Surrogate-assisted evolutionary algorithm with stage-adaptive infill sampling criterion for expensive multimodal multi-objective optimization

Abstract

The key issue in handling expensive multimodal multi-objective optimization problems is to balance convergence and diversity in both the decision and objective spaces with limited function evaluations available. To tackle this issue, this paper proposes a surrogate-assisted multimodal multi-objective evolutionary algorithm with stage-adaptive infill sampling criterion. In the proposed algorithm, a multi-surrogate cooperative framework is developed, where multiple extreme gradient boosting models are used to approximate the objective functions for replacing real function evaluations, and a self-organizing map (SOM) network is used to learn the topologies of Pareto sets in the decision space and corresponding features in the objective space for reducing the approximation errors. Then, a stage-adaptive infill sampling criterion is designed to select the most suitable candidates for expensive function evaluations. Specifically, in the first stage, a convergence-first infill sampling criterion is used to accelerate convergence to the global Pareto front; In the second stage, an indicator-based infill sampling criterion according to neuron weights of the SOM network and a diversity-based infill sampling criterion are used to improve diversity in decision and objective spaces. Experimental results on two benchmark test suites demonstrate the competitiveness of the proposed algorithm against eight state-of-the-art methods.