an increase in \( FE _{\max }\) for all dimensions, but the statistical test results obtained in comparison with EBADE did not improve, as presented in Table  7 . Thus, the state-of-the-art CSDE is specialized for cases with plentiful FE budgets. EDEV seemed to consume a large number of FEs to improve performance, because it has a huge search space of parameter configurations. In comparison with SAEAs, EBADE was highly competitive beyond the type of ML used in compared SAEAs, since its rank was higher than those of GPEME and SAHO, at least for \( FE _{\max } \ge 6000\) , as in Fig.  1 . Although S-JADE and ESMDE adaptively control DE parameter configurations, further consideration may be required in the combined implementation of SAEAs and adaptation methods to solve moderately EOPs effectively, especially owing to the low rank of ESMDE in Fig.  1 .

In summary, the compared SAEAs exhibited excellent performances when \( FE _{\max } = 2000\) , but EBADE derived good performances when \( FE _{\max } \ge 6000\) . This observation shows the effectiveness of EBADE on moderately EOPs.

figure 1

Average rank of all nine algorithms over the number of FEs

In this section, the results of ablation studies are reported to confirm the effectiveness of the main components of EBADE. First, we discuss the effect of controlling the DE parameter configurations in moderately EOPs. Subsequently, the effectiveness of the prior validation and subpopulation-based adaptation is discussed. Finally, the adaptation results of the DE parameter configurations are investigated. Experimental environments identical to those reported in Sect. 4.1 are used with \( FE _{\max }\in \{2000, 4000, 6000, 8000, 10,000\}\) unless stated otherwise.

Impact of parameter adaptation in moderately EOPs

We empirically demonstrate that controlling the DE parameter configuration is crucial to improve the performance of adaptive DEs even for moderately EOPs. To this end, we compared the performances of EBADE and various DEs with fixed parameter configurations. In particular, we introduced eight DE variants with different combinations of mutation and crossover strategies; best/1/bin (b/1/b), current-to-best/1/bin (cb/1/b), current-to- p best/1/bin (cpb/1/b), rand-to-best/1/bin (rb/1/b), best/1/exp (b/1/e), current-to-best/1/exp (cb/1/e), current-to- p best/1/exp (cpb/1/e), and rand-to-best/1/exp (rb/1/e), where bin and exp denote binomial and exponential crossover, respectively; and \(F=0.5\) and \(CR=0.9\) were used for all variants. For cpb/1/b and cpb/1/e, we used \(p=0.5\) .

Table  8 summarizes the statistical results in terms of the counts of \(+/-/\sim \) , where “ \(+\) ”, “−”, and “ \(\sim \) ” indicate that the performance of a DE variant is statistically better than, statistically worse than, and comparable with that of EBADE, respectively. Further, Fig.  2 depicts the average ranks. In Table  8 , two DE variants using cb/1/b and rb/1/b were observed to outperform EBADE on several problem instances, with \( FE _{\max } \le 4000\) as a sufficiently large number of “ \(+\) ”. However, when \( FE _{\max }\) was increased to 6000, the performance of EBADE was gradually improved. When \( FE _{\max }\) was further increased to 8000 and 10,000, EBADE statistically outperformed all DE variants on at least 13 problem instances. Almost an identical trend was observed in Fig.  2 . Specifically, although the average rank of EBADE was sometimes below those of cb/1/b and rb/1/b for \( FE _{\max } \le 4000\) , EBADE always ranked first for \( FE _{\max } \ge 6000\) .

These results indicate that the configurations of cb/1/b and rb/1/b, i.e., providing a strong bias for exploitation, enhanced DE performance when \( FE _{\max }\) was highly restricted; however, this benefit may be less important as SAEAs performed well under such restricted budgets. An important drawback of using these settings was observed to be premature convergence when \( FE _{\max }\) was increased to, for example, 6000 or even 10,000. Actually, the average ranks of cb/1/b and rb/1/b were rapidly degraded as \( FE _{\max }\) was increased, as depicted in Fig.  2 . In contrast, EBADE performed well by controlling the DE parameter configurations, especially for \( FE _{\max } \ge 6000\) , i.e., under moderately restricted FE budgets.

