DESIGN OF A SURROGATE ASSISTED (1 + 1)-ES

Abstract

The information gained from previous iterations of an evolution strategy (ES) can be used to create a surrogate model based on the real objective function. While surrogate models are not as accurate as objective functions, they could distinguish more promising candidate solutions. To develop a better understanding of surrogate-assisted ESs, we simulate the behavior of a surrogate-assisted (1 + 1)-ES on the quadratic sphere. These simulations are made using a noisy objective function as the surrogate model. We introduce some measures to quantify the trade-off of saving expensive objective function evaluations at the cost of taking poorer steps. Using these findings, we present a mechanism to adapt the step-size based on model accuracy. We empirically evaluate the performance of this step-size adaptation mechanism in surrogate-assisted (1 + 1)-ES and compare it to that of the canonical (1 + 1)-ES on several simple test functions.