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Analysis of multi-objective Kriging-based methods for constrained global optimization

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  • Cédric Durantin
  • Julien Marzat
  • Mathieu Balesdent

Abstract

Metamodeling, i.e., building surrogate models to expensive black-box functions, is an interesting way to reduce the computational burden for optimization purpose. Kriging is a popular metamodel based on Gaussian process theory, whose statistical properties have been exploited to build efficient global optimization algorithms. Single and multi-objective extensions have been proposed to deal with constrained optimization when the constraints are also evaluated numerically. This paper first compares these methods on a representative analytical benchmark. A new multi-objective approach is then proposed to also take into account the prediction accuracy of the constraints. A numerical evaluation is provided on the same analytical benchmark and a realistic aerospace case study. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:63:y:2016:i:3:p:903-926
    DOI: 10.1007/s10589-015-9789-6
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    References listed on IDEAS

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    1. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    2. Audet, Charles & Savard, Gilles & Zghal, Walid, 2010. "A mesh adaptive direct search algorithm for multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 204(3), pages 545-556, August.
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    Cited by:

    1. Kleijnen, Jack & van Nieuwenhuyse, I. & van Beers, W.C.M., 2022. "Constrained Optimization in Simulation : Efficient Global Optimization and Karush-Kuhn-Tucker Conditions (revision of 2021-031)," Discussion Paper 2022-015, Tilburg University, Center for Economic Research.
    2. Dawei Zhan & Huanlai Xing, 2020. "Expected improvement for expensive optimization: a review," Journal of Global Optimization, Springer, vol. 78(3), pages 507-544, November.
    3. Angelina Roche, 2018. "Local optimization of black-box functions with high or infinite-dimensional inputs: application to nuclear safety," Computational Statistics, Springer, vol. 33(1), pages 467-485, March.
    4. Shengguan Xu & Hongquan Chen, 2018. "Nash game based efficient global optimization for large-scale design problems," Journal of Global Optimization, Springer, vol. 71(2), pages 361-381, June.
    5. 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.
    6. Julien Pelamatti & Loïc Brevault & Mathieu Balesdent & El-Ghazali Talbi & Yannick Guerin, 2019. "Efficient global optimization of constrained mixed variable problems," Journal of Global Optimization, Springer, vol. 73(3), pages 583-613, March.
    7. Lei, Fei & Gu, Ke & Du, Bin & Xie, Xiaoping, 2017. "Comprehensive global optimization of an implicit constrained multi-physics system for electric vehicles with in-wheel motors," Energy, Elsevier, vol. 139(C), pages 523-534.

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