A memetic algorithm for the minimum sum coloring problem

TL;DR

This paper introduces a memetic algorithm for the Minimum Sum Coloring problem that combines tabu search and crossover operators, achieving competitive results and improving known solutions on benchmark instances.

Contribution

The paper proposes a novel memetic algorithm with a tabu search and multi-parent crossover for MSCP, outperforming existing algorithms on several benchmarks.

Findings

Improved best known results for 17 instances.

Provided new upper bounds for 18 instances.

Achieved competitive results on 77 benchmark instances.

Abstract

Given an undirected graph $G$, the Minimum Sum Coloring problem (MSCP) is to find a legal assignment of colors (represented by natural numbers) to each vertex of $G$ such that the total sum of the colors assigned to the vertices is minimized. This paper presents a memetic algorithm for MSCP based on a tabu search procedure with two neighborhoods and a multi-parent crossover operator. Experiments on a set of 77 well-known DIMACS and COLOR 2002-2004 benchmark instances show that the proposed algorithm achieves highly competitive results in comparison with five state-of-the-art algorithms. In particular, the proposed algorithm can improve the best known results for 17 instances. We also provide upper bounds for 18 additional instances for the first time.