A Novel Bi-objective Genetic Algorithm for the Graph Coloring Problem

Graph coloring problem is a classical NP-hard combinatorial optimization problem. In this paper, a new bi-objective model for the coloring problem is presented. Based on this new model, a bi-objective genetic algorithm is proposed which employs effective crossover and simple mutation operator as the genetic operators. The global convergence of the proposed algorithm to globally optimal set with probability one is proved. Experimental results demonstrate that the proposed algorithm is expected.