Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem

S. Consoli, K. Darby-Dowman, N. Mladenovic and J.A. Moreno Pérez

European Journal of Operational Research, 2009, vol. 196, issue 2, 440-449

Abstract: 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: Metaheuristics; Combinatorial; optimisation; Minimum; labelling; spanning; tree; Variable; Neighbourhood; Search; Greedy; Randomized; Adaptive; Search; Procedure (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:196:y:2009:i:2:p:440-449

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