A Surrogate-Assisted Evolutionary Algorithm for Seeking Multiple Solutions of Expensive Multimodal Optimization Problems

Surrogate-assisted evolutionary algorithms for expensive optimization problems have gained considerable attention in recent years. In many real-world optimization problems, we may face expensive optimization problems with multiple optimal solutions. Locating multiple optima for such expensive problems is qualitatively challenging. This study proposes a surrogate-assisted differential evolution based on region decomposition to seek multiple optima for expensive multimodal optimization problems. In this study, we have designed three major components: 1) the adaptive region decomposition, 2) the multilayer perceptron-based global surrogate, and 3) the self-adaptive gradient descent-based local search. First, the improved adaptive region decomposition detects promising subregions at the beginning phase, and continuously discards inferior subregions successively. Second, the multilayer perceptron-based surrogate and self-adaptive gradient-based mutation work in a collaborative manner on distinct sub-populations to seek multiple optimal solutions. Overall, an attempt has been made to solve expensive multimodal optimization problems. Systematic experiments on 20 test functions show the encouraging and promising performance of our proposed approach.