Adaptive Constraint Relaxation-Based Evolutionary Algorithm for Constrained Multi-Objective Optimization
The key problem to solving constrained multi-objective optimization problems (CMOPs) is how to achieve a balance between objectives and constraints. Unfortunately, most existing methods for CMOPs still cannot achieve the above balance. To this end, this paper proposes an adaptive constraint relaxati...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/19/3075 |
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| author | Junming Chen Kai Zhang Hui Zeng Jin Yan Jin Dai Zhidong Dai |
| author_facet | Junming Chen Kai Zhang Hui Zeng Jin Yan Jin Dai Zhidong Dai |
| author_sort | Junming Chen |
| collection | DOAJ |
| description | The key problem to solving constrained multi-objective optimization problems (CMOPs) is how to achieve a balance between objectives and constraints. Unfortunately, most existing methods for CMOPs still cannot achieve the above balance. To this end, this paper proposes an adaptive constraint relaxation-based evolutionary algorithm (ACREA) for CMOPs. ACREA adaptively relaxes the constraints according to the iteration information of population, whose purpose is to induce infeasible solutions to transform into feasible ones and thus improve the ability to explore the unknown regions. Completely ignoring constraints can cause the population to waste significant resources searching for infeasible solutions, while excessively satisfying constraints can trap the population in local optima. Therefore, balancing constraints and objectives is a crucial approach to improving algorithm performance. By appropriately relaxing the constraints, it induces infeasible solutions to be transformed into feasible ones, thus obtaining more information from infeasible solutions. At the same time, it also establishes an archive for the storage and update of solutions. In the archive update process, a diversity-based ranking is proposed to improve the convergence speed of the algorithm. In the selection process of the mating pool, common density selection metrics are incorporated to enable the algorithm to obtain higher-quality solutions. The experimental results show that the proposed ACREA algorithm not only achieved the best Inverse Generation Distance (IGD) value in 54.6% of the 44 benchmark test problems and the best Hyper Volume (HV) value in 50% of them, but also obtained the best results in seven out of nine real-world problems. Clearly, CP-TSEA outperforms its competitors. |
| first_indexed | 2025-03-19T23:15:47Z |
| format | Article |
| id | doaj.art-ee74b7a90bfe4b078eb37c7b1bcde880 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2025-03-19T23:15:47Z |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ee74b7a90bfe4b078eb37c7b1bcde8802024-10-15T13:00:16ZengMDPI AGMathematics2227-73902024-09-011219307510.3390/math12193075Adaptive Constraint Relaxation-Based Evolutionary Algorithm for Constrained Multi-Objective OptimizationJunming Chen0Kai Zhang1Hui Zeng2Jin Yan3Jin Dai4Zhidong Dai5School of Art and Design, Guangzhou University, Guangzhou 510006, ChinaFaculty of Humanities and Arts, Macau University of Science and Technology, Macau 999078, ChinaSchool of Design, Jiangnan University, Wuxi 214122, ChinaSchool of Computer Science and Engineering, Macau University of Science and Technology, Macau 999078, ChinaGraduate School of International Studies, Yonsei University, Seoul 03722, Republic of KoreaSchool of Art and Design, Guangzhou University, Guangzhou 510006, ChinaThe key problem to solving constrained multi-objective optimization problems (CMOPs) is how to achieve a balance between objectives and constraints. Unfortunately, most existing methods for CMOPs still cannot achieve the above balance. To this end, this paper proposes an adaptive constraint relaxation-based evolutionary algorithm (ACREA) for CMOPs. ACREA adaptively relaxes the constraints according to the iteration information of population, whose purpose is to induce infeasible solutions to transform into feasible ones and thus improve the ability to explore the unknown regions. Completely ignoring constraints can cause the population to waste significant resources searching for infeasible solutions, while excessively satisfying constraints can trap the population in local optima. Therefore, balancing constraints and objectives is a crucial approach to improving algorithm performance. By appropriately relaxing the constraints, it induces infeasible solutions to be transformed into feasible ones, thus obtaining more information from infeasible solutions. At the same time, it also establishes an archive for the storage and update of solutions. In the archive update process, a diversity-based ranking is proposed to improve the convergence speed of the algorithm. In the selection process of the mating pool, common density selection metrics are incorporated to enable the algorithm to obtain higher-quality solutions. The experimental results show that the proposed ACREA algorithm not only achieved the best Inverse Generation Distance (IGD) value in 54.6% of the 44 benchmark test problems and the best Hyper Volume (HV) value in 50% of them, but also obtained the best results in seven out of nine real-world problems. Clearly, CP-TSEA outperforms its competitors.https://www.mdpi.com/2227-7390/12/19/3075adaptive relaxationarchivemating pooldiversity-based rankingconstrained multi-objective optimization |
| spellingShingle | Junming Chen Kai Zhang Hui Zeng Jin Yan Jin Dai Zhidong Dai Adaptive Constraint Relaxation-Based Evolutionary Algorithm for Constrained Multi-Objective Optimization Mathematics adaptive relaxation archive mating pool diversity-based ranking constrained multi-objective optimization |
| title | Adaptive Constraint Relaxation-Based Evolutionary Algorithm for Constrained Multi-Objective Optimization |
| title_full | Adaptive Constraint Relaxation-Based Evolutionary Algorithm for Constrained Multi-Objective Optimization |
| title_fullStr | Adaptive Constraint Relaxation-Based Evolutionary Algorithm for Constrained Multi-Objective Optimization |
| title_full_unstemmed | Adaptive Constraint Relaxation-Based Evolutionary Algorithm for Constrained Multi-Objective Optimization |
| title_short | Adaptive Constraint Relaxation-Based Evolutionary Algorithm for Constrained Multi-Objective Optimization |
| title_sort | adaptive constraint relaxation based evolutionary algorithm for constrained multi objective optimization |
| topic | adaptive relaxation archive mating pool diversity-based ranking constrained multi-objective optimization |
| url | https://www.mdpi.com/2227-7390/12/19/3075 |
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