A Bayesian approach to constrained multi-objective optimization of expensive-to-evaluate functions
Résumé
This communication addresses the problem of derivative-free multi-objective optimization of real-valued functions subject to multiple inequality constraints, under a Bayesian framework. Both the objective and constraint functions are assumed to be smooth, non-linear and expensive-to-evaluate. As a consequence, the number of evaluations to carry out the optimization is very limited. This set-up typically applies to complex industrial design optimization problems. The method we propose to overcome this difficulty has its roots in both the Bayesian and the multi-objective optimization literatures. More specifically, an extended domination rule is used to handle the constraints and a corresponding expected hyper-volume improvement criterion is proposed. The calculation of this class of criteria is known to become difficult as the number of objectives increases. To address this difficulty, we propose a novel approach, making use of Sequential Monte Carlo techniques. Moreover we also use Sequential Monte Carlo techniques for the optimization of our new criterion. The performance of the proposed method is evaluated on a set of test problems coming from the literature and compared with reference methods.