Variations on Memetic Algorithms for Graph Coloring Problems

Laurent Moalic (1) , Alexandre Gondran (2)

1 IRTES - SET - Laboratoire Systèmes et Transports
2 MAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l'Aérien

Graph vertices coloring with a given number of colors is a famous and much-studied NP-complete problem. The best methods to solve this problem are hybrid algorithms such as memetic algorithms [Galinier99, Lu10, Wu12] or quantum annealing [Titiloye11a, Titiloye11b, Titiloye12]. Those hybrid algorithms use a powerful local search inside a population-based algorithm. The balance between intensification and diversification is essential for those metaheuristics but difficult to archieve. Customizing metaheuristics takes long time and is one of the main weak points of these approaches. This paper studies the impact of the increase and the decrease of diversification in one of the most effective algorithms known: the Hybrid Evolutionary Algorithm (HEA) from Galinier and Hao [Galinier99]. We then propose a modification of this memetic algorithm in order to work with a population of only two individuals. This new algorithm more effectively manages the correct 'dose' of diversification to add into the included local search - TabuCol [Hertz87] in the case of the HEA. It has produced several good results for the well-known DIMACS benchmark graphs, such as 47-colorings for DSJC500.5, 82-colorings for DSJC1000.5, 222-colorings for DSJC1000.9 and 81-colorings for flat1000\_76\_0, which have so far only been produced by quantum annealing [Titiloye12] in 2012 with massive multi-CPUs.

Mots clés: coloring; graph; tabu search; memetic; evolutionary

Domaines: Recherche opérationnelle [math.OC]; Optimisation et contrôle [math.OC]

Laurent Moalic, Alexandre Gondran. Variations on Memetic Algorithms for Graph Coloring Problems. 2014. ⟨hal-00925911v1⟩