On the occasion of the 30-year anniversary of the Evolutionary Computation journal, I was invited by Professor Hart to offer some reflections on the article on evolving behaviors in the iterated prisoner's dilemma that I contributed to its first issue in 1993. It's an honor to do so. I would like to thank Professor Ken De Jong, the journal's first editor-in-chief, for his vision in creating the journal, and the editors who have followed and maintained that vision. This article contains some personal reflections on the topic and the field as a whole.
在《进化计算》杂志创刊30周年之际，Hart教授邀请我就我在1993年创刊的那篇关于反复囚徒困境中的进化行为的文章发表一些感想。我很荣幸能这样做。我要感谢该杂志的首任主编Ken De Jong教授，感谢他在创办该杂志时的远见卓识，以及追随并保持这一远见卓识的编辑们。这篇文章包含了对这个话题和整个领域的一些个人思考。
{"title":"Personal Reflections on Some Early Work in Evolving Strategies in the Iterated Prisoner's Dilemma","authors":"David B. Fogel","doi":"10.1162/evco_a_00322","DOIUrl":"10.1162/evco_a_00322","url":null,"abstract":"On the occasion of the 30-year anniversary of the Evolutionary Computation journal, I was invited by Professor Hart to offer some reflections on the article on evolving behaviors in the iterated prisoner's dilemma that I contributed to its first issue in 1993. It's an honor to do so. I would like to thank Professor Ken De Jong, the journal's first editor-in-chief, for his vision in creating the journal, and the editors who have followed and maintained that vision. This article contains some personal reflections on the topic and the field as a whole.","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"31 2","pages":"157-161"},"PeriodicalIF":6.8,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9670243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently a mechanism called stagnation detection was proposed that automatically adjusts the mutation rate of evolutionary algorithms when they encounter local optima. The so-called SD-(1+1) EA introduced by Rajabi and Witt (2022) adds stagnation detection to the classical (1+1) EA with standard bit mutation. This algorithm flips each bit independently with some mutation rate, and stagnation detection raises the rate when the algorithm is likely to have encountered a local optimum. In this article, we investigate stagnation detection in the context of the k-bit flip operator of randomized local search that flips k bits chosen uniformly at random and let stagnation detection adjust the parameter k. We obtain improved runtime results compared with the SD-(1+1) EA amounting to a speedup of at least (1-o(1))2πm, where m is the so-called gap size, that is, the distance to the next improvement. Moreover, we propose additional schemes that prevent infinite optimization times even if the algorithm misses a working choice of k due to unlucky events. Finally, we present an example where standard bit mutation still outperforms the k-bit flip operator with stagnation detection.
{"title":"Stagnation Detection with Randomized Local Search*","authors":"Amirhossein Rajabi;Carsten Witt","doi":"10.1162/evco_a_00313","DOIUrl":"10.1162/evco_a_00313","url":null,"abstract":"Recently a mechanism called stagnation detection was proposed that automatically adjusts the mutation rate of evolutionary algorithms when they encounter local optima. The so-called SD-(1+1) EA introduced by Rajabi and Witt (2022) adds stagnation detection to the classical (1+1) EA with standard bit mutation. This algorithm flips each bit independently with some mutation rate, and stagnation detection raises the rate when the algorithm is likely to have encountered a local optimum. In this article, we investigate stagnation detection in the context of the k-bit flip operator of randomized local search that flips k bits chosen uniformly at random and let stagnation detection adjust the parameter k. We obtain improved runtime results compared with the SD-(1+1) EA amounting to a speedup of at least (1-o(1))2πm, where m is the so-called gap size, that is, the distance to the next improvement. Moreover, we propose additional schemes that prevent infinite optimization times even if the algorithm misses a working choice of k due to unlucky events. Finally, we present an example where standard bit mutation still outperforms the k-bit flip operator with stagnation detection.","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"31 1","pages":"1-29"},"PeriodicalIF":6.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9359552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Model management is an essential component in data-driven surrogate-assisted evolutionary optimization. In model management, the solutions with a large degree of uncertainty in approximation play an important role. They can strengthen the exploration ability of algorithms and improve the accuracy of surrogates. However, there is no theoretical method to measure the uncertainty of prediction of Non-Gaussian process surrogates. To address this issue, this article proposes a method to measure the uncertainty. In this method, a stationary random field with a known zero mean is used to measure the uncertainty of prediction of Non-Gaussian process surrogates. Based on experimental analyses, this method is able to measure the uncertainty of prediction of Non-Gaussian process surrogates. The method's effectiveness is demonstrated on a set of benchmark problems in single surrogate and ensemble surrogates cases.
