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Worst-case global optimization of black-box functions through Kriging and relaxation

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  • Julien Marzat
  • Eric Walter
  • Hélène Piet-Lahanier

Abstract

A new algorithm is proposed to deal with the worst-case optimization of black-box functions evaluated through costly computer simulations. The input variables of these computer experiments are assumed to be of two types. Control variables must be tuned while environmental variables have an undesirable effect, to which the design of the control variables should be robust. The algorithm to be proposed searches for a minimax solution, i.e., values of the control variables that minimize the maximum of the objective function with respect to the environmental variables. The problem is particularly difficult when the control and environmental variables live in continuous spaces. Combining a relaxation procedure with Kriging-based optimization makes it possible to deal with the continuity of the variables and the fact that no analytical expression of the objective function is available in most real-case problems. Numerical experiments are conducted to assess the accuracy and efficiency of the algorithm, both on analytical test functions with known results and on an engineering application. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:4:p:707-727
    DOI: 10.1007/s10898-012-9899-y
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    References listed on IDEAS

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    1. D. Huang & T. Allen & W. Notz & N. Zeng, 2006. "Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models," Journal of Global Optimization, Springer, vol. 34(3), pages 441-466, March.
    2. Dellino, Gabriella & Kleijnen, Jack P.C. & Meloni, Carlo, 2010. "Robust optimization in simulation: Taguchi and Response Surface Methodology," International Journal of Production Economics, Elsevier, vol. 125(1), pages 52-59, May.
    3. Deng Huang & Theodore T. Allen, 2005. "Design and analysis of variable fidelity experimentation applied to engine valve heat treatment process design," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(2), pages 443-463, April.
    4. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    5. P. Parpas & B. Rustem, 2009. "An Algorithm for the Global Optimization of a Class of Continuous Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 461-473, May.
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    Cited by:

    1. 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).
    2. Margarita Antoniou & Gregor Papa, 2021. "Differential Evolution with Estimation of Distribution for Worst-Case Scenario Optimization," Mathematics, MDPI, vol. 9(17), pages 1-22, September.

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