Genetic Algorithms for Word Problems in Partially Commutative Groups

Matthew Craven

Published 2004-05-20, updated 2007-05-02Version 2

We describe an implementation of a genetic algorithm on partially commutative groups and apply it to the double coset search problem on a subclass of groups. This transforms a combinatorial group theory problem to a problem of combinatorial optimisation. We obtain a method applicable to a wide range of problems and give results which indicate good behaviour of the genetic algorithm, hinting at the presence of a new deterministic solution and a framework for further results.