General trends of fixed DE variants are as follows. When \( FE _{\max }\) was increased from 2000 to 10,000, the average ranks of DE variants using the binomial crossover strategy, except for cpb/1/b, i.e., b/1/b, cb/1/b, and rb/1/b, continued to decrease, while those of cpb/1/b or DE variants using the exponential crossover strategy, i.e., b/1/e, cb/1/e, cpb/1/e, and rb/1/e, continued to improve. EBADE was assigned consistently to good ranks. This result shows that the adaptation of the DE parameter configurations was effective in solving moderately EOPs.

figure 2

Average ranks of fixed DE variants and EBADE over the number of FEs

Impact of adaptation of DE parameters

EBADE is designed to simultaneously adapt the DE parameter configurations ( \(F, CR \) , and the mutation and crossover strategies) to determine good parameter configurations from a variety of candidates. We further validate the effectiveness of this strategy by comparing EBADE with its variant using fixed values of \({\theta }_{F}\) and \({\theta }_{ CR }\) , denoted as EBADE-fix FCR .

Specifically, EBADE-fix FCR is designed to always use \({\theta }_{F}=0.5\) and \({\theta }_{ CR }=0.9\) [ 46 ]; it tunes only the mutation and crossover strategies. Table  9 presents the statistical results summarized as the counts of \(+/-/\sim \) with \( FE _{\max } \in \{2000, 4000, 6000, 8000, 10,\!000\}\) . In the table, “ \(+\) ”, “−”, and “ \(\sim \) ” indicate that the performance of EBADE-fix FCR is statistically better than, statistically worse than, and comparable to that of EBADE, respectively.

When \( FE _{\max }\) was 2000, EBADE-fix FCR statistically outperformed EBADE on more than seven problems for all problem dimensions. This indicates that the recommended values of \({\theta }_{F}\) and \({\theta }_{ CR }\) boost the convergence speed of EBADE-fix FCR under the restricted budgets of FEs, by reducing the search space of parameter configurations. However, with \( FE _{\max } \ge 6000\) , the number of “−” was larger than that of “ \(+\) ” for all D . This is highlighted particularly for \(D=20\) and 30. For example, EBADE outperformed EBADE-fix FCR on 12 problems with \(D=20, FE _{\max } = 8000\) while reducing the number of “ \(+\) ”. Consequently, the adaptation of DE parameter configurations including \({\theta }_{F}\) and \({\theta }_{ CR }\) is important to enhance the performance of EBADE in moderately EOPs.

Parameter analysis for the number of candidate configurations

Now, we evaluate the effectiveness of the prior validation process. To this end, we introduce an EBADE variant without the prior validation process, which can be implemented by setting K to 1. EBADE with \(K=1\) always generates only one candidate parameter configuration, and thus randomly selects a parameter configuration. Further, a sensitivity analysis is performed for K . In particular, we evaluate the performance of EBADE with \(K\in \{1, 2, 4, 8, 10\}\) in addition to its default value, six.

Table  10 summarizes the statistical results of the counts of \(+/-/\sim \) , where “ \(+\) ”, “−”, and “ \(\sim \) ” indicate that the performance of an EBADE variant is statistically better than, statistically worse than, and comparable with that of EBADE with the default value \(K=6\) , respectively. To denote the variant without the prior validation process, “(w/o PV)” is appended to \(K=1\) in the table. As shown in the table, the performance of EBADE was sensitive to the parameter K , because the statistical results changed dramatically as K shifted. In particular, when prior validation was excluded ( \(K=1\) ), the performance of EBADE degraded significantly on multiple problem instances compared to EBADE using the default value \(K=6\) , confirming the effectiveness of the prior validation process. Moreover, \(K=2\) was inappropriate, since EBADE with the default setting ( \(K=6\) ) statistically outperformed that with \(K=2\) . Thus, two candidates of parameter configurations are insufficient to conduct prior validation efficiently. When the value of K increased to 10, the performance of EBADE slightly improved for \( FE _{\max } \le 4000\) ; however, it degraded for \( FE _{\max } \ge 8000\) . This is because a large value of K tends to increase the exploitation bias in the search, and thereby EBADE may suffer from premature convergence. Specifically, when the value of K increases, a greater variety of parameter configurations is sampled and then EBADE tends to select DE parameter configurations that generate overly similar solutions to the target solution.

