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A rigorous analysis of the compact genetic algorithm for linear functions

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Abstract

Estimation of distribution algorithms (EDAs) solve an optimization problem heuristically by finding a probability distribution focused around its optima. Starting with the uniform distribution, points are sampled with respect to this distribution and the distribution is changed according to the function values of the sampled points. Although there are many successful experiments suggesting the usefulness of EDAs, there are only few rigorous theoretical results apart from convergence results without time bounds. Here we present first rigorous runtime analyses of a simple EDA, the compact genetic algorithm (cGA), for linear pseudo-Boolean functions on n variables. We prove a general lower bound for all functions and a general upper bound for all linear functions. Simple test functions show that not all linear functions are optimized in the same runtime by the cGA.

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Acknowledgements

I thank Jens Jägersküpper, Tobias Storch, Ingo Wegener, and Carsten Witt for valuable advice and discussions.

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Authors and Affiliations

  1. LS Informatik 2, Universität Dortmund, 44221, Dortmund, Germany

    Stefan Droste

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  1. Stefan Droste
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Correspondence to Stefan Droste.

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This research was partly supported by the Deutsche Forschungsgemeinschaft as part of the Collaborative Research Center “Computational Intelligence”(531).

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Droste, S. A rigorous analysis of the compact genetic algorithm for linear functions. Nat Comput 5, 257–283 (2006). https://doi.org/10.1007/s11047-006-9001-0

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