Expensive Multiobjective Evolutionary Optimization Assisted by Dominance Prediction

Abstract

We propose a new surrogate-assisted evolutionary algorithm for expensive multiobjective optimization. Two classification-based surrogate models are used, which can predict the Pareto dominance relation and <inline-formula> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula>-dominance relation between two solutions, respectively. To make such surrogates as accurate as possible, we formulate dominance prediction as an imbalanced classification problem and address this problem using deep learning techniques. Furthermore, to integrate the surrogates based on dominance prediction with multiobjective evolutionary optimization, we develop a two-stage preselection strategy. This strategy aims to select a promising solution to be evaluated among those produced by genetic operations, taking proper account of the balance between convergence and diversity. We conduct an empirical study on a number of well-known multiobjective and many-objective benchmark problems, over a relatively small number of function evaluations. Our experimental results demonstrate the superiority of the proposed algorithm compared with several representative surrogate-assisted algorithms.