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

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 [4], presented at EvoCOP 2007.