Global convergence for evolution strategies in spherical problems:: some simple proofs and difficulties

This paper presents simple proofs for the global convergence of evolution strategies in spherical problems. We investigate convergence properties for both adaptive and self-adaptive strategies. Regarding adaptive strategies, the convergence rates are computed explicitly and compared with the results obtained in the so-called "rate-of-progress" theory. Regarding self-adaptive strategies, the computation is conditional to the knowledge of a specific induced Markov chain. An explicit example of chaotic behavior illustrates the complexity in dealing with such chains. In addition to these proofs, this work outlines a number of difficulties in dealing with evolution strategies. (C) 2003 Elsevier B.V. All rights reserved.