A Grouping Genetic Algorithm for graph colouring and exam timetabling

Abstract

It has frequently been reported that pure genetic algorithms for graph colouring are in general outperformed by more conventional methods. There is every reason to believe that this is mainly due to the choice of an unsuitable encoding of solutions. Therefore, an alternative representation, based on the grouping character of the graph colouring problem, was chosen. Furthermore, a fitness function defined on the set of partitions of vertices, guiding the Grouping Genetic Algorithm well in the search, was developed. This algorithm has been applied to a choice of hard-to-colour graph examples, with good results. It has also been extended to the application to real-world timetabling problems. As a by-product, phase transition regions of a class of randomly generated graphs have been located. © Springer-Verlag Berlin Heidelberg 2001.