A New Expected Improvement Acquisition Function for Expensive Multi-Objective Optimization - Wang, Xilu; Jin, Yaochu (2023 5th International Conference on Data-driven Optimization of Complex Systems (DOCS), 2023)
While Bayesian optimization, a popular solution to black-box optimization problems, has been extended to handle expensive multi-objective optimization problems (MOPs), expected improvement (EI), a commonly used acquisition function, for MOPs is often either computationally expensive or inefficient to balance convergence and diversity. This paper proposes a new expected improvement acquisition function for MOPs, which can take advantage of both EI and multi-objective optimization. To extend the EI to MOPs, all Pareto optimal solutions obtained so far are used to calculate the EI values, resulting in an EI matrix. Instead of transferring the matrix into a scalar value, the proposed algorithm identifies the Pareto optimal solution with the minimum sum of EI values, and utilizes the corresponding EI vector from the matrix as the final value of the acquisition function. The efficiency of the proposed acquisition function is validated by comparing it with state-of-the-art multi-objective Bayesian approaches on two widely used test suites.