A Kriging-Assisted Evolutionary Algorithm with Two-Stage Environmental Selection Strategy for Expensive Multimodal Multi-Objective Optimization

Plenty of evolutionary algorithms have been developed for solving multimodal multi-objective optimization problems. However, most existing multimodal multi-objective evolutionary algorithms cannot meet expectations in complex and time-consuming situations due to a limited number of real fitness evaluations are been implemented. Therefore, a Kriging-assisted evolutionary algorithm with two-stage environmental selection strategy is developed for expensive multimodal multi-objective optimization. With the help of Kriging model, the future evolutionary information of the population is explored through simulated evolution at each generation. In addition, a two-stage environmental selection strategy is employed to generate offspring population. In the environmental selection, an improved dual clustering method is used to choose promising solutions from the historical data of simulated evolution in two stages. The experimental results demonstrate that performance of proposed algorithm is more superior than its competing algorithms on ten benchmark problems.