On applications of extreme value theory in optimization

Abstract

We present a statistical study of the distribution of the objective value of solutions (outcomes) obtained by stochastic optimizers, applied for continuous objective functions. We discuss the application of extreme value theory for the optimization procedures. A short review of the extreme value theory is presented to understand the investigations. In this chapter three optimization procedures are compared in this context: the random search and two evolution strategies. The outcomes of these optimizers applied to three objective functions are discussed in the context of extreme value theory and the performances of the procedures investigated, analytically and by simulations. In particular, we find that the estimated extreme value distributions and the fit to the outcomes characterize the performance of the optimizer in one single instance. © 2010 Springer-Verlag Berlin Heidelberg.