This article deals with Gaussian process surrogate models for the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES)-several already existing and two by the authors recently proposed models are presented. The work discusses different variants of surrogate model exploitation and focuses on the benefits of employing the Gaussian process uncertainty prediction, especially during the selection of points for the evaluation with a surrogate model. The experimental part of the article thoroughly compares and evaluates the five presented Gaussian process surrogate and six other state-of-the-art optimizers on the COCO benchmarks. The algorithm presented in most detail, DTS-CMA-ES, which combines cheap surrogate-model predictions with the objective function evaluations in every iteration, is shown to approach the function optimum at least comparably fast and often faster than the state-of-the-art black-box optimizers for budgets of roughly 25-100 function evaluations per dimension, in 10- and less-dimensional spaces even for 25-250 evaluations per dimension.
Keywords: Black-box optimization; CMA-ES.; Gaussian processes; evolution strategies; surrogate modeling.