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Robust optimization: A kriging-based multi-objective optimization approach

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  • Ribaud, Mélina
  • Blanchet-Scalliet, Christophette
  • Helbert, Céline
  • Gillot, Frédéric

Abstract

In the robust shape optimization context, the evaluation cost of numerical models is reduced by the use of a response surface. Multi-objective methodologies for robust optimization that consist in simultaneously minimizing the expectation and variance of a function have already been developed to answer to this question. However, efficient estimation in the framework of time-consuming simulation has not been completely explored. In this paper, a robust optimization procedure based on Taylor expansion, kriging prediction and a genetic NSGA-II algorithm is proposed. The two objectives are the Taylor expansion of expectation and variance. The kriging technique is chosen to surrogate the function and its derivatives. Afterwards, NSGA-II is performed on kriging response surfaces or kriging expected improvements to construct a Pareto front. One point or a batch of points is chosen carefully to enrich the learning set of the model. When the budget is reached the non-dominated points provide designs that make compromises between optimization and robustness. Seven relevant strategies based on this main procedure are detailed and compared in two test functions (2D and 6D). In each case, the results are compared when the derivatives are observed and when they are not. The procedure is also applied to an industrial case study where the objective is to optimize the shape of a motor fan.

Suggested Citation

  • Ribaud, Mélina & Blanchet-Scalliet, Christophette & Helbert, Céline & Gillot, Frédéric, 2020. "Robust optimization: A kriging-based multi-objective optimization approach," Reliability Engineering and System Safety, Elsevier, vol. 200(C).
    • Handle: RePEc:eee:reensy:v:200:y:2020:i:c:s0951832019301516
    DOI: 10.1016/j.ress.2020.106913
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    References listed on IDEAS

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    1. Julien Marzat & Eric Walter & Hélène Piet-Lahanier, 2013. "Worst-case global optimization of black-box functions through Kriging and relaxation," Journal of Global Optimization, Springer, vol. 55(4), pages 707-727, April.
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    3. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    4. Dupuy, Delphine & Helbert, Céline & Franco, Jessica, 2015. "DiceDesign and DiceEval: Two R Packages for Design and Analysis of Computer Experiments," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 65(i11).
    5. Svenson, Joshua & Santner, Thomas, 2016. "Multiobjective optimization of expensive-to-evaluate deterministic computer simulator models," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 250-264.
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    Cited by:

    1. Li, Xiaoke & Zhu, Heng & Chen, Zhenzhong & Ming, Wuyi & Cao, Yang & He, Wenbin & Ma, Jun, 2022. "Limit state Kriging modeling for reliability-based design optimization through classification uncertainty quantification," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    2. You, Geonhwa, 2024. "A comprehensive approach for calibrating anthropogenic effects on atmosphere degradation," Renewable and Sustainable Energy Reviews, Elsevier, vol. 191(C).
    3. Xiaodong Song & Mingyang Li & Zhitao Li & Fang Liu, 2021. "Global Optimization Algorithm Based on Kriging Using Multi-Point Infill Sampling Criterion and Its Application in Transportation System," Sustainability, MDPI, vol. 13(19), pages 1-17, September.
    4. Marrel, Amandine & Iooss, Bertrand, 2024. "Probabilistic surrogate modeling by Gaussian process: A new estimation algorithm for more robust prediction," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    5. Teixeira, Rui & Martinez-Pastor, Beatriz & Nogal, Maria & O’Connor, Alan, 2021. "Reliability analysis using a multi-metamodel complement-basis approach," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    6. Marrel, Amandine & Iooss, Bertrand, 2024. "Probabilistic surrogate modeling by Gaussian process: A review on recent insights in estimation and validation," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    7. Nan, Hang & Liang, Hao & Di, Haoyuan & Li, Hongshuang, 2024. "A gradient-assisted learning strategy of Kriging model for robust design optimization," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    8. Rivier, M. & Congedo, P.M., 2022. "Surrogate-Assisted Bounding-Box approach applied to constrained multi-objective optimisation under uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 217(C).

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