A Metaheuristic Approach for the Vertex Coloring Problem

Authors:
Enrico Malaguti;Michele Monaci;Paolo Toth
Affiliations:
Dipartimento di Elettronica, Informatica e Sistemistica, University of Bologna, 40136 Bologna, Italy;Dipartimento di Ingegneria dell'Informazione, University of Padova, 35131 Padova, Italy;Dipartimento di Elettronica, Informatica e Sistemistica, University of Bologna, 40136 Bologna, Italy
Venue:
INFORMS Journal on Computing
Year:
2008

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Abstract

Given an undirected graph G = (V, E), the vertex coloring problem (VCP) requires to assign a color to each vertex in such a way that colors on adjacent vertices are different and the number of colors used is minimized. In this paper, we propose a metaheuristic approach for VCP that performs two phases: the first phase is based on an evolutionary algorithm, whereas the second one is a postoptimization phase based on the set covering formulation of the problem. Computational results on a set of DIMACS instances show that the overall algorithm is able to produce high-quality solutions in a reasonable amount of time. For four instances, the proposed algorithm is able to improve the best-known solution while for almost all the remaining instances, it finds the best-known solution in the literature.