A tabu search heuristic for the Equitable Coloring Problem

TL;DR

This paper introduces a tabu search heuristic tailored for the Equitable Coloring Problem, effectively handling the problem's complexity and constraints, and demonstrating strong performance on benchmark instances.

Contribution

The paper develops a novel tabu search heuristic specifically adapted for the Equitable Coloring Problem, incorporating new local search criteria to satisfy equity constraints.

Findings

The heuristic outperforms existing methods on benchmark instances.

Parameter tuning improves the heuristic's effectiveness.

The approach efficiently handles large-sized instances.

Abstract

The Equitable Coloring Problem is a variant of the Graph Coloring Problem where the sizes of two arbitrary color classes differ in at most one unit. This additional condition, called equity constraints, arises naturally in several applications. Due to the hardness of the problem, current exact algorithms can not solve large-sized instances. Such instances must be addressed only via heuristic methods. In this paper we present a tabu search heuristic for the Equitable Coloring Problem. This algorithm is an adaptation of the dynamic TabuCol version of Galinier and Hao. In order to satisfy equity constraints, new local search criteria are given. Computational experiments are carried out in order to find the best combination of parameters involved in the dynamic tenure of the heuristic. Finally, we show the good performance of our heuristic over known benchmark instances.