Impact of Ill-Conditioning in RBF Interpolation on the Optimization Performance of Surrogate-Assisted Evolutionary Algorithms

Abstract

Surrogate-assisted evolutionary algorithms (SAEAs) are practical approaches for solving computationally expensive optimization problems, and RBF interpolation is widely used as a surrogate model. However, as sample points become dense during the search, the kernel matrix of the RBF model tends to become ill-conditioned, leading to numerical instability. This study aims to investigate how such ill-conditioning in RBF affects the prediction accuracy of the surrogate model and the overall optimization performance of SAEAs. Specifically, we evaluate the approximation accuracy of RBF surrogates under both ill-conditioned and well-conditioned scenarios during the optimization process. Furthermore, we compare the optimization performance of SAEAs that use RBF models trained under ill-conditioned settings with those using models in which the ill-conditioning has been mitigated.