A robust multi-objective Bayesian optimization framework considering input uncertainty

• Published in: Journal of global optimization Vol. 86; no. 3; pp. 693 - 711
• Main Authors: Qing, Jixiang, Couckuyt, Ivo, Dhaene, Tom
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.07.2023; Springer; Springer Nature B.V
• Subjects: Active learning; Approximation; Bayesian analysis; Computer Science; Design; Design engineering; Gaussian process; Mathematics; Mathematics and Statistics; Multiple objective analysis; Objectives; Operations Research/Decision Theory; Optimization; Optimization techniques; Pareto optimization; Random variables; Real Functions; Robustness (mathematics); Uncertainty; Efficient global optimization; Robust optimization; Gaussian process; Bayesian optimization
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-022-01262-9

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.