Computers & Operations Research 33 (2006) 2547 – 2562 www.elsevier.com/locate/cor A survey of local search methods for graph coloring Philippe Galinier a , ∗ , Alain Hertz b a CRT-Ecole Polytechnique, 3000 chemin de la Cote Sainte-Catherine, Montreal, Que., H3T 2A7, Canada b GERAD-Ecole Polytechnique, 3000 chemin de la Cote Sainte-Catherine, Montreal, Que., H3T 2A7, Canada Available online 12 October 2005 Abstract Tabucol is a tabu search algorithm that tries to determine whether the vertices of a given graph can be colored with a fixed number k of colors such that no edge has both endpoints with the same color. This algorithm was proposed in 1987, one year after Fred Glover’s article that launched tabu search. While more performing local search algorithms have now been proposed, Tabucol remains very popular and is often chosen as a subroutine in hybrid algorithms that combine a local search with a population based method. In order to explain this unfailing success, we make a thorough survey of local search techniques for graph coloring problems, and we point out the main differences between all these techniques.  2005 Elsevier Ltd. All rights reserved. 1. Introduction The graph coloring problem is a famous difficult combinatorial optimization problem. Examples of applications include time tabling and scheduling [1,2], radio frequency assignment [3], computer register allocation [4,5], and printed circuit board testing [6]. While exact algorithms can solve instances with up to 100 vertices, heuristic methods are needed for larger instances. Most recent graph coloring heuristics are either local search methods or hybrid algorithms that combine a local search with a population based algorithm. The objective of this paper is to present a survey of metaheuristics proposed for graph coloring. In particular we analyze in detail local search metaheuristics. One of the first local search methods that has been proposed for solving graph coloring problems is Tabucol [7], a tabu search algorithm that was developed in 1986 and published in 1987, one year after Fred ∗ Corresponding author. E-mail addresses: philippe.galinier@polymtl.ca (P. Galinier), alain.hertz@gerad.ca (A. Hertz). 0305-0548/$ - see front matter  2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2005.07.028