You can manage bookmarks using lists, please log in to your user account for this.
Media type:
E-Article
Title:
Evolution Strategies under the 1/5 Success Rule
Contributor:
Agapie, Alexandru
Published:
MDPI AG, 2022
Published in:
Mathematics, 11 (2022) 1, Seite 201
Language:
English
DOI:
10.3390/math11010201
ISSN:
2227-7390
Origination:
Footnote:
Description:
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.