An Ensemble Surrogate-Based Framework for Expensive Multiobjective Evolutionary Optimization

Surrogate-assisted evolutionary algorithms (SAEAs) have become very popular for tackling computationally expensive multiobjective optimization problems (EMOPs), as the surrogate models in SAEAs can approximate EMOPs well, thereby reducing the time cost of the optimization process. However, with the increased number of decision variables in EMOPs, the prediction accuracy of surrogate models will deteriorate, which inevitably worsens the performance of SAEAs. To deal with this issue, this article suggests an ensemble surrogate-based framework for tackling EMOPs. In this framework, a global surrogate model is trained under the entire search space to explore the global area, while a number of surrogate submodels are trained under different search subspaces to exploit the subarea, so as to enhance the prediction accuracy and reliability. Moreover, a new infill sampling criterion is designed based on a set of reference vectors to select promising samples for training the models. To validate the generality and effectiveness of our framework, three state-of-the-art evolutionary algorithms [nondominated sorting genetic algorithm III (NSGA-III), multiobjective evolutionary algorithm based on decomposition with differential evolution (MOEA/D-DE) and reference vector-guided evolutionary algorithm (RVEA)] are embedded, which significantly improve their performance for solving most of the test EMOPs adopted in this article. When compared to some competitive SAEAs for solving EMOPs with up to 30 decision variables, the experimental results also validate the advantages of our approach in most cases.

I. Introduction

In engineering applications, there exist some multiobjective optimization problems (MOPs) that require the simultaneous optimization of multiple (often conflicting) objectives. As multiobjective evolutionary algorithms (MOEAs) can find a set of Pareto-optimal solutions in a single run, they become an effective and popular tool for tackling MOPs [1]. Based on the selection criteria, most MOEAs can be classified into three main categories [2]: 1) Pareto-based MOEAs [3], [4]; 2) decomposition-based MOEAs [5], [6]; and 3) indicator-based MOEAs [7], [8]. These traditional MOEAs generally assume a sufficient number of function evaluations, so that the population can converge. However, for some MOPs modeled from practical applications, e.g., finite element analysis [9], computational fluid dynamics [10], and computational electromagnetics [11], the function evaluations require computationally expensive simulations, which consume a considerable amount of time or material resources. These problems are often called expensive MOPs (EMOPs) [12].