Evolution Strategies on Noisy Functions: How to Improve Convergence Properties

Evolution Strategies are reported to be robust in the presence of noise which in general hinders the optimization process. In this paper we discuss the innuence of some of the stratey parameters and strategy variants on the convergence process and discuss measures for improvement of the convergence properties. After having a broad look to the theory for the dynamics of a (1,)-ES on a simple quadratic function we numerically investigate the innuence of the parent population size and the introduction of recombination. Finally we compare the eeects of multiple sampling of the objective function versus the enlargment of the population size for the convergence precision as well as the convergence reliability by the example of the multimodal Rastrigins function. 1 Introduction Evolution strategies are claimed to be well suited for experimental optimization 8, 7], where optimal features of a physical system, e.g. the shape of a nozzel 6], are searched for through a series of experiments. Typically a formal model describing the system properties apropriately is not available such that the system has to be viewed as a black box, in the sense that, given a set of parameter values, we observe a corresponding model quality. This complicates the search process, because we can not derive analytical information like gradients directly. Furthermore the observations are usually disturbed, e.g. due to the limited accuracy of experimentation and observation. An optimization strategie to be of any value in this eld must be robust with respect to noise. It is this aspect of evolution strategies that we want to investigate in the following. We consider only the case of real valued objective functions f : M IR n ! IR with additive normal distributed noise, where we call M the search space: F(x) = f(x) + ; (1) where is a random variable with a Gaussian distribution (N(0;)). It is the task to nd a global optimum point x with 8x 2 M : f(x) f(x) ; (2) by observations of F(x).