Toward a Theory of Evolution Strategies: Some Asymptotical Results from the (1,+ )-Theory

A method for the determination of the progress rate and the probability of success for the Evolution Strategy (ES) is presented. The new method is based on the asymptotical behavior of the -distribution and yields exact results in the case of infinite-dimensional parameter spaces. The technique is demonstrated for the (l,+ ) ES using a spherical model including noisy quality functions. The results are used to discuss the convergence behavior of the ES.