On the Impact of Covariance Functions in Multi-Objective Bayesian Optimization for Engineering Design

Multi-objective Bayesian optimization (BO) is a highly useful class of methods that can effectively solve computationally expensive engineering design optimization problems with multiple objectives. However, the impact of covariance function, which is an important part of multi-objective BO, is rarely studied in the context of engineering optimization. We aim to shed light on this issue by performing numerical experiments on engineering design optimization problems, primarily low-fidelity problems so that we are able to statistically evaluate the performance of BO methods with various covariance functions. In this paper, we performed the study using a set of subsonic airfoil optimization cases as benchmark problems. Expected hypervolume improvement was used as the acquisition function to enrich the experimental design. Results show that the choice of the covariance function give a notable impact on the performance of multi-objective BO. In this regard, Kriging models with Matern-3/2 is the most robust method in terms of the diversity and convergence to the Pareto front that can handle problems with various complexities