An ensemble surrogate-assisted adaptive reference point guided evolutionary algorithm for expensive many-objective irregular problem

Abstract

Surrogate-assisted evolutionary algorithms (SAEAs) are one effective method for solving expensive optimization problems. However, there has been little attention to expensive many-objective irregular problems. To address this issue, we propose an ensemble surrogate-assisted adaptive reference point guided evolutionary algorithm for dealing with expensive many-objective irregular problems. Firstly, a reference point adaptation method is adopted in the proposed algorithm to adjust the reference point for calculating indicators and guide the search process. Secondly, the enhanced inverted generational distance (IGD-NS) indicator is improved by using the modified distance to obey the Pareto compliant, which can maintain a balance between convergence and diversity in the population. Thirdly, an infill sampling criterion is designed to select elite individuals for re-evaluation in case the Pareto fronts are irregular. The added elite individuals update the ensemble surrogate model, which is expected to assist the algorithm in efficiently finding the Pareto optimal solutions in a limited computational resource. Finally, experimental results on several benchmark problems demonstrate that the proposed algorithm performs well in solving expensive many-objective optimization problems with irregular and regular Pareto fronts. A real-world application problem also confirms the effectiveness and competitiveness of the proposed algorithm.