Ant Colony System for Graph Coloring Problem

Abstract

In this paper, we present a first ACO approach, namely ant colony system (ACS) for the graph colouring problem (GCP). We implemented two strategies of ACS for the GCP; construction strategy and improvement strategy. In construction strategy, the algorithm iteratively constructs feasible solutions. The phase of construction is carried out by a specific constructive method for the problem, that is: recursive largest first (RLF) or DSATUR. These two constructive methods take into account different updates of pheromone trails and the heuristic information. The improvement strategy uses a local search, namely tabu search, to improve the best solution obtained at each iteration of the algorithm. To test the efficiency of our approach, we also implement best-known algorithms for the GCP. That is, scatter search (SS) which, integrates also tabu search (TS), ant system (AS), RLF and DSATUR. This paper report experimental results on some well studied Dimacs graphs. A comparison between the different algorithms shows that the algorithm we called ACS1_R (construction strategy, construction done by RLF) gives best results. It approaches the best colouring algorithms and outperforms some hybrid algorithms on some large instances of the famous Dimacs benchmarks