Abstract
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.
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Jebalia, M., Auger, A. (2010). Log-Linear Convergence of the Scale-Invariant (μ/μ w ,λ)-ES and Optimal μ for Intermediate Recombination for Large Population Sizes. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds) Parallel Problem Solving from Nature, PPSN XI. PPSN 2010. Lecture Notes in Computer Science, vol 6238. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15844-5_6
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DOI: https://doi.org/10.1007/978-3-642-15844-5_6
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