Deep Gaussian process for multi-objective Bayesian optimization

Bayesian Optimization has become a widely used approach to perform optimization involving computationally intensive black-box functions, such as the design optimization of complex engineering systems. It is often based on Gaussian Process regression as a Bayesian surrogate model of the exact functions. Bayesian Optimization has been applied to single and multi-objective optimization problems. In case of multi-objective optimization, the Bayesian models used in optimization often consider the multiple objectives separately and do not take into account the possible correlation between them near the Pareto front. In this paper, a Multi-Objective Bayesian Optimization algorithm based on Deep Gaussian Process is proposed in order to jointly model the objective functions. It allows to take advantage of the correlations (linear and non-linear) between the objectives in order to improve the search space exploration and speed up the convergence to the Pareto front. The proposed algorithm is compared to classical Bayesian Optimization in four analytical functions and two aerospace engineering problems.