Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective Optimization
Decomposition-based multiobjective evolutionary algorithms (MOEA/Ds) have become increasingly popular in recent years. In these MOEA/Ds, evolutionary search is guided by the used weight vectors in decomposition function to approximate the Pareto front (PF). Generally, the decomposition function will...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/7436712 |
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| author | Wu Lin Qiuzhen Lin Zexuan Zhu Jianqiang Li Jianyong Chen Zhong Ming |
| author_facet | Wu Lin Qiuzhen Lin Zexuan Zhu Jianqiang Li Jianyong Chen Zhong Ming |
| author_sort | Wu Lin |
| collection | DOAJ |
| description | Decomposition-based multiobjective evolutionary algorithms (MOEA/Ds) have become increasingly popular in recent years. In these MOEA/Ds, evolutionary search is guided by the used weight vectors in decomposition function to approximate the Pareto front (PF). Generally, the decomposition function will be constructed by the weight vectors and the reference point, which play an important role to balance convergence and diversity during the evolutionary search. However, in most existing MOEA/Ds, only one ideal point is used as the reference point for all the evolutionary search, which is harmful to search the entire PF when tackling the problems with difficult-to-approximate PF boundaries. To address the above problem, this paper proposes an evolutionary search method with multiple utopian reference points in MOEA/Ds. Similar to the existing MOEA/Ds, each solution is associated with one weight vector, which provides an evolutionary search direction, while the novelty of our approach is to use multiple utopian reference points, which can provide evolutionary search directions for different weight vectors. Corner solutions are used to approximate the nadir point and then multiple utopian reference points for evolutionary search can be constructed based on the ideal point and the nadir point, which are uniformly distributed on the coordinate axis or planes. The use of these utopian points can prevent solutions to gather in the same region of PF and helps to strike a good balance of exploration and exploitation in the search space. The performance of our proposed algorithm is validated on tackling 16 recently proposed test problems with difficult-to-approximate PF boundaries and empirically compared to eight state-of-the-art multiobjective evolutionary algorithms. The experimental results demonstrate the superiority of the proposed algorithm on solving most of the test problems adopted. |
| format | Article |
| id | doaj-art-e56994e5deeb4402b460cd6fefa9db4d |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-e56994e5deeb4402b460cd6fefa9db4d2025-08-20T03:26:17ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/74367127436712Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective OptimizationWu Lin0Qiuzhen Lin1Zexuan Zhu2Jianqiang Li3Jianyong Chen4Zhong Ming5College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, ChinaCollege of Computer Science and Software Engineering, Shenzhen University, Shenzhen, ChinaCollege of Computer Science and Software Engineering, Shenzhen University, Shenzhen, ChinaCollege of Computer Science and Software Engineering, Shenzhen University, Shenzhen, ChinaCollege of Computer Science and Software Engineering, Shenzhen University, Shenzhen, ChinaCollege of Computer Science and Software Engineering, Shenzhen University, Shenzhen, ChinaDecomposition-based multiobjective evolutionary algorithms (MOEA/Ds) have become increasingly popular in recent years. In these MOEA/Ds, evolutionary search is guided by the used weight vectors in decomposition function to approximate the Pareto front (PF). Generally, the decomposition function will be constructed by the weight vectors and the reference point, which play an important role to balance convergence and diversity during the evolutionary search. However, in most existing MOEA/Ds, only one ideal point is used as the reference point for all the evolutionary search, which is harmful to search the entire PF when tackling the problems with difficult-to-approximate PF boundaries. To address the above problem, this paper proposes an evolutionary search method with multiple utopian reference points in MOEA/Ds. Similar to the existing MOEA/Ds, each solution is associated with one weight vector, which provides an evolutionary search direction, while the novelty of our approach is to use multiple utopian reference points, which can provide evolutionary search directions for different weight vectors. Corner solutions are used to approximate the nadir point and then multiple utopian reference points for evolutionary search can be constructed based on the ideal point and the nadir point, which are uniformly distributed on the coordinate axis or planes. The use of these utopian points can prevent solutions to gather in the same region of PF and helps to strike a good balance of exploration and exploitation in the search space. The performance of our proposed algorithm is validated on tackling 16 recently proposed test problems with difficult-to-approximate PF boundaries and empirically compared to eight state-of-the-art multiobjective evolutionary algorithms. The experimental results demonstrate the superiority of the proposed algorithm on solving most of the test problems adopted.http://dx.doi.org/10.1155/2019/7436712 |
| spellingShingle | Wu Lin Qiuzhen Lin Zexuan Zhu Jianqiang Li Jianyong Chen Zhong Ming Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective Optimization Complexity |
| title | Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective Optimization |
| title_full | Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective Optimization |
| title_fullStr | Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective Optimization |
| title_full_unstemmed | Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective Optimization |
| title_short | Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective Optimization |
| title_sort | evolutionary search with multiple utopian reference points in decomposition based multiobjective optimization |
| url | http://dx.doi.org/10.1155/2019/7436712 |
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