Landscape Analysis for Surrogate Models in the Evolutionary Black-Box Context

Surrogate modeling has become a valuable technique for black-box optimization tasks with expensive evaluation of the objective function. In this paper, we investigate the relationships between the predictive accuracy of surrogate models, their settings, and features of the black-box function landscape during evolutionary optimization by the covariance matrix adaptation evolution strategy (CMA-ES) state-of-the-art optimizer for expensive continuous black-box tasks. This study aims to establish the foundation for specific rules and automated methods for selecting and tuning surrogate models by exploring relationships between landscape features and model errors, focusing on the behavior of a specific model within each generation in contrast to selecting a specific algorithm at the outset. We perform a feature analysis process, identifying a significant number of non-robust features and clustering similar landscape features, resulting in the selection of 14 features out of 384, varying with input data selection methods. Our analysis explores the error dependencies of four models across 39 settings, utilizing three methods for input data selection, drawn from surrogate-assisted CMA-ES runs on noiseless benchmarks within the comparing continuous optimizers (COCO) framework.