Breaking the Symmetry of the Graph Colouring Problem with Genetic Algorithms

The graph colouring problem is a widely studied combinatorial optimisation problem with a highly symmetric solution space. Many heuristics and search algorithms are unattractive for general solution, i.e. they generate poor approximate solutions, because they were originally designed for specific problem instances. Population-based approaches like genetic algorithms do not provide a good alternative because of the danger of recombining good individuals from different regions of the search space (having different symmetries) to produce poor offspring. This paper presents a genetic algorithm that breaks the symmetry of the graph colouring problem by fixing the colours of the nodes in a large clique of the graph. Experiments have been conducted on both structured and random graphs to demonstrate the effectiveness of the approach.