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Achievement scalarizing function sorting for strength Pareto evolutionary algorithm in many-objective optimization

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Abstract

Multi-objective evolutionary algorithms (MOEAs) have proven their effectiveness in solving two or three objective problems. However, recent research shows that Pareto-based MOEAs encounter selection difficulties facing many similar non-dominated solutions in dealing with many-objective problems. In order to reduce the selection pressure and improve the diversity, we propose achievement scalarizing function sorting strategy to make strength Pareto evolutionary algorithm suitable for many-objective optimization. In the proposed algorithm, we adopt density estimation strategy to redefine a new fitness value of a solution, which can select solution with good convergence and distribution. In addition, a clustering method is used to classify the non-dominated solutions, and then, an achievement scalarizing function ranking method is designed to layer different frontiers and eliminate redundant solutions in the environment selection stage, thus ensuring the convergence and diversity of non-dominant solutions. The performance of the proposed algorithm is validated and compared with some state-of-the-art algorithms on a number of test problems with 3, 5, 8, 10 objectives. Experimental studies demonstrate that the proposed algorithm shows very competitive performance.

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Acknowledgements

The authors would like to thank the editor and reviewers for their helpful comments and suggestions to improve the quality of this paper. This work was supported in part by the National Key Research and Development Project (2018YFC1602704, Grant 2018YFB1702704), and in part by the National Natural Science Foundation of China (61873006, 61673053).

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Authors and Affiliations

  1. Faculty of Information Technology, Beijing University of Technology, Beijing, 100124, China

    Xin Li, Xiaoli Li & Kang Wang

  2. Beijing Key Laboratory of Computational Intelligence and Intelligent System Engineering Research Center of Digital Community, Ministry of Education, Beijing, 100124, China

    Xiaoli Li

  3. Centre for Computational Intelligence School of Computer Science and Informatics, De Montfort University, Leicester, United Kingdom

    Shengxiang Yang

  4. Communication University of China, Beijing, 100024, China

    Yang Li

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  1. Xin Li
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  2. Xiaoli Li
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Correspondence to Xiaoli Li.

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The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. The work is original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. The manuscript is approved by all authors for publication.

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Li, X., Li, X., Wang, K. et al. Achievement scalarizing function sorting for strength Pareto evolutionary algorithm in many-objective optimization . Neural Comput & Applic 33, 6369–6388 (2021). https://doi.org/10.1007/s00521-020-05398-1

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  • DOI: https://doi.org/10.1007/s00521-020-05398-1

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