BI-Objective Bayesian Optimization with Transformed Additive Gaussian Processes

Simulation is often used to optimize the performance of an engineering or scientific process. The input-output relation of a simulation model can be black-box functions and expensive to evaluate. Bayesian optimization, popularly used to improve efficiency in searching for optimal input settings, has been extended to bi-objective optimization problems. However, the common challenge in bi-objective Bayesian optimization is the computational challenge of maximizing the expected hypervolume improvement (EHI) to search for the input point to evaluate. In this paper, we utilize the transformed additive Gaussian process to simplify the objectives to additive functions for each dimension of the input space. Under this model assumption, the maximization of EHI over the entire decision space is reduced to the maximization of the resulting EHI functions for each dimension separately. We demonstrate the performances of the proposed method through numerical comparisons of the bi-objective Bayesian optimization with the traditional Gaussian process model.