An Analysis of the RBF Hyperparameter Impact on Surrogate-Assisted Evolutionary Optimization

Computationally expensive optimization problems are often solved using surrogates and a common variant is the radial basis functions (RBF) model. It aggregates several basis functions which all depend on a hyperparameter affecting their individual outputs and consequentially the overall surrogate prediction. However, the optimal value of the hyperparameter is typically unknown and should therefore be calibrated. This raises the question how does the hyperparameter affect the overall optimization search effectiveness (and not just the stand-alone surrogate accuracy) and to what extent is such a calibration beneficial, which is an important consideration both for end-users and algorithm researchers alike. To rigorously address this issue this paper presents an analysis based on an extensive set of numerical experiments with an RBF surrogate-assisted evolutionary algorithm. It follows that the hyperparameter strongly affected performance and that the extent of its impact varied depending on the basis function, objective function modality, and problem dimension. Overall, calibration of the hyperparameter was typically highly beneficial to the search performance while dynamically optimizing the hyperparameter during the search yielded additional performance gains.