Enhancing hierarchical surrogate-assisted evolutionary algorithm for high-dimensional expensive optimization via random projection

TL;DR

This paper introduces a hierarchical surrogate-assisted evolutionary algorithm that employs random projection to improve local model accuracy in high-dimensional expensive optimization problems, outperforming existing methods.

Contribution

The study proposes a novel hierarchical SAEA using random projection for local surrogate training, enhancing performance on high-dimensional problems.

Findings

Random projection significantly improves local surrogate model accuracy.

The proposed algorithm outperforms state-of-the-art SAEAs on benchmark functions.

Effective in 100 and 200-dimensional optimization tasks.

Abstract

By remarkably reducing real fitness evaluations, surrogate-assisted evolutionary algorithms (SAEAs), especially hierarchical SAEAs, have been shown to be effective in solving computationally expensive optimization problems. The success of hierarchical SAEAs mainly profits from the potential benefit of their global surrogate models known as "blessing of uncertainty" and the high accuracy of local models. However, their performance leaves room for improvement on highdimensional problems since now it is still challenging to build accurate enough local models due to the huge solution space. Directing against this issue, this study proposes a new hierarchical SAEA by training local surrogate models with the help of the random projection technique. Instead of executing training in the original high-dimensional solution space, the new algorithm first randomly projects training samples onto a set of low-dimensional subspaces, then trains a surrogate model in each subspace, and finally achieves evaluations of candidate solutions by averaging the resulting models. Experimental results on six benchmark functions of 100 and 200 dimensions demonstrate that random projection can significantly improve the accuracy of local surrogate models and the new proposed hierarchical SAEA possesses an obvious edge over state-of-the-art SAEAs