A multi-model assisted differential evolution algorithm for computationally expensive optimization problems

Abstract

Surrogate models are commonly used to reduce the number of required expensive fitness evaluations in optimizing computationally expensive problems. Although many competitive surrogate-assisted evolutionary algorithms have been proposed, it remains a challenging issue to develop an effective model management strategy to address problems with different landscape features under a limited computational budget. This paper adopts a coarse-to-fine evaluation scheme basing on two surrogate models, i.e., a coarse Gaussian process and a fine radial basis function, for assisting a differential evolution algorithm to solve computationally expensive optimization problems. The coarse Gaussian process model is meant to capture the general contour of the fitness landscape to estimate the fitness and its degree of uncertainty. A surrogate-assisted environmental selection strategy is then developed according to the non-dominance relationship between approximated fitness and estimated uncertainty. Meanwhile, the fine radial basis function model aims to learn the details of the local fitness landscape to refine the approximation quality of the new parent population and find the local optima for real-evaluations. The performance and scalability of the proposed method are extensively evaluated on two sets of widely used benchmark problems. Experimental results show that the proposed method can outperform several state-of-the-art algorithms within a limited computational budget.