A performance indicator-based evolutionary algorithm for expensive high-dimensional multi-/many-objective optimization

Abstract

Surrogate-assisted multi-objective evolutionary algorithms have shown considerable potential for solving optimization problems in which only a small number of expensive function evaluations are available. However, most existing research remains restricted to low-/medium-dimensional problems, with very little attention paid to addressing problems involving decision variables with more than 100 dimensions. In this study, a performance indicator-based evolutionary algorithm (PIEA) is proposed for expensive high-dimensional multi-/many-objective optimization. A surrogate model is employed to approximate the performance indicator rather than directly predicting the objective function, thus simplifying the optimization complexity and mitigating the impact of cumulative errors. An efficient indicator-based optimization strategy emphasising the balance between exploration and exploitation is designed for surrogate-assisted evolution and infill sampling. A history-based selection strategy is implemented to select a suitable indicator from the preset pool for each optimization cycle. An empirical study was conducted on two well-known benchmark suites, and the results demonstrate the superiority of the proposed algorithm over several state-of-the-art algorithms. Moreover, we integrate this concept into a classification-based framework, which further verifies its effectiveness.