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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.
Cited literature [11 references]
https://hal.inria.fr/hal-00977379
Contributor : Alexandre Chotard <>
Submitted on : Friday, December 5, 2014 - 2:44:17 PM
Last modification on : Wednesday, September 16, 2020 - 5:09:18 PM
Long-term archiving on: : Monday, March 9, 2015 - 7:55:29 AM
Contributor : Alexandre Chotard <>
Submitted on : Friday, December 5, 2014 - 2:44:17 PM
Last modification on : Wednesday, September 16, 2020 - 5:09:18 PM
Long-term archiving on: : Monday, March 9, 2015 - 7:55:29 AM
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