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A robust multi-objective Bayesian optimization framework considering input uncertainty

Author

Listed:
  • Jixiang Qing

    (Ghent University – imec)

  • Ivo Couckuyt

    (Ghent University – imec)

  • Tom Dhaene

    (Ghent University – imec)

Abstract

Bayesian optimization is a popular tool for optimizing time-consuming objective functions with a limited number of function evaluations. In real-life applications like engineering design, the designer often wants to take multiple objectives as well as input uncertainty into account to find a set of robust solutions. While this is an active topic in single-objective Bayesian optimization, it is less investigated in the multi-objective case. We introduce a novel Bayesian optimization framework to perform multi-objective optimization considering input uncertainty. We propose a robust Gaussian Process model to infer the Bayes risk criterion to quantify robustness, and we develop a two-stage Bayesian optimization process to search for a robust Pareto frontier, i.e., solutions that have good average performance under input uncertainty. The complete framework supports various distributions of the input uncertainty and takes full advantage of parallel computing. We demonstrate the effectiveness of the framework through numerical benchmarks.

Suggested Citation

  • Jixiang Qing & Ivo Couckuyt & Tom Dhaene, 2023. "A robust multi-objective Bayesian optimization framework considering input uncertainty," Journal of Global Optimization, Springer, vol. 86(3), pages 693-711, July.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:3:d:10.1007_s10898-022-01262-9
    DOI: 10.1007/s10898-022-01262-9
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    References listed on IDEAS

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    1. Ivo Couckuyt & Dirk Deschrijver & Tom Dhaene, 2014. "Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization," Journal of Global Optimization, Springer, vol. 60(3), pages 575-594, November.
    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.
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