New order-based crossovers for the graph coloring problem

Huge color class redundancy makes the graph coloring problem (GCP) very challenging for genetic algorithms (GAs), and designing effective crossover operators is notoriously difficult. Thus, despite the predominance of population based methods, crossover plays a minor role in many state-of-the-art approaches to solving the GCP. Two main encoding methods have been adopted for heuristic and GA methods: direct encoding, and order based encoding. Although more success has been achieved with direct approaches, algorithms using an order based representation have one powerful advantage: every chromosome decodes as a feasible solution. This paper introduces some new order based crossover variations and demonstrates that they are much more effective on the GCP than other order based crossovers taken from the literature.