Scaling Up Radial Basis Function for High-Dimensional Expensive Optimization Using Random Projection

Abstract

Surrogate model assisted evolutionary algorithms (SAEAs) have attracted much research attention in solving computationally expensive optimization problems. They show excellent performance on low-dimensional optimization problems by saving a large number of real fitness evaluations, but generally fail on high-dimensional problems due to the contradiction between the huge solution space and the limited computational resources. To alleviate this issue, this study attempts to scale up radial basis function (RBF), which is a kind of widely used surrogate model, by taking advantage of the random projection (RP) technique, and thus develops a RP-based RBF (RP-RBF). Different from existing methods that directly train RBF in the original solution space, RP-RBF first randomly projects the original high-dimensional solution space onto many low-dimensional subspaces, and then trains an RBF in each subspace. The resulting low-dimensional RBFs are finally used together to approximate the fitness values of new candidate solutions. The introduction of RP greatly reduces the number of training samples required by RBF on the one hand, and helps RBF still capture the main characteristics of the original problems on the other hand. To verify the effectiveness of RP-RBF, this study integrates it with a differential evolution (DE) and develops a novel SAEA named RP-RBF-DE. Experimental results on a set of 12 benchmark functions demonstrate that RP-RBF significantly improves the accuracy of the traditional RBF and RP-RBF-DE outperforms the traditional DE and a general RBF-assisted DE.