Tree Search Methods versus Genetic Algorithms for Over-Constrained Graph Coloring Problems

Constraint satisfaction problems (CSP) are widely studied in a large area of computer sciences, and many problems can be treated as CSPs. Furthermore, many solving methods exist such as complete methods, local search (for example tabu search) and genetic algorithms (GA) [4]. The goal of this paper is to show that for some graph coloring problems, especially over-constrained, using genetic algorithms can be advantageous. In the first part, we show the results of using GA versus tree search methods, to find the minimal number of conflicts for coloring the n-queen problem (from Dimacs Challenge) with less colors than necessary. In the second part we introduce two graphs extracted from the wavelength division multiplexing (WDM) problem in all-optical networks [1], and we show the efficiency of GA to find the optimal (i.e. the minimal number of conflict in number of violated constraints) solution compared to tree search methods. We show that without special tuning of its parameters, GA outperforms these methods.