A grouping genetic algorithm for coloring the edges of graphs

Abstract

This paper investigates applications of heuristic techniques for solving the edge coloring problem, which seeks the minimum number of colors to color the edges of a graph such that no two adjacent edges (edges that share a common vertex) get the same color. Except for special cases, such as bipartite graphs, the edge coloring problem is NP-complete. Thus, the search for exact algorithms is replaced by the investigation of approximation and heuristic algorithms (unless P=NP). In this work, we consider both simple graphs and multigraphs, and compare three heuristics for the edge coloring problem. The first is a greedy algorithm, and the two others are genetic algorithms: a genetic algorithm that makes use of LibGA and a grouping genetic algorithm. Our results show that the grouping genetic algorithm outperforms the greedy heuristic for many problem instances. This paper supports the claim that the edge coloring problem is more amenable to grouping genetic algorithms. © 2000 ACM.