A Bayesian subset simulation approach to constrained global optimization of expensive-to-evaluate black-box functions

Paul Feliot (1, 2) , Julien Bect (2, 3, 1) , Emmanuel Vazquez (2, 3, 1)

1 IRT SystemX
2 E3S - Supélec Sciences des Systèmes
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

This talk addresses the problem of derivative-free global optimization of a real-valued function under multiple inequality constraints. Both the objective function and the constraint functions are assumed to be smooth, nonlinear, expensive-to-evaluate black-box functions. As a consequence, the number of evaluations that can be used to carry out the optimization is very limited. We focus in this work on the case of strongly constrained problems, where finding a feasible design, using such a limited budget of simulations, is a challenge in itself. The method that we propose to overcome this difficulty has its roots in the recent literature on Gaussian process-based methods for reliability analysis—in particular, the Bayesian Subset Simulation (BSS) algorithm of Li, Bect and Vazquez—and multi-objective optimization. More specifically, we consider a decreasing sequence of nested subsets of the design space, which is defined and explored sequentially using a combination of Sequential Monte Carlo (SMC) techniques and sequential Bayesian design of experiments. The proposed method obtains promising result on challenging test cases from the literature.

Domaines: Optimisation et contrôle [math.OC]

Paul Feliot, Julien Bect, Emmanuel Vazquez. A Bayesian subset simulation approach to constrained global optimization of expensive-to-evaluate black-box functions. PGMO-COPI’14, Oct 2014, Palaiseau, France. ⟨hal-01078397v2⟩