IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v196y2009i2p440-449.html
   My bibliography  Save this article

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

Author

Listed:
  • Consoli, S.
  • Darby-Dowman, K.
  • Mladenovic, N.
  • Moreno Pérez, J.A.

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.

Suggested Citation

  • Consoli, S. & Darby-Dowman, K. & Mladenovic, N. & Moreno Pérez, J.A., 2009. "Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem," European Journal of Operational Research, Elsevier, vol. 196(2), pages 440-449, July.
    • Handle: RePEc:eee:ejores:v:196:y:2009:i:2:p:440-449
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00295-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Stefan Voßs & Andreas Fink & Cees Duin, 2005. "Looking Ahead with the Pilot Method," Annals of Operations Research, Springer, vol. 136(1), pages 285-302, April.
    2. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhaowei Miao & Feng Yang & Ke Fu & Dongsheng Xu, 2012. "Transshipment service through crossdocks with both soft and hard time windows," Annals of Operations Research, Springer, vol. 192(1), pages 21-47, January.
    2. Thiago Gouveia da Silva & Serigne Gueye & Philippe Michelon & Luiz Satoru Ochi & Lucídio dos Anjos Formiga Cabral, 2019. "A polyhedral approach to the generalized minimum labeling spanning tree problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(1), pages 47-77, March.
    3. Silva, Thiago Gouveia da & Queiroga, Eduardo & Ochi, Luiz Satoru & Cabral, Lucídio dos Anjos Formiga & Gueye, Serigne & Michelon, Philippe, 2019. "A hybrid metaheuristic for the minimum labeling spanning tree problem," European Journal of Operational Research, Elsevier, vol. 274(1), pages 22-34.
    4. Raffaele Cerulli & Ciriaco D'Ambrosio & Domenico Serra & Carmine Sorgente, 2024. "The Budgeted Labeled Minimum Spanning Tree Problem," Mathematics, MDPI, vol. 12(2), pages 1-22, January.
    5. Clímaco, João C.N. & Eugénia Captivo, M. & Pascoal, Marta M.B., 2010. "On the bicriterion - minimal cost/minimal label - spanning tree problem," European Journal of Operational Research, Elsevier, vol. 204(2), pages 199-205, July.
    6. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Maenhout, Broos & Vanhoucke, Mario, 2010. "A hybrid scatter search heuristic for personalized crew rostering in the airline industry," European Journal of Operational Research, Elsevier, vol. 206(1), pages 155-167, October.
    2. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2018. "Minimizing Piecewise-Concave Functions Over Polyhedra," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 580-597, May.
    3. Amina Lamghari & Roussos Dimitrakopoulos & Jacques Ferland, 2015. "A hybrid method based on linear programming and variable neighborhood descent for scheduling production in open-pit mines," Journal of Global Optimization, Springer, vol. 63(3), pages 555-582, November.
    4. Patricia Domínguez-Marín & Stefan Nickel & Pierre Hansen & Nenad Mladenović, 2005. "Heuristic Procedures for Solving the Discrete Ordered Median Problem," Annals of Operations Research, Springer, vol. 136(1), pages 145-173, April.
    5. Ali Shahabi & Sadigh Raissi & Kaveh Khalili-Damghani & Meysam Rafei, 2021. "Designing a resilient skip-stop schedule in rapid rail transit using a simulation-based optimization methodology," Operational Research, Springer, vol. 21(3), pages 1691-1721, September.
    6. Wilson, Duncan T. & Hawe, Glenn I. & Coates, Graham & Crouch, Roger S., 2013. "A multi-objective combinatorial model of casualty processing in major incident response," European Journal of Operational Research, Elsevier, vol. 230(3), pages 643-655.
    7. Felipe, Ángel & Ortuño, M. Teresa & Righini, Giovanni & Tirado, Gregorio, 2014. "A heuristic approach for the green vehicle routing problem with multiple technologies and partial recharges," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 71(C), pages 111-128.
    8. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    9. Véronique François & Yasemin Arda & Yves Crama, 2019. "Adaptive Large Neighborhood Search for Multitrip Vehicle Routing with Time Windows," Transportation Science, INFORMS, vol. 53(6), pages 1706-1730, November.
    10. Tino Henke & M. Grazia Speranza & Gerhard Wäscher, 2014. "The Multi-Compartment Vehicle Routing Problem with Flexible Compartment Sizes," FEMM Working Papers 140006, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    11. Timo Hintsch, 2019. "Large Multiple Neighborhood Search for the Soft-Clustered Vehicle-Routing Problem," Working Papers 1904, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    12. Olcay Polat & Can B. Kalayci & Özcan Mutlu & Surendra M. Gupta, 2016. "A two-phase variable neighbourhood search algorithm for assembly line worker assignment and balancing problem type-II: an industrial case study," International Journal of Production Research, Taylor & Francis Journals, vol. 54(3), pages 722-741, February.
    13. Janssens, Jochen & Van den Bergh, Joos & Sörensen, Kenneth & Cattrysse, Dirk, 2015. "Multi-objective microzone-based vehicle routing for courier companies: From tactical to operational planning," European Journal of Operational Research, Elsevier, vol. 242(1), pages 222-231.
    14. Jiang, Min & Huang, George Q., 2022. "Intralogistics synchronization in robotic forward-reserve warehouses for e-commerce last-mile delivery," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    15. Xiao, Yiyong & Kaku, Ikou & Zhao, Qiuhong & Zhang, Renqian, 2011. "A reduced variable neighborhood search algorithm for uncapacitated multilevel lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 214(2), pages 223-231, October.
    16. Bani, Abderrahman & El Hallaoui, Issmail & Corréa, Ayoub Insa & Tahir, Adil, 2023. "Solving a real-world multi-depot multi-period petrol replenishment problem with complex loading constraints," European Journal of Operational Research, Elsevier, vol. 311(1), pages 154-172.
    17. Roe, R.A. & Smeelen, M. & Hoefeld, C., 2005. "Outsourcing and organizational change : an employee perspective," Research Memorandum 045, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    18. Bruglieri, Maurizio & Liberti, Leo, 2008. "Optimal running and planning of a biomass-based energy production process," Energy Policy, Elsevier, vol. 36(7), pages 2430-2438, July.
    19. Pan, Quan-Ke & Gao, Liang & Li, Xin-Yu & Gao, Kai-Zhou, 2017. "Effective metaheuristics for scheduling a hybrid flowshop with sequence-dependent setup times," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 89-112.
    20. Drezner, Zvi, 2005. "The extended concentric tabu for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 160(2), pages 416-422, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:196:y:2009:i:2:p:440-449. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.