Adaptive Function Value Warping for Surrogate Model Assisted Evolutionary Optimization

Abstract

Invariance to strictly monotonic transformations of the objective function is an important feature in the design of black-box optimization algorithms. For this reason, ordinal surrogates have been established as an attractive class of models for integration into comparison-based optimizers. The recovery of this desirable property has not been explored for value-based surrogates. In this thesis, we adopt warping as a strategy to partially regain invariance lost by value-based models and propose a simple warped Gaussian process assisted covariance matrix adaptation evolution strategy. The algorithm is validated on families of parametrized, unimodal test problems and its performance compared with those of several related strategies. More intensive surrogate model exploitation is empirically demonstrated to benefit performance on ill-conditioned test problems. The simplicity and competitive performance of the proposed approach make it an appealing choice as a baseline for the evaluation of comparators on unimodal test problems.