Authors: Consoli, Sergio
Darby-Dowman, Kenneth
Mladenović, Nenad 
Moreno Pérez, José Andrés
Title: Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem
Journal: European Journal of Operational Research
Volume: 196
Issue: 2
First page: 440
Last page: 449
Issue Date: 16-Jul-2009
Rank: M21
ISSN: 0377-2217
DOI: 10.1016/j.ejor.2008.03.014
This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-hard. A Greedy Randomized Adaptive Search Procedure (GRASP) and a Variable Neighbourhood Search (VNS) are proposed in this paper. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics.
Keywords: Combinatorial optimisation | Greedy Randomized Adaptive Search Procedure | Metaheuristics | Minimum labelling spanning tree | Variable Neighbourhood Search
Publisher: Elsevier
Project: Marie Curie Fellowship for Early Stage Researcher Training (EST-FP6), Grant no. MEST-CT-2004-006724
Brunel University (project NET-ACE)
Spanish Government, Grant no. TIN2005-08404-C04-03
Canary Government, Grant no. PI042005/044

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