Evolution Strategies under the 1/5 Success Rule

Alexandru Agapie ()
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Alexandru Agapie: Department of Applied Mathematics, Faculty of Economic Cybernetics, Statistics and Informatics, Bucharest University of Economic Studies, Calea Dorobantilor 15-17, 010552 Bucharest, Romania

Mathematics, 2022, vol. 11, issue 1, 1-20

Abstract: For large space dimensions, the log-linear convergence of the elitist evolution strategy with a 1/5 success rule on the sphere fitness function has been observed, experimentally, from the very beginning. Finding a mathematical proof took considerably more time. This paper presents a review and comparison of the most consistent theories developed so far, in the critical interpretation of the author, concerning both global convergence and the estimation of convergence rates. I discuss the local theory of the one-step expected progress and success probability for the (1+1) ES with a normal/uniform distribution inside the sphere mutation, thereby minimizing the SPHERE function, but also the adjacent global convergence and convergence rate theory, essentially based on the 1/5 rule. Small digressions into complementary theories (martingale, irreducible Markov chain, drift analysis) and different types of algorithms (population based, recombination, covariance matrix adaptation and self-adaptive ES) complete the review.

Keywords: continuous evolutionary algorithm; Markov chain; martingale; drift analysis; Wald’s equation; computational complexity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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