Using Differential Evolution for the Graph Coloring

TL;DR

This paper explores the application of differential evolution, a method for continuous optimization, to the combinatorial problem of graph coloring, proposing a hybrid algorithm that shows promising results compared to existing heuristics.

Contribution

It introduces a hybrid self-adaptive differential evolution algorithm tailored for graph 3-coloring, demonstrating its competitiveness with state-of-the-art heuristics.

Findings

Differential evolution can be adapted for graph coloring.

The proposed hybrid algorithm performs comparably to top heuristics.

Results suggest differential evolution could be a future tool for combinatorial problems.

Abstract

Differential evolution was developed for reliable and versatile function optimization. It has also become interesting for other domains because of its ease to use. In this paper, we posed the question of whether differential evolution can also be used by solving of the combinatorial optimization problems, and in particular, for the graph coloring problem. Therefore, a hybrid self-adaptive differential evolution algorithm for graph coloring was proposed that is comparable with the best heuristics for graph coloring today, i.e. Tabucol of Hertz and de Werra and the hybrid evolutionary algorithm of Galinier and Hao. We have focused on the graph 3-coloring. Therefore, the evolutionary algorithm with method SAW of Eiben et al., which achieved excellent results for this kind of graphs, was also incorporated into this study. The extensive experiments show that the differential evolution could become a competitive tool for the solving of graph coloring problem in the future.