A self-organizing decomposition based evolutionary algorithm with cooperative diversity measure for many-objective optimization

Siyuan Zhao; Zichun Shao; Yile Chen; Liang Zheng; Junming Chen; Siyuan Zhao; Zichun Shao; Yile Chen; Liang Zheng; Junming Chen

doi:10.3934/math.2025625

AIMS Mathematics

2025, Volume 10, Issue 6: 13880-13907. doi: 10.3934/math.2025625

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A self-organizing decomposition based evolutionary algorithm with cooperative diversity measure for many-objective optimization

Faculty of Humanities and Arts, Macau University of Science and Technology, Macau 999078, China

Received: 28 April 2025 Revised: 02 June 2025 Accepted: 10 June 2025 Published: 17 June 2025
MSC : 68T20

Decomposition based many-objective evolutionary algorithms have received wide attention over the years. However, most of them 1) are sensitive to the Pareto front shapes due to the dependence on the predefined reference vectors, and 2) only consider the global diversity but ignore the local diversity. These severely limit the using scope of decomposition based MaOEAs. Therefore, we propose a self-organizing decomposition based evolutionary algorithm with cooperative diversity measure (SDEA) for many-objective optimization in this work. In SDEA, a self-organizing decomposition manner is developed to automatically divide the objective space into different sub-regions instead of using the predefined reference vectors, which enables SDEA adapt to different Pareto front shapes. Such essence is that the self-organizing decomposition manner makes individuals with good diversity act as the reference vectors. Moreover, a cooperative diversity measure is designed to better promote the diversity, which takes the global diversity and local diversity into account. To validate the performance of SDEA, SDEA is compared with seven state-of-the-art methods on three benchmark test suites and two real-world applications. The corresponding results demonstrate that SDEA has higher competitiveness in dealing with different many-objective optimization problems.
- many-objective optimization,
- evolutionary algorithm,
- self-organizing decomposition,
- cooperative diversity measure
Citation: Siyuan Zhao, Zichun Shao, Yile Chen, Liang Zheng, Junming Chen. A self-organizing decomposition based evolutionary algorithm with cooperative diversity measure for many-objective optimization[J]. AIMS Mathematics, 2025, 10(6): 13880-13907. doi: 10.3934/math.2025625

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Abstract

Decomposition based many-objective evolutionary algorithms have received wide attention over the years. However, most of them 1) are sensitive to the Pareto front shapes due to the dependence on the predefined reference vectors, and 2) only consider the global diversity but ignore the local diversity. These severely limit the using scope of decomposition based MaOEAs. Therefore, we propose a self-organizing decomposition based evolutionary algorithm with cooperative diversity measure (SDEA) for many-objective optimization in this work. In SDEA, a self-organizing decomposition manner is developed to automatically divide the objective space into different sub-regions instead of using the predefined reference vectors, which enables SDEA adapt to different Pareto front shapes. Such essence is that the self-organizing decomposition manner makes individuals with good diversity act as the reference vectors. Moreover, a cooperative diversity measure is designed to better promote the diversity, which takes the global diversity and local diversity into account. To validate the performance of SDEA, SDEA is compared with seven state-of-the-art methods on three benchmark test suites and two real-world applications. The corresponding results demonstrate that SDEA has higher competitiveness in dealing with different many-objective optimization problems.

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