Parameter analysis for the number of subpopulations

We also validate the effectiveness of subpopulation-based adaptation. For this purpose, an EBADE variant that adapts DEs for individual-based adaptation is prepared. This variant can be implemented by setting \(M=100\) and \(N=1\) . The size of the whole population of this variant is the same as the original EBADE; \(N \times M = 4 \times 25 = 100\) and \(N \times M = 1 \times 100 = 100\) for EBADE and this variant, respectively. Thus, they can be fairly compared. The number of top solutions in the post hoc validation phase, described in line  20 in Algorithm 4, is set to 25 for this variant, as all parameter configurations remain constant throughout the search stage otherwise. Additionally, we conduct a sensitivity analysis for M . Specifically, we evaluate the performance of EBADE with \(M\in \{2, 4, 5, 10, 20, 50, 100\}\) in addition to its default value 25. For these M , N was set to \(N\in \{50, 25, 20, 10, 5, 2, 1\}\) , respectively, to ensure that the population size remains 100.

Table  11 presents the statistical results in terms of the count of \(+/-/\sim \) . The symbols are defined as in the previous subsection, where the default value of M is \(M=25\) . To highlight the variant with individual-based adaptation, “(Indiv.)” is appended to \(M=100\) in the table. When individual-based adaptation was conducted ( \(M=100\) ), the performance of EBADE degraded significantly on multiple problem instances compared with EBADE using the default value \(M=25\) , confirming the effectiveness of the proposed subpopulation-based adaptation. This is because the proposed subpopulation-based adaptation can improve the validation accuracy of the effectiveness of parameter configuration by validating those with multiple samples. Specifically, the subpopulation-based adaptation can mitigate the risk of a sample moving in an unintended direction due to random numbers, resulting in an unjustified evaluation of parameter configurations. However, the individual-based adaptation is designed to validate a parameter configuration using a single sample, and thereby, this risk should occur frequently. Accordingly, EBADE performed well using good parameter configurations, which were well detected by the subpopulation-based adaptation.

Moreover, EBADE with \(M\in \{2, 4, 5\}\) should be avoided as they statistically underperformed compared to EBADE with the default setting ( \(M=25\) ). These results suggest that the number of parameter configurations tested in parallel should be greater than five and the number of solutions validating one parameter configuration should be less than 20. Further, EBADE with \(M=50\) is also inappropriate, because two solutions are insufficient to validate one parameter configuration. Increasing the value of N while decreasing M can improve this validation accuracy, because the number of validation samples, N , increases; however, the number of parameter configurations decreases, leading to a poor diversity of solutions. On the other hand, increasing M (and thus decreasing N ) can improve the diversity of solutions; however, less effective configurations may be used owing to low validation accuracy. Thus, it is important to use a parameter setting of \(\{N, M\}\) that balances this trade-off. Our experimental result suggests that \(\{N, M\} = \{10, 10\}, \{5, 20\}, \{4, 25\}\) produces a good balance, as EBADE with these settings performed well.

Adaptation results

Finally, we verify whether the high performance of EBADE  was achieved after EBADE performed adaptation without biasing the use of only certain DE parameter configurations. Specifically, for each element of the parameter configurations, i.e., the scaling factor F , the crossover rate \(\textit{CR}\) , the mutation strategy, and the crossover strategy, we enumerated the number of times the subpopulations of EBADE used each candidate within 10,000 FEs, and reported it as a ratio. For F and \(\textit{CR}\) , the domains of definition \(F,\textit{CR}\in [0, 1]\) were divided into five ranges with widths of 0.2, and the number of samples was examined for each range.

