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Bi-objective decision making in global optimization based on statistical models

Author

Listed:
  • Antanas Žilinskas

    (Vilnius University)

  • James Calvin

    (New Jersey Institute of Technology)

Abstract

A global optimization problem is considered where the objective functions are assumed “black box” and “expensive”. An algorithm is theoretically substantiated using a statistical model of objective functions and the theory of rational decision making under uncertainty. The search process is defined as a sequence of bi-objective selections of sites for the computation of the objective function values. It is shown that two well known (the maximum average improvement, and the maximum improvement probability) algorithms are special cases of the proposed general approach.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:4:d:10.1007_s10898-018-0622-5
    DOI: 10.1007/s10898-018-0622-5
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    References listed on IDEAS

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    1. Jack Kleijnen & Wim Beers & Inneke Nieuwenhuyse, 2012. "Expected improvement in efficient global optimization through bootstrapped kriging," Journal of Global Optimization, Springer, vol. 54(1), pages 59-73, September.
    2. Antanas Žilinskas, 2014. "A statistical model-based algorithm for ‘black-box’ multi-objective optimisation," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(1), pages 82-93.
    3. Anatoly Zhigljavsky & Antanas Žilinskas, 2008. "Stochastic Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-74740-8, June.
    4. J. Calvin & A. Žilinskas, 2000. "One-Dimensional P-Algorithm with Convergence Rate O(n−3+δ) for Smooth Functions," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 297-307, August.
    5. Michael Emmerich & Kaifeng Yang & André Deutz & Hao Wang & Carlos M. Fonseca, 2016. "A Multicriteria Generalization of Bayesian Global Optimization," Springer Optimization and Its Applications, in: Panos M. Pardalos & Anatoly Zhigljavsky & Julius Žilinskas (ed.), Advances in Stochastic and Deterministic Global Optimization, pages 229-242, Springer.
    6. Albertas Gimbutas & Antanas Žilinskas, 2018. "An algorithm of simplicial Lipschitz optimization with the bi-criteria selection of simplices for the bi-section," Journal of Global Optimization, Springer, vol. 71(1), pages 115-127, May.
    7. Antanas Žilinskas & Julius Žilinskas, 2013. "A hybrid global optimization algorithm for non-linear least squares regression," Journal of Global Optimization, Springer, vol. 56(2), pages 265-277, June.
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    Cited by:

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    2. Jolan Wauters & Andy Keane & Joris Degroote, 2020. "Development of an adaptive infill criterion for constrained multi-objective asynchronous surrogate-based optimization," Journal of Global Optimization, Springer, vol. 78(1), pages 137-160, September.
    3. François Bachoc & Céline Helbert & Victor Picheny, 2020. "Gaussian process optimization with failures: classification and convergence proof," Journal of Global Optimization, Springer, vol. 78(3), pages 483-506, November.
    4. Krityakierne, Tipaluck & Baowan, Duangkamon, 2020. "Aggregated GP-based Optimization for Contaminant Source Localization," Operations Research Perspectives, Elsevier, vol. 7(C).
    5. Qiang Yang & Litao Hua & Xudong Gao & Dongdong Xu & Zhenyu Lu & Sang-Woon Jeon & Jun Zhang, 2022. "Stochastic Cognitive Dominance Leading Particle Swarm Optimization for Multimodal Problems," Mathematics, MDPI, vol. 10(5), pages 1-34, February.

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