Variable Neighborhood Search for solving Bandwidth Coloring Problem

TL;DR

This paper introduces a variable neighborhood search algorithm for solving bandwidth coloring and multicoloring problems, effectively improving solution quality and demonstrating competitiveness with existing methods.

Contribution

The paper proposes a novel VNS algorithm combining shaking and variable neighborhood descent tailored for BCP and BMCP, enhancing solution search strategies.

Findings

Outperforms previous algorithms on benchmark instances.

Improves 2 out of 33 best known solutions for BMCP.

Demonstrates high competitiveness with state-of-the-art methods.

Abstract

This paper presents a variable neighborhood search (VNS) algorithm for solving bandwidth coloring problem (BCP) and bandwidth multicoloring problem (BMCP). BCP and BMCP are generalizations of the well known vertex coloring problem and they are of a great interest from both theoretical and practical points of view. Presented VNS combines a shaking procedure which perturbs the colors for an increasing number of vertices and a specific variable neighborhood descent (VND) procedure, based on the specially designed arrangement of the vertices which are the subject of re-coloring. By this approach, local search is split in a series of disjoint procedures, enabling better choice of the vertices which are addressed to re-color. The experiments show that proposed method is highly competitive with the state-of-the-art algorithms and improves 2 out of 33 previous best known solutions for BMCP.