Figure  3 summarizes the ratio of each candidate used by problem function and the dimension. Because the selected ratio did not depend on D significantly, the results are reported with \(D\in \{10, 30\}\) and those with \(D=20\) are omitted. As illustrated in this figure, EBADE selected various parameter configurations of F , \( CR \) , and the mutation and crossover strategies over the search process. As in Fig.  3 a), values of the scaling factor F in [0.0, 0.2] were most frequently used, while higher values like \(F \in (0.8, 1.0]\) were less frequently used. This may be attributed to premature convergence to the local optima induced by larger values or slow convergence as the solutions continue to move widely through the search space. On the other hand, larger crossover rate values \(\textit{CR}\) were often selected, as illustrated in Fig.  3 b), especially in unimodal functions, i.e., F1–F5. In other words, mutant solutions generated with mutation strategies to accelerate convergence should be actively utilized in EOPs. The best/1 mutation strategy was the most selected, as depicted in Fig.  3 c). This tendency is natural, since the best/1 strategy exhibits the strongest exploitation ability, which is suitable for EOPs. However, the other strategies were used adequately to maintain the diversity of solutions and the combined use of these four strategies contributed to the high performance of EBADE, which can be also confirmed in the comparison between EBADE and DE with best/1/bin or best/1/exp in Sect.  5.1 . In Fig.  3 d), the binomial crossover strategy was used slightly more. This tendency was reinforced as D was increased. Since the importance of solution diversity became more notable as D was increased, the binomial strategy, which conducts crossover more uniformly, was more suitable. In summary, EBADE exhibited high performance by selecting more candidates appropriate for EOPs. However, it avoided heavy bias by adaptively selecting all of them.

figure 3

Adaptation results obtained from EBADE

Conclusions

In this paper, we introduced a new adaptive DE variant named emulation-based adaptive DE (EBADE). An adaptive EA for EOPs with moderately restricted budgets was developed for the first time by emulating the principle of sample-efficient approaches, e.g., SAEAs. Specifically, EBADE is characterized by prior validation and subpopulation-based adaptation; emulating the EI-based solution screening with surrogates in SAEAs. EBADE pre-screens for expected improvements from candidate DE parameter configurations before using them without any surrogate. It adopts a multi-population mechanism and each parameter configuration is assigned to a subpopulation to determine the effectiveness of parameter configurations accurately by validating one configuration with respect to multiple solutions. The experimental results obtained in moderately expensive cases demonstrated the statistically significant superiority of EBADE among popular and modern adaptive DEs. Additionally, EBADE was also highly competitive with state-of-the-art SAEAs in moderately EOPs; while SAEAs induced premature convergence, EBADE continued to improve in performance with the shortest runtime. Consequently, this paper contributes to solving moderately EOPs with high-performance, computationally efficient, and auto-tunable approaches.

Despite the effectiveness of EBADE, some possible drawbacks can be pointed out. First, EBADE employs FIR to detect good parameter configurations, but this may be hindered until EBADE discovers good solutions. Accordingly, we will explore alternative indicators instead of FIR to detect good parameter configurations even with a small improvement in fitness values. Second, the Euclidean distance is utilized in the prior validation phase, but it may not be adequate when the problem dimension increases. Thus, we will consider other metrics such as the Mahalanobis distance and cosine similarity to improve the scalability of EBADE to problem dimensions. Finally, we plan to extend this framework for multi-objective optimization problems and compare the performances of the extended EBADE and multi-objective SAEAs.

Data Availability

The source code that supports the findings of this study is openly available at https://github.com/YNU-NakataLab/EBADE .

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This work was supported by JSPS KAKENHI under Grant Nos. 22J21254 and 20H04254.

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