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Multimodal multi-objective optimization via determinantal point process-assisted evolutionary algorithm

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Abstract

Multimodal multi-objective optimization problems (MMOPs) are widely present in real life. Due to the need of balancing between convergence and diversity in multi-objective optimization, as well as the need of balancing between diversities in objective and decision spaces, exploring the Pareto optimal front and Pareto optimal solution set becomes rather difficult in solving MMOPs. Recently, some multimodal multi-objective optimization algorithms have emerged. However, most of them are convergence-first, which may result in poor diversity of the solution set in decision space. To remedy this defect, in this paper, a determinantal point process (DPP)-assisted evolutionary algorithm is proposed to effectively solve MMOPs. In the proposed method, i) the DPPs are used to select subsets to consider convergence and diversity in both objective and decision spaces; ii) a kernel matrix is designed to retain solutions with poor convergence but good diversity in the decision space to explore the equivalent Pareto optimal solution sets; and iii) we propose a framework that combines the population and archive to better solve MMOPs. The results show that the proposed algorithm achieves the best performance in 18 of the 28 benchmark problems compared to six state-of-the-art algorithms.

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Data availability

Comparison algorithms and benchmarks are available on Platemo [35] (https://github.com/BIMK/PlatEMO).

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Acknowledgements

This work was partly supported by the National Natural Science Foundation of China under Grant No. 62076225.

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Authors and Affiliations

  1. School of Computer Science, China University of Geosciences, Wuhan, 430074, Hubei, China

    Xinyu Cheng, Wenyin Gong & Fei Ming

  2. School of Computer Science and Artificial Intelligence, Wuhan University of Technology, Wuhan, 430071, Hubei, China

    Xiaofang Zhu

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  1. Xinyu Cheng
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Correspondence to Wenyin Gong.

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Cheng, X., Gong, W., Ming, F. et al. Multimodal multi-objective optimization via determinantal point process-assisted evolutionary algorithm. Neural Comput & Applic 36, 1381–1411 (2024). https://doi.org/10.1007/s00521-023-09110-x

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