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In graph theory, Graph Colouring Problem (GCP) is an assignment of colours tovertices of any given graph such that the colours on adjacent vertices aredifferent. The GCP is known to be an optimization and NP-hard problem.Imperialist Competitive Algorithm (ICA) is a meta-heuristic optimization andstochastic search strategy which is inspired from socio-political phenomenon ofimperialistic competition. The ICA contains two main operators: theassimilation and the imperialistic competition. The ICA has excellentcapabilities such as high convergence rate and better global optimumachievement. In this research, a discrete version of ICA is proposed to dealwith the solution of GCP. We call this algorithm as the DICA. The performanceof the proposed method is compared with Genetic Algorithm (GA) on sevenwell-known graph colouring benchmarks. Experimental results demonstrate thesuperiority of the DICA for the benchmarks. This means DICA can produce optimaland valid solutions for different GCP instances.

Graph Colouring Problem Based on Discrete Imperialist Competitive Algorithm