Two novel evolutionary formulations of the graph coloring problem

TL;DR

This paper presents two innovative evolutionary approaches for graph coloring, one focusing on acyclic orientations and the other evolving a universal coloring program for graph classes, demonstrating competitive performance on benchmark graphs.

Contribution

Introduces two new evolutionary formulations for graph coloring, one based on acyclic orientations and the other on evolving a universal coloring program for graph classes.

Findings

Both heuristics are competitive with existing methods.

The acyclic orientation approach leverages graph structure.

The program-evolving approach generalizes across graph classes.

Abstract

We introduce two novel evolutionary formulations of the problem of coloring the nodes of a graph. The first formulation is based on the relationship that exists between a graph's chromatic number and its acyclic orientations. It views such orientations as individuals and evolves them with the aid of evolutionary operators that are very heavily based on the structure of the graph and its acyclic orientations. The second formulation, unlike the first one, does not tackle one graph at a time, but rather aims at evolving a `program' to color all graphs belonging to a class whose members all have the same number of nodes and other common attributes. The heuristics that result from these formulations have been tested on some of the Second DIMACS Implementation Challenge benchmark graphs, and have been found to be competitive when compared to the several other heuristics that have also been tested on those graphs.