Graph Colouring Problem Based on Discrete Imperialist Competitive Algorithm

In graph theory, Graph Colouring Problem (GCP) is an assignment of colours to vertices of any given graph such that the colours on adjacent vertices are different. The GCP is known to be an optimization and NP-hard problem. Imperialist Competitive Algorithm (ICA) is a meta-heuristic optimization and stochastic search strategy which is inspired from socio-political phenomenon of imperialistic competition. The ICA contains two main operators: the assimilation and the imperialistic competition. The ICA has excellent capabilities such as high convergence rate and better global optimum achievement. In this research, a discrete version of ICA is proposed to deal with the solution of GCP. We call this algorithm as the DICA. The performance of the proposed method is compared with Genetic Algorithm (GA) on seven well-known graph colouring benchmarks. Experimental results demonstrate the superiority of the DICA for the benchmarks. This means DICA can produce optimal and valid solutions for different GCP instances.