Neutrality in the Graph Coloring Problem

TL;DR

This paper investigates the neutrality property in hard instances of the graph coloring problem, quantifies its impact on local search algorithms, and proposes a neutral-aware local search method called NILS.

Contribution

It provides the first deep analysis of neutrality in graph coloring, quantifies its effects, and introduces a new local search algorithm tailored for neutral landscapes.

Findings

Neutrality significantly affects local search performance.

NILS outperforms traditional local search on neutral problem instances.

Neutrality can be exploited to improve search efficiency.

Abstract

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.