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Simultaneous kriging-based estimation and optimization of mean response

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  • Janis Janusevskis
  • Rodolphe Le Riche

Abstract

Robust optimization is typically based on repeated calls to a deterministic simulation program that aim at both propagating uncertainties and finding optimal design variables. Often in practice, the “simulator” is a computationally intensive software which makes the computational cost one of the principal obstacles to optimization in the presence of uncertainties. This article proposes a new efficient method for minimizing the mean of the objective function. The efficiency stems from the sampling criterion which simultaneously optimizes and propagates uncertainty in the model. Without loss of generality, simulation parameters are divided into two sets, the deterministic optimization variables and the random uncertain parameters. A kriging (Gaussian process regression) model of the simulator is built and a mean process is analytically derived from it. The proposed sampling criterion that yields both optimization and uncertain parameters is the one-step ahead minimum variance of the mean process at the maximizer of the expected improvement. The method is compared with Monte Carlo and kriging-based approaches on analytical test functions in two, four and six dimensions. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Janis Janusevskis & Rodolphe Le Riche, 2013. "Simultaneous kriging-based estimation and optimization of mean response," Journal of Global Optimization, Springer, vol. 55(2), pages 313-336, February.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:2:p:313-336
    DOI: 10.1007/s10898-011-9836-5
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    References listed on IDEAS

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    1. Dellino, G. & Kleijnen, Jack P.C. & Meloni, C., 2009. "Robust Optimization in Simulation : Taguchi and Krige Combined," Other publications TiSEM d919b893-db2b-4d97-a392-4, Tilburg University, School of Economics and Management.
    2. 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.
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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. Torossian, Léonard & Picheny, Victor & Faivre, Robert & Garivier, Aurélien, 2020. "A review on quantile regression for stochastic computer experiments," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    3. Lauvernet, Claire & Helbert, Céline, 2020. "Metamodeling methods that incorporate qualitative variables for improved design of vegetative filter strips," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    4. 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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