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An Evolutionary Algorithm for the Solution of Two-Variable Word Equations in Partially Commutative Groups

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Recent Advances in Evolutionary Computation for Combinatorial Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 153))

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Summary

We describe an implementation of an evolutionary algorithm on partially commutative groups and apply it to solve certain two-variable word equations on a subclass of these groups, transforming a problem in combinatorial group theory into one of combinatorial optimisation. We give results which indicate efficient and successful behaviour of the evolutionary algorithm, hinting at the presence of a new degenerate deterministic solution and a framework for further results in similar group-theoretic problems. This paper is an expanded and updated version of [14], presented at EvoCOP 2007.

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Carlos Cotta Jano van Hemert

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© 2008 Springer-Verlag Berlin Heidelberg

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Craven, M.J. (2008). An Evolutionary Algorithm for the Solution of Two-Variable Word Equations in Partially Commutative Groups. In: Cotta, C., van Hemert, J. (eds) Recent Advances in Evolutionary Computation for Combinatorial Optimization. Studies in Computational Intelligence, vol 153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70807-0_1

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  • DOI: https://doi.org/10.1007/978-3-540-70807-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70806-3

  • Online ISBN: 978-3-540-70807-0

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