A cellular learning automata-based algorithm for solving the vertex coloring problem

Vertex coloring problem is a combinatorial optimization problem in which a color is assigned to each vertex of the graph such that no two adjacent vertices have the same color. Cellular learning automata (CLA) is an effective probabilistic learning model combining cellular automata and learning automata. Irregular cellular learning automata (ICLA) is a generalization of cellular learning automata in which the restriction of rectangular grid structure in traditional CLA is removed. In this paper, an ICLA-based algorithm is proposed for finding a near optimal solution of the vertex coloring problem. The proposed coloring algorithm is a fully distributed algorithm in which each vertex chooses its optimal color based solely on the colors selected by its adjacent vertices. The time complexity of the proposed algorithm is computed for finding a 11-∊ optimal solution of the vertex coloring problem in an arbitrary graph. To show the superiority of our proposed algorithm over the existing methods, simulation experiments have been conducted. The obtained results show that the proposed algorithm outperforms the others in terms of the required number of colors and running time of algorithm.

Research highlights
► Using irregular cellular learning automata for solving the vertex coloring problem.
► Solving the vertex coloring problem based solely on the local information of the neighboring vertices.
► Computing the lower and upper bounds for the proposed vertex coloring algorithm.
► Comparing with the best existing vertex coloring approaches.