Annals of Operations Research

, 172:71

Variable neighbourhood search for the minimum labelling Steiner tree problem

Authors

    • CARISMA and NET-ACE, School of Information Systems, Computing and MathematicsBrunel University
  • Kenneth Darby-Dowman
    • CARISMA and NET-ACE, School of Information Systems, Computing and MathematicsBrunel University
  • Nenad Mladenović
    • CARISMA and NET-ACE, School of Information Systems, Computing and MathematicsBrunel University
  • José Andrés Moreno-Pérez
    • Facultad de Matemáticas, DEIOC, IUDRUniversidad de La Laguna
Article

DOI: 10.1007/s10479-008-0507-y

Cite this article as:
Consoli, S., Darby-Dowman, K., Mladenović, N. et al. Ann Oper Res (2009) 172: 71. doi:10.1007/s10479-008-0507-y

Abstract

We present a study on heuristic solution approaches to the minimum labelling Steiner tree problem, an NP-hard graph problem related to the minimum labelling spanning tree problem. Given an undirected labelled connected graph, the aim is to find a spanning tree covering a given subset of nodes of the graph, whose edges have the smallest number of distinct labels. Such a model may be used to represent many real world problems in telecommunications and multimodal transportation networks. Several metaheuristics are proposed and evaluated. The approaches are compared to the widely adopted Pilot Method and it is shown that the Variable Neighbourhood Search that we propose is the most effective metaheuristic for the problem, obtaining high quality solutions in short computational running times.

Keywords

MetaheuristicsCombinatorial optimizationMinimum labelling Steiner tree problemVariable neighbourhood searchGraphs

Copyright information

© Springer Science+Business Media, LLC 2009