Modified cuckoo optimization algorithm (MCOA) to solve graph coloring problem

Abstract

In recent years, various heuristic optimization methods have been developed. Many of these methods are inspired by swarm behaviors in nature, such as particle swarm optimization (PSO), firefly algorithm (FA) and cuckoo optimization algorithm (COA). Recently introduced COA, has proven its excellent capabilities, such as faster convergence and better global minimum achievement. In this paper a new approach for solving graph coloring problem based on COA was presented. Since COA at first was presented for solving continuous optimization problems, in this paper we use the COA for the graph coloring problem, we need a discrete COA. Hence, to apply COA to discrete search space, the standard arithmetic operators such as addition, subtraction and multiplication existent in COA migration operator based on the distance's theory needs to be redefined in the discrete space. Redefinition of the concept of the difference between the two habitats as the list of differential movements, COA is equipped with a means of solving the discrete nature of the non-permutation. A set of graph coloring benchmark problems are solved and its performance is compared with some well-known heuristic search methods. The obtained results confirm the high performance of the proposed method.