{"title":"An Uncertainty Measure for Prediction of Non-Gaussian Process Surrogates","authors":"Caie Hu;Sanyou Zeng;Changhe Li","doi":"10.1162/evco_a_00316","DOIUrl":"10.1162/evco_a_00316","url":null,"abstract":"Model management is an essential component in data-driven surrogate-assisted evolutionary optimization. In model management, the solutions with a large degree of uncertainty in approximation play an important role. They can strengthen the exploration ability of algorithms and improve the accuracy of surrogates. However, there is no theoretical method to measure the uncertainty of prediction of Non-Gaussian process surrogates. To address this issue, this article proposes a method to measure the uncertainty. In this method, a stationary random field with a known zero mean is used to measure the uncertainty of prediction of Non-Gaussian process surrogates. Based on experimental analyses, this method is able to measure the uncertainty of prediction of Non-Gaussian process surrogates. The method's effectiveness is demonstrated on a set of benchmark problems in single surrogate and ensemble surrogates cases.","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"31 1","pages":"53-71"},"PeriodicalIF":6.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10801408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Christian Cintrano;Javier Ferrer;Manuel López-Ibáñez;Enrique Alba
In the traffic light scheduling problem, the evaluation of candidate solutions requires the simulation of a process under various (traffic) scenarios. Thus, good solutions should not only achieve good objective function values, but they must be robust (low variance) across all different scenarios. Previous work has shown that combining IRACE with evolutionary operators is effective for this task due to the power of evolutionary operators in numerical optimization. In this article, we further explore the hybridization of evolutionary operators and the elitist iterated racing of IRACE for the simulation–optimization of traffic light programs. We review previous works from the literature to find the evolutionary operators performing the best when facing this problem to propose new hybrid algorithms. We evaluate our approach over a realistic case study derived from the traffic network of Málaga (Spain) with 275 traffic lights that should be scheduled optimally. The experimental analysis reveals that the hybrid algorithm comprising IRACE plus differential evolution offers statistically better results than the other algorithms when the budget of simulations is low. In contrast, IRACE performs better than the hybrids for a high simulations budget, although the optimization time is much longer.
{"title":"Hybridization of Evolutionary Operators with Elitist Iterated Racing for the Simulation Optimization of Traffic Lights Programs","authors":"Christian Cintrano;Javier Ferrer;Manuel López-Ibáñez;Enrique Alba","doi":"10.1162/evco_a_00314","DOIUrl":"10.1162/evco_a_00314","url":null,"abstract":"In the traffic light scheduling problem, the evaluation of candidate solutions requires the simulation of a process under various (traffic) scenarios. Thus, good solutions should not only achieve good objective function values, but they must be robust (low variance) across all different scenarios. Previous work has shown that combining IRACE with evolutionary operators is effective for this task due to the power of evolutionary operators in numerical optimization. In this article, we further explore the hybridization of evolutionary operators and the elitist iterated racing of IRACE for the simulation–optimization of traffic light programs. We review previous works from the literature to find the evolutionary operators performing the best when facing this problem to propose new hybrid algorithms. We evaluate our approach over a realistic case study derived from the traffic network of Málaga (Spain) with 275 traffic lights that should be scheduled optimally. The experimental analysis reveals that the hybrid algorithm comprising IRACE plus differential evolution offers statistically better results than the other algorithms when the budget of simulations is low. In contrast, IRACE performs better than the hybrids for a high simulations budget, although the optimization time is much longer.","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"31 1","pages":"31-51"},"PeriodicalIF":6.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10814046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Active-set approaches are commonly used in algorithms for constrained numerical optimization. We propose that active-set techniques can beneficially be employed for evolutionary black-box optimization with explicit constraints and present an active-set evolution strategy. We experimentally evaluate its performance relative to those of several algorithms for constrained optimization and find that the active-set evolution strategy compares favourably for the problem set under consideration.
