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A strengthened diversity indicator and reference vector-based evolutionary algorithm for many-objective optimization

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Abstract

As pointed out in recent studies, most evolutionary algorithms have shown their promise in dealing with many-objective optimization problems (MaOPs). However, the ability to balance convergence and diversity and the scalability of objectives are still far from perfect. To address these issues, this paper proposes a strengthened diversity indicator and reference vector-based evolutionary algorithm for many-objective optimization, termed SDIEA. In the proposed SDIEA, a new adaptive indicator is proposed, namely, strengthened diversity indicator (SDI). The proposed SDI is adopted to effectively emphasize the pressure of convergence and diversity in the many-objective space, by preserving the achievement scalarizing function (ASF) metric and considering angle information between individuals and reference vectors with the number of objectives and generations. Moreover, in order to further enhance the diversity management in global space, the reference vectors are used to guide population partition selection. Finally, the selected solutions based on SDI and reference vector are merged for the next generation. Experimental results show that the proposed SDIEA achieves competitive performance on MaF and WFG, compared with several state-of-the-art algorithms. Additionally, SDIEA obtains good performance on 20-objective test instances and still has the potential to strive for scalability of higher objectives.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China [Grant 61440049, Grant 61866025 and Grant 61866026], the Natural Science Foundation of Jiangxi Province [Grant 20181BAB202025], the Superiority Science and Technology Innovation Team Program of Jiangxi Province [Grant 20181BCB24008], and the Graduate Innovation Fund of Jiangxi Province [Grant YC2019-S400].

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  1. Key Laboratory of Jiangxi Province for Image Processing and Pattern Recognition, Nanchang Hangkong University, Nanchang, 330063, China

    Wenjing Sun & Junhua Li

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  1. Wenjing Sun
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  2. Junhua Li
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Correspondence to Junhua Li.

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Appendix

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Table 8 Summary of symbols involved in this paper (Note that No. is the abbreviation of Number)
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Sun, W., Li, J. A strengthened diversity indicator and reference vector-based evolutionary algorithm for many-objective optimization. Soft Comput 25, 10257–10273 (2021). https://doi.org/10.1007/s00500-021-05981-1

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