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A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions

Author

Listed:
  • Yaohui Li

    (School of Mechanical and Electrical Engineering, Xuchang University, Xuchang 461000, China
    College of Science, Huazhong Agricultural University, Wuhan 430070, China)

  • Jingfang Shen

    (College of Science, Huazhong Agricultural University, Wuhan 430070, China)

  • Ziliang Cai

    (School of Mechanical and Electrical Engineering, Xuchang University, Xuchang 461000, China)

  • Yizhong Wu

    (National CAD Centre, Huazhong University of Science and Technology, Wuhan 430070, China)

  • Shuting Wang

    (National CAD Centre, Huazhong University of Science and Technology, Wuhan 430070, China)

Abstract

The kriging optimization method that can only obtain one sampling point per cycle has encountered a bottleneck in practical engineering applications. How to find a suitable optimization method to generate multiple sampling points at a time while improving the accuracy of convergence and reducing the number of expensive evaluations has been a wide concern. For this reason, a kriging-assisted multi-objective constrained global optimization (KMCGO) method has been proposed. The sample data obtained from the expensive function evaluation is first used to construct or update the kriging model in each cycle. Then, kriging-based estimated target, RMSE (root mean square error), and feasibility probability are used to form three objectives, which are optimized to generate the Pareto frontier set through multi-objective optimization. Finally, the sample data from the Pareto frontier set is further screened to obtain more promising and valuable sampling points. The test results of five benchmark functions, four design problems, and a fuel economy simulation optimization prove the effectiveness of the proposed algorithm.

Suggested Citation

  • Yaohui Li & Jingfang Shen & Ziliang Cai & Yizhong Wu & Shuting Wang, 2021. "A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions," Mathematics, MDPI, vol. 9(2), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:149-:d:478381
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    References listed on IDEAS

    as
    1. Cédric Durantin & Julien Marzat & Mathieu Balesdent, 2016. "Analysis of multi-objective Kriging-based methods for constrained global optimization," Computational Optimization and Applications, Springer, vol. 63(3), pages 903-926, April.
    2. Yaohui Li & Yizhong Wu & Jianjun Zhao & Liping Chen, 2017. "A Kriging-based constrained global optimization algorithm for expensive black-box functions with infeasible initial points," Journal of Global Optimization, Springer, vol. 67(1), pages 343-366, January.
    3. Haoxiang Jie & Yizhong Wu & Jianjun Zhao & Jianwan Ding & Liangliang, 2017. "An efficient multi-objective PSO algorithm assisted by Kriging metamodel for expensive black-box problems," Journal of Global Optimization, Springer, vol. 67(1), pages 399-423, January.
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