Regularized Infill Criteria for Multi-objective Bayesian Optimization with Application to Aircraft Design

Bayesian optimization is an advanced tool to perform efficient global optimization. It consists on enriching iteratively surrogate Kriging models of the objective and the constraints (both supposed to be computationally expensive) of the targeted optimization problem. Nowadays, efficient extensions of Bayesian optimization to solve expensive multi-objective problems are of high interest. The proposed method, in this paper, extends the super efficient global optimization with mixture of experts (SEGOMOE) to solve constrained multi-objective problems. To cope with the ill-posedness of the multi-objective infill criteria, different enrichment procedures using regularization techniques are proposed. The merit of the proposed approaches are shown on known multi-objective benchmark problems with and without constraints. The proposed methods are then used to solve a bi-objective application related to conceptual aircraft design with five unknown design variables and three nonlinear inequality constraints. The preliminary results show a reduction of the total cost in terms of function evaluations by a factor of 20 compared to the evolutionary algorithm NSGA-II.