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A Multicriteria Generalization of Bayesian Global Optimization

In: Advances in Stochastic and Deterministic Global Optimization

Author

Listed:
  • Michael Emmerich

    (Leiden University)

  • Kaifeng Yang

    (Leiden University)

  • André Deutz

    (Leiden University)

  • Hao Wang

    (Leiden University)

  • Carlos M. Fonseca

    (University of Coimbra)

Abstract

This chapter discusses a generalization of the expected improvement used in Bayesian global optimization to the multicriteria optimization domain, where the goal is to find an approximation to the Pareto front. The expected hypervolume improvement (EHVI) measures improvement as the gain in dominated hypervolume relative to a given approximation to the Pareto front. We will review known properties of the EHVI, applications in practice and propose a new exact algorithm for computing EHVI. The new algorithm has asymptotically optimal time complexity O(nlogn). This improves existing computation schemes by a factor of n∕logn. It shows that this measure, at least for a small number of objective functions, is as fast as other simpler measures of multicriteria expected improvement that were considered in recent years.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:spochp:978-3-319-29975-4_12
    DOI: 10.1007/978-3-319-29975-4_12
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    Citations

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    Cited by:

    1. Bhupinder Singh Saini & Michael Emmerich & Atanu Mazumdar & Bekir Afsar & Babooshka Shavazipour & Kaisa Miettinen, 2022. "Optimistic NAUTILUS navigator for multiobjective optimization with costly function evaluations," Journal of Global Optimization, Springer, vol. 83(4), pages 865-889, August.
    2. Kaifeng Yang & Michael Emmerich & André Deutz & Thomas Bäck, 2019. "Efficient computation of expected hypervolume improvement using box decomposition algorithms," Journal of Global Optimization, Springer, vol. 75(1), pages 3-34, September.
    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. Dawei Zhan & Huanlai Xing, 2020. "Expected improvement for expensive optimization: a review," Journal of Global Optimization, Springer, vol. 78(3), pages 507-544, November.
    5. Audet, Charles & Bigeon, Jean & Cartier, Dominique & Le Digabel, Sébastien & Salomon, Ludovic, 2021. "Performance indicators in multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 292(2), pages 397-422.
    6. Eric Bradford & Artur M. Schweidtmann & Alexei Lapkin, 2018. "Efficient multiobjective optimization employing Gaussian processes, spectral sampling and a genetic algorithm," Journal of Global Optimization, Springer, vol. 71(2), pages 407-438, June.

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