{"title":"Active Sets for Explicitly Constrained Evolutionary Optimization","authors":"Patrick Spettel;Zehao Ba;Dirk V. Arnold","doi":"10.1162/evco_a_00311","DOIUrl":"10.1162/evco_a_00311","url":null,"abstract":"Active-set approaches are commonly used in algorithms for constrained numerical optimization. We propose that active-set techniques can beneficially be employed for evolutionary black-box optimization with explicit constraints and present an active-set evolution strategy. We experimentally evaluate its performance relative to those of several algorithms for constrained optimization and find that the active-set evolution strategy compares favourably for the problem set under consideration.","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"30 4","pages":"531-553"},"PeriodicalIF":6.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41589162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Benedict A. H. Jones;John L. P. Chouard;Bianca C. C. Branco;Eléonore G. B. Vissol-Gaudin;Christopher Pearson;Michael C. Petty;Noura Al Moubayed;Dagou A. Zeze;Chris Groves
Evolution-in-Materio is a computational paradigm in which an algorithm reconfigures a material's properties to achieve a specific computational function. This article addresses the question of how successful and well performing Evolution-in-Materio processors can be designed through the selection of nanomaterials and an evolutionary algorithm for a target application. A physical model of a nanomaterial network is developed which allows for both randomness, and the possibility of Ohmic and non-Ohmic conduction, that are characteristic of such materials. These differing networks are then exploited by differential evolution, which optimises several configuration parameters (e.g., configuration voltages, weights, etc.), to solve different classification problems. We show that ideal nanomaterial choice depends upon problem complexity, with more complex problems being favoured by complex voltage dependence of conductivity and vice versa. Furthermore, we highlight how intrinsic nanomaterial electrical properties can be exploited by differing configuration parameters, clarifying the role and limitations of these techniques. These findings provide guidance for the rational design of nanomaterials and algorithms for future Evolution-in-Materio processors.
{"title":"Towards Intelligently Designed Evolvable Processors","authors":"Benedict A. H. Jones;John L. P. Chouard;Bianca C. C. Branco;Eléonore G. B. Vissol-Gaudin;Christopher Pearson;Michael C. Petty;Noura Al Moubayed;Dagou A. Zeze;Chris Groves","doi":"10.1162/evco_a_00309","DOIUrl":"10.1162/evco_a_00309","url":null,"abstract":"Evolution-in-Materio is a computational paradigm in which an algorithm reconfigures a material's properties to achieve a specific computational function. This article addresses the question of how successful and well performing Evolution-in-Materio processors can be designed through the selection of nanomaterials and an evolutionary algorithm for a target application. A physical model of a nanomaterial network is developed which allows for both randomness, and the possibility of Ohmic and non-Ohmic conduction, that are characteristic of such materials. These differing networks are then exploited by differential evolution, which optimises several configuration parameters (e.g., configuration voltages, weights, etc.), to solve different classification problems. We show that ideal nanomaterial choice depends upon problem complexity, with more complex problems being favoured by complex voltage dependence of conductivity and vice versa. Furthermore, we highlight how intrinsic nanomaterial electrical properties can be exploited by differing configuration parameters, clarifying the role and limitations of these techniques. These findings provide guidance for the rational design of nanomaterials and algorithms for future Evolution-in-Materio processors.","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"30 4","pages":"479-501"},"PeriodicalIF":6.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48671640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article investigates the performance of multistart next ascent hillclimbing and well-known evolutionary algorithms incorporating diversity preservation techniques on instances of the multimodal problem generator. This generator induces a class of problems in the bitstring domain which is interesting to study from a theoretical perspective in the context of multimodal optimization, as it is a generalization of the classical OneMax and TwoMax functions for an arbitrary number of peaks. An average-case runtime analysis for multistart next ascent hillclimbing is presented for uniformly distributed equal-height instances of this class of problems. It is shown empirically that conventional niching and mating restriction techniques incorporated in an evolutionary algorithm are not sufficient to make them competitive with the hillclimbing strategy. We conjecture the reason for this behavior is the lack of structure in the space of local optima on instances of this problem class, which makes an optimization algorithm unable to exploit information from one optimum to infer where another optimum might be. When no such structure exists, it seems that the best strategy for discovering all optima is a brute-force one. Overall, our study gives insights with respect to the adequacy of hillclimbers and evolutionary algorithms for multimodal optimization, depending on properties of the fitness landscape.
