A Bayesian Optimization Algorithm for Constrained Simulation Optimization Problems with Heteroscedastic Noise

Abstract

In this research, we develop a Bayesian optimization algorithm to solve expensive, constrained problems. We consider the presence of heteroscedastic noise in the evaluations and thus propose a new acquisition function to account for this noise in the search for the optimal point. We use stochastic kriging to fit the metamodels, and we provide computational results to highlight the importance of accounting for the heteroscedastic noise in the search for the optimal solution. Finally, we propose some promising directions for further research.