On Optimization and Extreme Value Theory

Abstract

We present a statistical study of the distribution of the objective value of solutions (outcomes) obtained by stochastic optimizers. Our results are based on three optimization procedures: random search and two evolution strategies. We study the fit of the outcomes to an extreme value distribution, namely the Weibull distribution through parametric estimation. We discuss the interpretation of the parameters of the estimated extreme value distribution in the context of the optimization problem and suggest that they can be used to characterize the performance of the optimizer.