Towards statistical convergence criteria for mutation-based evolutionary algorithms

This work presents theoretical results on the development of a statistical convergence criterion for evolutionary algorithms. An analytical formula is derived for the probability of success in isotropic Gaussian mutation operators over spherical functions, and statistical criteria are proposed for evaluating, with predefined confidence levels, the convergence of (1+1) and (1+A) Evolution Strategies. The results presented are intended as a first approach to the development of statistically based stop criteria for evolutionary optimizers, and as a contribution for the broader application of statistical modeling to the development and study of population-based algorithms.