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Constrained optimization in simulation: efficient global optimization and Karush-Kuhn-Tucker conditions

Author

Listed:
  • Jack P. C. Kleijnen

    (Tilburg University (TiU))

  • Ebru Angün

    (Galatasaray University)

  • Inneke Nieuwenhuyse

    (Hasselt University)

  • Wim C. M. Beers

Abstract

We develop a novel methodology for solving constrained optimization problems in deterministic simulation. In these problems, the goal (or objective) output is to be minimized, subject to one or more constraints for the other outputs and for the inputs. Our methododology combines the“Karush-Kuhn-Tucker”(KKT) conditions with“efficient global optimization”(EGO).These KKT conditions are well-known first-order necessary optimality conditions in white-box mathematical optimization, but our method is the first EGO method that uses these conditions. EGO is a popular type of algorithm that is closely related to“Bayesian optimization” and“active machine learning”, as they all use Gaussian processes or Kriging to approximate the input/output behavior of black-box models. We numerically compare the performance of our KKT-EGO algorithm and two alternative EGO algorithms, in several popular examples. In some examples our algorithm converges faster to the true optimum, so our algorithm may provide a suitable alternative.

Suggested Citation

  • Jack P. C. Kleijnen & Ebru Angün & Inneke Nieuwenhuyse & Wim C. M. Beers, 2025. "Constrained optimization in simulation: efficient global optimization and Karush-Kuhn-Tucker conditions," Journal of Global Optimization, Springer, vol. 91(4), pages 897-922, April.
    • Handle: RePEc:spr:jglopt:v:91:y:2025:i:4:d:10.1007_s10898-024-01448-3
    DOI: 10.1007/s10898-024-01448-3
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    References listed on IDEAS

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    1. Jack P. C. Kleijnen & Wim C. M. van Beers, 2022. "Statistical Tests for Cross-Validation of Kriging Models," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 607-621, January.
    2. Kleijnen, Jack P.C. & Mehdad, Ehsan, 2014. "Multivariate versus univariate Kriging metamodels for multi-response simulation models," European Journal of Operational Research, Elsevier, vol. 236(2), pages 573-582.
    3. Antanas Žilinskas & James Calvin, 2019. "Bi-objective decision making in global optimization based on statistical models," Journal of Global Optimization, Springer, vol. 74(4), pages 599-609, August.
    4. Lim, Chae Young & Wu, Wei-Ying, 2022. "Conditions on which cokriging does not do better than kriging," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    5. Dawei Zhan & Huanlai Xing, 2020. "Expected improvement for expensive optimization: a review," Journal of Global Optimization, Springer, vol. 78(3), pages 507-544, November.
    Full references (including those not matched with items on IDEAS)

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