Quality Gain Analysis of the Weighted Recombination Evolution Strategy on General Convex Quadratic Functions

Abstract : Quality gain is the expected relative improvement of the function value in a single step of a search algorithm. Quality gain analysis reveals the dependencies of the quality gain on the parameters of a search algorithm, based on which one can derive the optimal values for the parameters. In this paper, we investigate evolution strategies with weighted recombination on general convex quadratic functions. We derive a bound for the quality gain and two limit expressions of the quality gain. From the limit expressions, we derive the optimal recombination weights and the optimal step-size, and find that the optimal recombination weights are independent of the Hessian of the objective function. Moreover, the dependencies of the optimal parameters on the dimension and the population size are revealed. Differently from previous works where the population size is implicitly assumed to be smaller than the dimension, our results cover the population size proportional to or greater than the dimension. Simulation results show the optimal parameters derived in the limit approximates the optimal values in non-asymptotic scenarios.
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Pré-publication, Document de travail
Submitted to Journal of Theoretical Computer Science 2017
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Soumis le : mercredi 13 décembre 2017 - 11:43:13
Dernière modification le : mardi 17 avril 2018 - 09:04:31

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  • HAL Id : hal-01662568, version 1

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Youhei Akimoto, Anne Auger, Nikolaus Hansen. Quality Gain Analysis of the Weighted Recombination Evolution Strategy on General Convex Quadratic Functions. Submitted to Journal of Theoretical Computer Science 2017. 〈hal-01662568〉

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