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Journal of Global Optimization

, Volume 55, Issue 4, pp 707–727 | Cite as

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

  • Julien Marzat
  • Eric Walter
  • Hélène Piet-Lahanier
Article

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.

Keywords

Computer experiments Continuous minimax Efficient global optimization Expected improvement Fault diagnosis Kriging Robust optimization Worst-case analysis 

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Copyright information

© Springer Science+Business Media, LLC. 2012

Authors and Affiliations

  • Julien Marzat
    • 1
    • 2
  • Eric Walter
    • 2
  • Hélène Piet-Lahanier
    • 1
  1. 1.ONERA (The French Aerospace Lab)PalaiseauFrance
  2. 2.Gif-sur-YvetteFrance

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