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Exploring or reducing noise? A global optimization algorithm in the presence of noise

Author

Listed:
  • Didier Rullière

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Alaeddine Faleh

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Frédéric Planchet

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Wassim Youssef

    (Winter & associés - Winter & associés)

Abstract

We consider the problem of the global minimization of a function observed with noise. This problem occurs for example when the objective function is estimated through stochastic simulations. We propose an original method for iteratively partitioning the search domain when this area is a nite union of simplexes. On each subdomain of the partition, we compute an indicator measuring if the subdomain is likely or not to contain a global minimizer. Next areas to be explored are chosen in accordance with this indicator. Con dence sets for minimizers are given. Numerical applications show empirical convergence results, and illustrate the compromise to be made between the global exploration of the search domain and the focalization around potential minimizers of the problem.

Suggested Citation

  • Didier Rullière & Alaeddine Faleh & Frédéric Planchet & Wassim Youssef, 2013. "Exploring or reducing noise? A global optimization algorithm in the presence of noise," Post-Print hal-00759677, HAL.
    • Handle: RePEc:hal:journl:hal-00759677
    DOI: 10.1007/s00158-012-0874-5
    Note: View the original document on HAL open archive server: https://hal.science/hal-00759677
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    References listed on IDEAS

    as
    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. E. L. Lawler & D. E. Wood, 1966. "Branch-and-Bound Methods: A Survey," Operations Research, INFORMS, vol. 14(4), pages 699-719, August.
    3. V.I. Norkin & G.C. Pflug & A. Ruszczynski, 1996. "A Branch and Bound Method for Stochastic Global Optimization," Working Papers wp96065, International Institute for Applied Systems Analysis.
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    Cited by:

    1. Sass, Susanne & Mitsos, Alexander & Bongartz, Dominik & Bell, Ian H. & Nikolov, Nikolay I. & Tsoukalas, Angelos, 2024. "A branch-and-bound algorithm with growing datasets for large-scale parameter estimation," European Journal of Operational Research, Elsevier, vol. 316(1), pages 36-45.

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    Keywords

    Golbal Optimisation; Simplex; Branch-and-Bound; Kriging;
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