{"title":"When Hillclimbers Beat Genetic Algorithms in Multimodal Optimization","authors":"Fernando G. Lobo;Mosab Bazargani","doi":"10.1162/evco_a_00312","DOIUrl":"10.1162/evco_a_00312","url":null,"abstract":"This article investigates the performance of multistart next ascent hillclimbing and well-known evolutionary algorithms incorporating diversity preservation techniques on instances of the multimodal problem generator. This generator induces a class of problems in the bitstring domain which is interesting to study from a theoretical perspective in the context of multimodal optimization, as it is a generalization of the classical OneMax and TwoMax functions for an arbitrary number of peaks. An average-case runtime analysis for multistart next ascent hillclimbing is presented for uniformly distributed equal-height instances of this class of problems. It is shown empirically that conventional niching and mating restriction techniques incorporated in an evolutionary algorithm are not sufficient to make them competitive with the hillclimbing strategy. We conjecture the reason for this behavior is the lack of structure in the space of local optima on instances of this problem class, which makes an optimization algorithm unable to exploit information from one optimum to infer where another optimum might be. When no such structure exists, it seems that the best strategy for discovering all optima is a brute-force one. Overall, our study gives insights with respect to the adequacy of hillclimbers and evolutionary algorithms for multimodal optimization, depending on properties of the fitness landscape.","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"30 4","pages":"535-559"},"PeriodicalIF":6.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41240529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a novel constraint-handling technique for the covariance matrix adaptation evolution strategy (CMA-ES). The proposed technique is aimed at solving explicitly constrained black-box continuous optimization problems, in which the explicit constraint is a constraint whereby the computational time for the constraint violation and its (numerical) gradient are negligible compared to that for the objective function. This method is designed to realize two invariance properties: invariance to the affine transformation of the search space, and invariance to the increasing transformation of the objective and constraint functions. The CMA-ES is designed to possess these properties for handling difficulties that appear in black-box optimization problems, such as non-separability, ill-conditioning, ruggedness, and the different orders of magnitude in the objective. The proposed constraint-handling technique (CHT), known as ARCH, modifies the underlying CMA-ES only in terms of the ranking of the candidate solutions. It employs a repair operator and an adaptive ranking aggregation strategy to compute the ranking. We developed test problems to evaluate the effects of the invariance properties, and performed experiments to empirically verify the invariance of the algorithm. We compared the proposed method with other CHTs on the CEC 2006 constrained optimization benchmark suite to demonstrate its efficacy. Empirical studies reveal that ARCH is able to exploit the explicitness of the constraint functions effectively, sometimes even more efficiently than an existing box-constraint handling technique on box-constrained problems, while exhibiting the invariance properties. Moreover, ARCH overwhelmingly outperforms CHTs by not exploiting the explicit constraints in terms of the number of objective function calls.
{"title":"Adaptive Ranking-Based Constraint Handling for Explicitly Constrained Black-Box Optimization","authors":"Naoki Sakamoto;Youhei Akimoto","doi":"10.1162/evco_a_00310","DOIUrl":"https://doi.org/10.1162/evco_a_00310","url":null,"abstract":"We propose a novel constraint-handling technique for the covariance matrix adaptation evolution strategy (CMA-ES). The proposed technique is aimed at solving explicitly constrained black-box continuous optimization problems, in which the explicit constraint is a constraint whereby the computational time for the constraint violation and its (numerical) gradient are negligible compared to that for the objective function. This method is designed to realize two invariance properties: invariance to the affine transformation of the search space, and invariance to the increasing transformation of the objective and constraint functions. The CMA-ES is designed to possess these properties for handling difficulties that appear in black-box optimization problems, such as non-separability, ill-conditioning, ruggedness, and the different orders of magnitude in the objective. The proposed constraint-handling technique (CHT), known as ARCH, modifies the underlying CMA-ES only in terms of the ranking of the candidate solutions. It employs a repair operator and an adaptive ranking aggregation strategy to compute the ranking. We developed test problems to evaluate the effects of the invariance properties, and performed experiments to empirically verify the invariance of the algorithm. We compared the proposed method with other CHTs on the CEC 2006 constrained optimization benchmark suite to demonstrate its efficacy. Empirical studies reveal that ARCH is able to exploit the explicitness of the constraint functions effectively, sometimes even more efficiently than an existing box-constraint handling technique on box-constrained problems, while exhibiting the invariance properties. Moreover, ARCH overwhelmingly outperforms CHTs by not exploiting the explicit constraints in terms of the number of objective function calls.","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"30 4","pages":"503-529"},"PeriodicalIF":6.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71903200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Francisco Chicano;Gabriela Ochoa;L. Darrell Whitley;Renato Tinós
An optimal recombination operator for two-parent solutions provides the best solution among those that take the value for each variable from one of the parents (gene transmission property). If the solutions are bit strings, the offspring of an optimal recombination operator is optimal in the smallest hyperplane containing the two parent solutions. Exploring this hyperplane is computationally costly, in general, requiring exponential time in the worst case. However, when the variable interaction graph of the objective function is sparse, exploration can be done in polynomial time. In this article, we present a recombination operator, called Dynastic Potential Crossover (DPX), that runs in polynomial time and behaves like an optimal recombination operator for low-epistasis combinatorial problems. We compare this operator, both theoretically and experimentally, with traditional crossover operators, like uniform crossover and network crossover, and with two recently defined efficient recombination operators: partition crossover and articulation points partition crossover. The empirical comparison uses NKQ Landscapes and MAX-SAT instances. DPX outperforms the other crossover operators in terms of quality of the offspring and provides better results included in a trajectory and a population-based metaheuristic, but it requires more time and memory to compute the offspring.
