Updating Kriging Surrogate Models Based on the Hypervolume Indicator in Multi-Objective Optimization

Abstract

This paper presents a comparison of the criteria for updating the Kriging surrogate models in multi-objective optimization: expected improvement (EI), expected hypervolume improvement (EHVI), estimation (EST), and those in combination (EHVI + EST). EI has been conventionally used as the criterion considering the stochastic improvement of each objective function value individually, while EHVI has recently been proposed as the criterion considering the stochastic improvement of the front of nondominated solutions in multi-objective optimization. EST is the value of each objective function estimated nonstochastically by the Kriging model without considering its uncertainties. Numerical experiments were implemented in the welded beam design problem, and empirically showed that, in an unconstrained case, EHVI maintains a balance between accuracy, spread, and uniformity in nondominated solutions for Kriging-model-based multiobjective optimization. In addition, the present experiments suggested future investigation into techniques for handling constraints with uncertainties to enhance the capability of EHVI in constrained cases.