Evolution Strategies (ESs) are population-based methods well suited for parallelization. In this paper, we study the convergence of the (μ/μ w ,λ)-ES, an ES with weighted recombination, and derive its optimal convergence rate and optimal μ especially for large population sizes. First, we theoretically prove the log-linear convergence of the algorithm using a scale-invariant adaptation rule for the step-size and minimizing spherical objective functions and identify its convergence rate as the expectation of an underlying random variable. Then, using Monte-Carlo computations of the convergence rate in the case of equal weights, we derive optimal values for μ that we compare with previously proposed rules. Our numerical computations show also a dependency of the optimal convergence rate in ln (λ) in agreement with previous theoretical results. © 2010 Springer-Verlag.
CITATION STYLE
Jebalia, M., & Auger, A. (2010). Log-linear convergence of the scale-invariant (μ/μw, λ)-ES and optimal μ for intermediate recombination for large population sizes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6238 LNCS, pp. 52–62). https://doi.org/10.1007/978-3-642-15844-5_6
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