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Conference Papers Year : 2014

Markov Chain Analysis of Evolution Strategies on a Linear Constraint Optimization Problem

Abstract

This paper analyses a $(1,\lambda)$-Evolution Strategy, a randomised comparison-based adaptive search algorithm, on a simple constraint optimisation problem. The algorithm uses resampling to handle the constraint and optimizes a linear function with a linear constraint. Two cases are investigated: first the case where the step-size is constant, and second the case where the step-size is adapted using path length control. We exhibit for each case a Markov chain whose stability analysis would allow us to deduce the divergence of the algorithm depending on its internal parameters. We show divergence at a constant rate when the step-size is constant. We sketch that with step-size adaptation geometric divergence takes place. Our results complement previous studies where stability was assumed.
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Dates and versions

hal-00977379 , version 1 (11-04-2014)
hal-00977379 , version 2 (05-12-2014)

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Cite

Alexandre Chotard, Anne Auger, Nikolaus Hansen. Markov Chain Analysis of Evolution Strategies on a Linear Constraint Optimization Problem. IEEE Congress on Evolutionary Computation, http://www.ieee-wcci2014.org/committees.htm, Jul 2014, Beijing, China. ⟨hal-00977379v2⟩
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