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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MDPI AG
2025-04-01
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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. |
| format | Article |
| id | doaj-art-65eca9eb5f984834bfe8a3fd51ef855a |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| 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 |
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