A Two-State Dynamic Decomposition-Based Evolutionary Algorithm for Handling Many-Objective Optimization Problems
Decomposition-based many-objective evolutionary algorithms (D-MaOEAs) are brilliant at keeping population diversity for predefined reference vectors or points. However, studies indicate that the performance of an D-MaOEA strongly depends on the similarity between the shape of the reference vectors (...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-01-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/3/493 |
| _version_ | 1797623937593507840 |
|---|---|
| author | Lining Xing Jun Li Zhaoquan Cai Feng Hou |
| author_facet | Lining Xing Jun Li Zhaoquan Cai Feng Hou |
| author_sort | Lining Xing |
| collection | DOAJ |
| description | Decomposition-based many-objective evolutionary algorithms (D-MaOEAs) are brilliant at keeping population diversity for predefined reference vectors or points. However, studies indicate that the performance of an D-MaOEA strongly depends on the similarity between the shape of the reference vectors (points) and that of the PF (a set of Pareto-optimal solutions symbolizing balance among objectives of many-objective optimization problems) of the many-objective problem (MaOP). Generally, MaOPs with expected PFs are not realistic. Consequently, the inevitable weak similarity results in many inactive subspaces, creating huge difficulties for maintaining diversity. To address these issues, we propose a two-state method to judge the decomposition status according to the number of inactive reference vectors. Then, two novel reference vector adjustment strategies, set as parts of the environmental selection approach, are tailored for the two states to delete inactive reference vectors and add new active reference vectors, respectively, in order to ensure that the reference vectors are as close as possible to the PF of the optimization problem. Based on the above strategies and an efficient convergence performance indicator, an active reference vector-based two-state dynamic decomposition-base MaOEA, referred to as ART-DMaOEA, is developed in this paper. Extensive experiments were conducted on ART-DMaOEA and five state-of-the-art MaOEAs on MaF1-MaF9 and WFG1-WFG9, and the comparative results show that ART-DMaOEA has the most competitive overall performance. |
| first_indexed | 2024-03-11T09:35:51Z |
| format | Article |
| id | doaj.art-b966c8d7e56d415d93748f7c7b36fa73 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T09:35:51Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b966c8d7e56d415d93748f7c7b36fa732023-11-16T17:20:23ZengMDPI AGMathematics2227-73902023-01-0111349310.3390/math11030493A Two-State Dynamic Decomposition-Based Evolutionary Algorithm for Handling Many-Objective Optimization ProblemsLining Xing0Jun Li1Zhaoquan Cai2Feng Hou3School of Mathematics and Big Data, Foshan University, Foshan 528225, ChinaSchool of Management, Hunan Institute of Engineering, Xiangtan 411104, ChinaShanwei Institute of Technology, Shanwei 516600, ChinaSchool of Mathematical and Computational Sciences, Massey University, Albany 4442, New ZealandDecomposition-based many-objective evolutionary algorithms (D-MaOEAs) are brilliant at keeping population diversity for predefined reference vectors or points. However, studies indicate that the performance of an D-MaOEA strongly depends on the similarity between the shape of the reference vectors (points) and that of the PF (a set of Pareto-optimal solutions symbolizing balance among objectives of many-objective optimization problems) of the many-objective problem (MaOP). Generally, MaOPs with expected PFs are not realistic. Consequently, the inevitable weak similarity results in many inactive subspaces, creating huge difficulties for maintaining diversity. To address these issues, we propose a two-state method to judge the decomposition status according to the number of inactive reference vectors. Then, two novel reference vector adjustment strategies, set as parts of the environmental selection approach, are tailored for the two states to delete inactive reference vectors and add new active reference vectors, respectively, in order to ensure that the reference vectors are as close as possible to the PF of the optimization problem. Based on the above strategies and an efficient convergence performance indicator, an active reference vector-based two-state dynamic decomposition-base MaOEA, referred to as ART-DMaOEA, is developed in this paper. Extensive experiments were conducted on ART-DMaOEA and five state-of-the-art MaOEAs on MaF1-MaF9 and WFG1-WFG9, and the comparative results show that ART-DMaOEA has the most competitive overall performance.https://www.mdpi.com/2227-7390/11/3/493decomposition-based MaOEAactive reference vectortwo-state methodART-DMaOEA |
| spellingShingle | Lining Xing Jun Li Zhaoquan Cai Feng Hou A Two-State Dynamic Decomposition-Based Evolutionary Algorithm for Handling Many-Objective Optimization Problems Mathematics decomposition-based MaOEA active reference vector two-state method ART-DMaOEA |
| title | A Two-State Dynamic Decomposition-Based Evolutionary Algorithm for Handling Many-Objective Optimization Problems |
| title_full | A Two-State Dynamic Decomposition-Based Evolutionary Algorithm for Handling Many-Objective Optimization Problems |
| title_fullStr | A Two-State Dynamic Decomposition-Based Evolutionary Algorithm for Handling Many-Objective Optimization Problems |
| title_full_unstemmed | A Two-State Dynamic Decomposition-Based Evolutionary Algorithm for Handling Many-Objective Optimization Problems |
| title_short | A Two-State Dynamic Decomposition-Based Evolutionary Algorithm for Handling Many-Objective Optimization Problems |
| title_sort | two state dynamic decomposition based evolutionary algorithm for handling many objective optimization problems |
| topic | decomposition-based MaOEA active reference vector two-state method ART-DMaOEA |
| url | https://www.mdpi.com/2227-7390/11/3/493 |
| work_keys_str_mv | AT liningxing atwostatedynamicdecompositionbasedevolutionaryalgorithmforhandlingmanyobjectiveoptimizationproblems AT junli atwostatedynamicdecompositionbasedevolutionaryalgorithmforhandlingmanyobjectiveoptimizationproblems AT zhaoquancai atwostatedynamicdecompositionbasedevolutionaryalgorithmforhandlingmanyobjectiveoptimizationproblems AT fenghou atwostatedynamicdecompositionbasedevolutionaryalgorithmforhandlingmanyobjectiveoptimizationproblems AT liningxing twostatedynamicdecompositionbasedevolutionaryalgorithmforhandlingmanyobjectiveoptimizationproblems AT junli twostatedynamicdecompositionbasedevolutionaryalgorithmforhandlingmanyobjectiveoptimizationproblems AT zhaoquancai twostatedynamicdecompositionbasedevolutionaryalgorithmforhandlingmanyobjectiveoptimizationproblems AT fenghou twostatedynamicdecompositionbasedevolutionaryalgorithmforhandlingmanyobjectiveoptimizationproblems |