High-dimensional expensive optimization by Kriging-assisted multiobjective evolutionary algorithm with dimensionality reduction

Abstract

Surrogate-assisted multi-objective evolutionary algorithms (SA-MOEAs) have made significant progress in solving expensive multi- and many-objective optimization problems. However, most of them perform well in low-dimensional settings but often struggle with high-dimensional problems. The main reason is that some techniques used in SA-MOEAs, like the Kriging model, are ineffective in exploring high-dimensional search spaces. As a result, this research investigates frameworks incorporating dimensionality reduction techniques to conduct modeling and optimization tasks on dimensionality reduction decision spaces. This article uses a singular value decomposition method to map the high-dimensional decision space into a low-dimensional one, then employs a feature fusion strategy to combine low-dimensional features with high-dimensional ones for better representation. Subsequently, these low-dimensional features are used to train the Kriging-based surrogates to select promising solutions within a limited number of function evaluations. In addition, this article provides two types of evolutionary modes to balance exploration and exploitation. Experimental results demonstrate the effectiveness of the proposed SA-MOEA compared to several state-of-the-art algorithms.