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An efficient multi-objective PSO algorithm assisted by Kriging metamodel for expensive black-box problems

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Abstract

The huge computational overhead is the main challenge in the application of community based optimization methods, such as multi-objective particle swarm optimization and multi-objective genetic algorithm, to deal with the multi-objective optimization involving costly simulations. This paper proposes a Kriging metamodel assisted multi-objective particle swarm optimization method to solve this kind of expensively black-box multi-objective optimization problems. On the basis of crowding distance based multi-objective particle swarm optimization algorithm, the new proposed method constructs Kriging metamodel for each expensive objective function adaptively, and then the non-dominated solutions of the metamodels are utilized to guide the update of particle population. To reduce the computational cost, the generalized expected improvements of each particle predicted by metamodels are presented to determine which particles need to perform actual function evaluations. The suggested method is tested on 12 benchmark functions and compared with the original crowding distance based multi-objective particle swarm optimization algorithm and non-dominated sorting genetic algorithm-II algorithm. The test results show that the application of Kriging metamodel improves the search ability and reduces the number of evaluations. Additionally, the new proposed method is applied to the optimal design of a cycloid gear pump and achieves desirable results.

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Acknowledgments

This work is supported by the National Nature Science Foundation of China (Number 51575205) and the National High Technology Research and Development Program (863 Program) of China (Number 2013AA041301).

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Authors and Affiliations

  1. Micropowers Engineering R&D Centre, China Shipbuilding Industry Corporation, Shanghai, China

    Haoxiang Jie

  2. National CAD supported Software Engineering Centre, Huazhong University of Science and Technology, Wuhan, People’s Republic of China

    Haoxiang Jie, Yizhong Wu, Jianjun Zhao & Jianwan Ding

  3. School of Engineering, Sun Yet-Sen University, Guangzhou, People’s Republic of China

    Liangliang

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  1. Haoxiang Jie
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  2. Yizhong Wu
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  5. Liangliang
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Correspondence to Jianjun Zhao.

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Jie, H., Wu, Y., Zhao, J. et al. An efficient multi-objective PSO algorithm assisted by Kriging metamodel for expensive black-box problems. J Glob Optim 67, 399–423 (2017). https://doi.org/10.1007/s10898-016-0428-2

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  • DOI: https://doi.org/10.1007/s10898-016-0428-2

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