Neutrality in the Graph Coloring Problem

Marie-Eleonore Marmion (1, 2) , Aymeric Blot (1, 2) , Laetitia Jourdan (1, 2) , Clarisse Dhaenens (1, 2)

1 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
2 LIFL - Laboratoire d'Informatique Fondamentale de Lille

The graph coloring problem is often investigated in the literature. Many insights about many neighboring solutions with the same fitness value are raised but as far as we know, no deep analysis of this neutrality has ever been conducted in the literature. In this paper, we quantify the neutrality of some hard instances of the graph coloring problem. This neutrality property has to be detected as it impacts the search process. Indeed, local optima may belong to plateaus that represents a barrier for local search methods. In this work, we also aim at pointing out the interest of exploiting neutrality during the search. Therefore, a generic local search dedicated to neutral problems, NILS, is performed on several hard instances.

Mots clés: Neutrality; Graph Coloring; Fitness Landscape

Domaines: Combinatoire [math.CO]

Marie-Eleonore Marmion, Aymeric Blot, Laetitia Jourdan, Clarisse Dhaenens. Neutrality in the Graph Coloring Problem. [Research Report] RR-8215, INRIA. 2013, pp.15. ⟨hal-00781001⟩