A novel transformation to improve the robustness of value-based surrogate models

Abstract

Surrogate-assisted evolutionary algorithms (SAEAs) are popular choices for solving computationally expensive problems. Widely used surrogate models, such as radial basis functions (RBFs) and Gaussian Processes (GPs), are value-based models, which means that they use fitness values for training; therefore, their predictive accuracy, and consequently the performance of SAEAs that use them, depend on and are potentially sensitive to order-preserving transformations (OPTs) of the fitness function, compromising the robustness and potentially efficiency of the optimization framework. This study proposes a parametric transformation, called sp2log, to mitigate this inherent shortcoming of these surrogates. The parameters of sp2log are tuned alongside other hyperparameters of the surrogate. The efficacy of sp2log is evaluated across three popular surrogates on a comprehensive test suite. This assessment involves subjecting each problem's fitness landscape to various OPTs with diverse degrees of non-linearity. Through comprehensive simulations, our findings demonstrate that integrating sp2log significantly improves the robustness of these surrogates to OPTs of the fitness landscape. Moreover, the merits of sp2log remain consistent (i) when the problem dimensionality increases and (ii) for diverse and reasonable values of data size. Finally, the effectiveness of sp2log is validated when integrated into a recent surrogate-assisted evolutionary algorithm (SAEA).