{"title":"Dynastic Potential Crossover Operator","authors":"Francisco Chicano;Gabriela Ochoa;L. Darrell Whitley;Renato Tinós","doi":"10.1162/evco_a_00305","DOIUrl":"10.1162/evco_a_00305","url":null,"abstract":"An optimal recombination operator for two-parent solutions provides the best solution among those that take the value for each variable from one of the parents (gene transmission property). If the solutions are bit strings, the offspring of an optimal recombination operator is optimal in the smallest hyperplane containing the two parent solutions. Exploring this hyperplane is computationally costly, in general, requiring exponential time in the worst case. However, when the variable interaction graph of the objective function is sparse, exploration can be done in polynomial time. In this article, we present a recombination operator, called Dynastic Potential Crossover (DPX), that runs in polynomial time and behaves like an optimal recombination operator for low-epistasis combinatorial problems. We compare this operator, both theoretically and experimentally, with traditional crossover operators, like uniform crossover and network crossover, and with two recently defined efficient recombination operators: partition crossover and articulation points partition crossover. The empirical comparison uses NKQ Landscapes and MAX-SAT instances. DPX outperforms the other crossover operators in terms of quality of the offspring and provides better results included in a trajectory and a population-based metaheuristic, but it requires more time and memory to compute the offspring.","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"30 3","pages":"409-446"},"PeriodicalIF":6.8,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/6720222/9931026/09931097.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39583646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Domination-based multiobjective (MO) evolutionary algorithms (EAs) are today arguably the most frequently used type of MOEA. These methods, however, stagnate when the majority of the population becomes nondominated, preventing further convergence to the Pareto set. Hypervolume-based MO optimization has shown promising results to overcome this. Direct use of the hypervolume, however, results in no selection pressure for dominated solutions. The recently introduced Sofomore framework overcomes this by solving multiple interleaved single-objective dynamic problems that iteratively improve a single approximation set, based on the uncrowded hypervolume improvement (UHVI). It thereby however loses many advantages of population-based MO optimization, such as handling multimodality. Here, we reformulate the UHVI as a quality measure for approximation sets, called the uncrowded hypervolume (UHV), which can be used to directly solve MO optimization problems with a single-objective optimizer. We use the state-of-the-art gene-pool optimal mixing evolutionary algorithm (GOMEA) that is capable of efficiently exploiting the intrinsically available grey-box properties of this problem. The resulting algorithm, UHV-GOMEA, is compared with Sofomore equipped with GOMEA, and the domination-based MO-GOMEA. In doing so, we investigate in which scenarios either domination-based or hypervolume-based methods are preferred. Finally, we construct a simple hybrid approach that combines MO-GOMEA with UHV-GOMEA and outperforms both.
{"title":"Uncrowded Hypervolume-Based Multiobjective Optimization with Gene-Pool Optimal Mixing","authors":"S.C. Maree;T. Alderliesten;P.A.N. Bosman","doi":"10.1162/evco_a_00303","DOIUrl":"10.1162/evco_a_00303","url":null,"abstract":"Domination-based multiobjective (MO) evolutionary algorithms (EAs) are today arguably the most frequently used type of MOEA. These methods, however, stagnate when the majority of the population becomes nondominated, preventing further convergence to the Pareto set. Hypervolume-based MO optimization has shown promising results to overcome this. Direct use of the hypervolume, however, results in no selection pressure for dominated solutions. The recently introduced Sofomore framework overcomes this by solving multiple interleaved single-objective dynamic problems that iteratively improve a single approximation set, based on the uncrowded hypervolume improvement (UHVI). It thereby however loses many advantages of population-based MO optimization, such as handling multimodality. Here, we reformulate the UHVI as a quality measure for approximation sets, called the uncrowded hypervolume (UHV), which can be used to directly solve MO optimization problems with a single-objective optimizer. We use the state-of-the-art gene-pool optimal mixing evolutionary algorithm (GOMEA) that is capable of efficiently exploiting the intrinsically available grey-box properties of this problem. The resulting algorithm, UHV-GOMEA, is compared with Sofomore equipped with GOMEA, and the domination-based MO-GOMEA. In doing so, we investigate in which scenarios either domination-based or hypervolume-based methods are preferred. Finally, we construct a simple hybrid approach that combines MO-GOMEA with UHV-GOMEA and outperforms both.","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"30 3","pages":"329-353"},"PeriodicalIF":6.8,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39702735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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