Objective-Constraint Mutual-Guided Surrogate-Based Particle Swarm Optimization for Expensive Constrained Multimodal Problems

Expensive constraint multimodal optimization problems (ECMMOPs) have such characteristics as expensive objectives and constraints, and multiple optimal modalities simultaneously, which pose severe challenges to evolutionary optimization methods. This article studies an objective-constraint mutual-guided surrogate-assisted particle swarm optimization algorithm for the kind of problem, aiming to discover multiple competing feasible optimal solutions at a lower calculation cost. The algorithm designs first a new two-layer cooperative surrogate model framework based on heterogeneous database to effectively adjust the prediction accuracies of objective surrogates and constraint surrogates on different search regions. An objective-constraint mutual-guided partial evaluation strategy (O-C-PES) is developed to generate high-quality infilling samples for objective and constraint surrogates, respectively, based on which the number of unnecessary real evaluations can be significantly reduced. Moreover, a position feature-guided hybrid update mechanism (PF-HUM) is proposed to find more optimal solutions by searching excellent infeasible and feasible areas at the same time, and a feasible ratio-driven local search (FR-LS) strategy is proposed to improve the algorithm’s exploitation. Compared with four existing surrogate-assisted evolutionary algorithms (EAs) and one constraint multimodal EAs on 21 benchmark problems and three engineering instances, experiment results show that the proposed algorithm can simultaneously obtain multiple highly-competitive feasible optimal solutions with less computational cost.