Comparison-based optimizers need comparison-based surrogates

Abstract

Taking inspiration from approximate ranking, this paper investigates the use of rank-based Support Vector Machine as surrogate model within CMA-ES, enforcing the invariance of the approach with respect to monotonous transformations of the fitness function. Whereas the choice of the SVM kernel is known to be a critical issue, the proposed approach uses the Covariance Matrix adapted by CMA-ES within a Gaussian kernel, ensuring the adaptation of the kernel to the currently explored region of the fitness landscape at almost no computational overhead. The empirical validation of the approach on standard benchmarks, comparatively to CMA-ES and recent surrogate-based CMA-ES, demonstrates the efficiency and scalability of the proposed approach. © 2010 Springer-Verlag.