Coevolutionary Algorithm with Bayes Theorem for Constrained Multiobjective Optimization

The effective resolution of constrained multi-objective optimization problems (CMOPs) requires a delicate balance between maximizing objectives and satisfying constraints. Previous studies have demonstrated that multi-swarm optimization models exhibit robust performance in CMOPs; however, their high...

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Main Authors: Shaoyu Zhao, Heming Jia, Yongchao Li, Qian Shi
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/7/1191
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author Shaoyu Zhao
Heming Jia
Yongchao Li
Qian Shi
author_facet Shaoyu Zhao
Heming Jia
Yongchao Li
Qian Shi
author_sort Shaoyu Zhao
collection DOAJ
description The effective resolution of constrained multi-objective optimization problems (CMOPs) requires a delicate balance between maximizing objectives and satisfying constraints. Previous studies have demonstrated that multi-swarm optimization models exhibit robust performance in CMOPs; however, their high computational resource demands can hinder convergence efficiency. This article proposes an environment selection model based on Bayes’ theorem, leveraging the advantages of dual populations. The model constructs prior knowledge using objective function values and constraint violation values, and then, it integrates this information to enhance selection processes. By dynamically adjusting the selection of the auxiliary population based on prior knowledge, the algorithm significantly improves its adaptability to various CMOPs. Additionally, a population size adjustment strategy is introduced to mitigate the computational burden of dual populations. By utilizing past prior knowledge to estimate the probability of function value changes, offspring allocation is dynamically adjusted, optimizing resource utilization. This adaptive adjustment prevents unnecessary computational waste during evolution, thereby enhancing both convergence and diversity. To validate the effectiveness of the proposed algorithm, comparative experiments were performed against seven constrained multi-objective optimization algorithms (CMOEAs) across three benchmark test sets and 12 real-world problems. The results show that the proposed algorithm outperforms the others in both convergence and diversity.
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spelling doaj-art-65eca9eb5f984834bfe8a3fd51ef855a2025-08-20T03:08:57ZengMDPI AGMathematics2227-73902025-04-01137119110.3390/math13071191Coevolutionary Algorithm with Bayes Theorem for Constrained Multiobjective OptimizationShaoyu Zhao0Heming Jia1Yongchao Li2Qian Shi3School of Information Engineering, Sanming University, Sanming 365004, ChinaSchool of Information Engineering, Sanming University, Sanming 365004, ChinaSchool of Information and Electrical Engineering, Heilongjiang Bayi Agricultural University, Daqing 163319, ChinaSchool of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, ChinaThe effective resolution of constrained multi-objective optimization problems (CMOPs) requires a delicate balance between maximizing objectives and satisfying constraints. Previous studies have demonstrated that multi-swarm optimization models exhibit robust performance in CMOPs; however, their high computational resource demands can hinder convergence efficiency. This article proposes an environment selection model based on Bayes’ theorem, leveraging the advantages of dual populations. The model constructs prior knowledge using objective function values and constraint violation values, and then, it integrates this information to enhance selection processes. By dynamically adjusting the selection of the auxiliary population based on prior knowledge, the algorithm significantly improves its adaptability to various CMOPs. Additionally, a population size adjustment strategy is introduced to mitigate the computational burden of dual populations. By utilizing past prior knowledge to estimate the probability of function value changes, offspring allocation is dynamically adjusted, optimizing resource utilization. This adaptive adjustment prevents unnecessary computational waste during evolution, thereby enhancing both convergence and diversity. To validate the effectiveness of the proposed algorithm, comparative experiments were performed against seven constrained multi-objective optimization algorithms (CMOEAs) across three benchmark test sets and 12 real-world problems. The results show that the proposed algorithm outperforms the others in both convergence and diversity.https://www.mdpi.com/2227-7390/13/7/1191multi-population optimization modelsconstrained multi-objective optimizationBayes theorem
spellingShingle Shaoyu Zhao
Heming Jia
Yongchao Li
Qian Shi
Coevolutionary Algorithm with Bayes Theorem for Constrained Multiobjective Optimization
Mathematics
multi-population optimization models
constrained multi-objective optimization
Bayes theorem
title Coevolutionary Algorithm with Bayes Theorem for Constrained Multiobjective Optimization
title_full Coevolutionary Algorithm with Bayes Theorem for Constrained Multiobjective Optimization
title_fullStr Coevolutionary Algorithm with Bayes Theorem for Constrained Multiobjective Optimization
title_full_unstemmed Coevolutionary Algorithm with Bayes Theorem for Constrained Multiobjective Optimization
title_short Coevolutionary Algorithm with Bayes Theorem for Constrained Multiobjective Optimization
title_sort coevolutionary algorithm with bayes theorem for constrained multiobjective optimization
topic multi-population optimization models
constrained multi-objective optimization
Bayes theorem
url https://www.mdpi.com/2227-7390/13/7/1191
work_keys_str_mv AT shaoyuzhao coevolutionaryalgorithmwithbayestheoremforconstrainedmultiobjectiveoptimization
AT hemingjia coevolutionaryalgorithmwithbayestheoremforconstrainedmultiobjectiveoptimization
AT yongchaoli coevolutionaryalgorithmwithbayestheoremforconstrainedmultiobjectiveoptimization
AT qianshi coevolutionaryalgorithmwithbayestheoremforconstrainedmultiobjectiveoptimization