An efficient global optimization algorithm for expensive constrained black-box problems by reducing candidate infilling region

Abstract

Surrogate-based optimization methods are usually employed to solve expensive black-box optimization problems. Constraints bring more challenges for optimization than unconstrained problems. This study proposes a novel three-stage infilling framework to solve expensive single-objective problems with equality and/or inequality constraints. In the first stage, a criterion for locating a feasible region is designed. Until a feasible solution is found, the first stage is removed in the subsequent process. The second stage exploits the current best feasible solution and explores potentially better solutions. If the infilled site is infeasible, the third stage will proceed to improve the surrogate accuracy around the feasible region boundary and an extra constraint derived from the objective is proposed to reduce the candidate infill region in this stage. Otherwise, the process stays in stage two. Stage two continues once one third-stage point has been sampled. For brevity, the three-stage framework is called CEGO-DI. The efficacy of CEGO-DI is demonstrated by comparing it with two variants of it. In addition, the method is also compared with several state-of-the-art algorithms on extensive problems. The experimental results show that CEGO-DI has a better or competitive performance on most problems.