Surrogate-assisted two-stage cooperative differential evolution for expensive constrained multimodal optimization problems

Abstract

The expensive calculation, constrained solution space and multimodal properties of expensive constrained multimodal optimization problems pose significant challenges for effective problem solving. Therefore, this study proposed a surrogate-assisted two-stage cooperative differential evolution algorithm, aiming to locate multiple optimal solutions at a low computational cost. The algorithm initially established a two-stage master–auxiliary problem cooperative framework to balance the search focus at various stages: the first stage emphasizes finding feasible regions, while the second stage focuses on tracking multiple modalities and locating the optimal solution within each modality. Then, to balance the feasibility, diversity, and accuracy of the solutions, a multi-indicator guided two-stage surrogate model management mechanism was proposed. Furthermore, a two-stage local search strategy for elite solutions was presented, which implements different local search schemes based on the existence of feasible solutions, in order to improve the quality of solutions while mining feasible ones. Finally, the proposed algorithm was compared with five existing expensive constrained surrogate-assisted evolutionary algorithms (SAEAs), one constrained multimodal evolutionary algorithm, and one expensive constrained multimodal SAEA. Experimental results on 21 benchmark problems and 1 rotor airfoil aerodynamic instance show that the proposed algorithm can obtain multiple highly competitive optimal solutions with less computational cost.