IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v75y2020i2d10.1007_s10589-019-00154-1.html
   My bibliography  Save this article

Empirical study of exact algorithms for the multi-objective spanning tree

Author

Listed:
  • I. F. C. Fernandes

    (Universidade Federal do Rio Grande do Norte)

  • E. F. G. Goldbarg

    (Universidade Federal do Rio Grande do Norte)

  • S. M. D. M. Maia

    (Universidade Federal do Rio Grande do Norte)

  • M. C. Goldbarg

    (Universidade Federal do Rio Grande do Norte)

Abstract

The multi-objective spanning tree (MoST) is an extension of the minimum spanning tree problem (MST) that, as well as its single-objective counterpart, arises in several practical applications. However, unlike the MST, for which there are polynomial-time algorithms that solve it, the MoST is NP-hard. Several researchers proposed techniques to solve the MoST, each of those methods with specific potentialities and limitations. In this study, we examine those methods and divide them into two categories regarding their outcomes: Pareto optimal sets and Pareto optimal fronts. To compare the techniques from the two groups, we investigated their behavior on 2, 3 and 4-objective instances from different classes. We report the results of a computational experiment on 8100 complete and grid graphs in which we analyze specific features of each algorithm as well as the computational effort required to solve the instances.

Suggested Citation

  • I. F. C. Fernandes & E. F. G. Goldbarg & S. M. D. M. Maia & M. C. Goldbarg, 2020. "Empirical study of exact algorithms for the multi-objective spanning tree," Computational Optimization and Applications, Springer, vol. 75(2), pages 561-605, March.
    • Handle: RePEc:spr:coopap:v:75:y:2020:i:2:d:10.1007_s10589-019-00154-1
    DOI: 10.1007/s10589-019-00154-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-019-00154-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-019-00154-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Eom, Cheoljun & Kwon, Okyu & Jung, Woo-Sung & Kim, Seunghwan, 2010. "The effect of a market factor on information flow between stocks using the minimal spanning tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1643-1652.
    2. Alonso, Sergio & Domínguez-Ríos, Miguel Ángel & Colebrook, Marcos & Sedeo-Noda, Antonio, 2009. "Optimality conditions in preference-based spanning tree problems," European Journal of Operational Research, Elsevier, vol. 198(1), pages 232-240, October.
    3. Dias, João, 2012. "Sovereign debt crisis in the European Union: A minimum spanning tree approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2046-2055.
    4. Perny, Patrice & Spanjaard, Olivier, 2005. "A preference-based approach to spanning trees and shortest paths problems***," European Journal of Operational Research, Elsevier, vol. 162(3), pages 584-601, May.
    5. Ramos, R. M. & Alonso, S. & Sicilia, J. & Gonzalez, C., 1998. "The problem of the optimal biobjective spanning tree," European Journal of Operational Research, Elsevier, vol. 111(3), pages 617-628, December.
    6. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    7. Paquete, Luis & Stutzle, Thomas, 2006. "A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices," European Journal of Operational Research, Elsevier, vol. 169(3), pages 943-959, March.
    8. Banu Lokman & Murat Köksalan, 2013. "Finding all nondominated points of multi-objective integer programs," Journal of Global Optimization, Springer, vol. 57(2), pages 347-365, October.
    9. José Arroyo & Pedro Vieira & Dalessandro Vianna, 2008. "A GRASP algorithm for the multi-criteria minimum spanning tree problem," Annals of Operations Research, Springer, vol. 159(1), pages 125-133, March.
    10. Galand, Lucie & Perny, Patrice & Spanjaard, Olivier, 2010. "Choquet-based optimisation in multiobjective shortest path and spanning tree problems," European Journal of Operational Research, Elsevier, vol. 204(2), pages 303-315, July.
    11. Francis Sourd & Olivier Spanjaard, 2008. "A Multiobjective Branch-and-Bound Framework: Application to the Biobjective Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 472-484, August.
    12. Sylva, John & Crema, Alejandro, 2004. "A method for finding the set of non-dominated vectors for multiple objective integer linear programs," European Journal of Operational Research, Elsevier, vol. 158(1), pages 46-55, October.
    13. Zhou, Gengui & Gen, Mitsuo, 1999. "Genetic algorithm approach on multi-criteria minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 114(1), pages 141-152, April.
    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. Iago A. Carvalho & Amadeu A. Coco, 2023. "On solving bi-objective constrained minimum spanning tree problems," Journal of Global Optimization, Springer, vol. 87(1), pages 301-323, September.

    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. Andréa Santos & Diego Lima & Dario Aloise, 2014. "Modeling and solving the bi-objective minimum diameter-cost spanning tree problem," Journal of Global Optimization, Springer, vol. 60(2), pages 195-216, October.
    2. Fernández, Elena & Pozo, Miguel A. & Puerto, Justo & Scozzari, Andrea, 2017. "Ordered Weighted Average optimization in Multiobjective Spanning Tree Problem," European Journal of Operational Research, Elsevier, vol. 260(3), pages 886-903.
    3. De Santis, Marianna & Grani, Giorgio & Palagi, Laura, 2020. "Branching with hyperplanes in the criterion space: The frontier partitioner algorithm for biobjective integer programming," European Journal of Operational Research, Elsevier, vol. 283(1), pages 57-69.
    4. Holzmann, Tim & Smith, J.C., 2018. "Solving discrete multi-objective optimization problems using modified augmented weighted Tchebychev scalarizations," European Journal of Operational Research, Elsevier, vol. 271(2), pages 436-449.
    5. Forget, Nicolas & Gadegaard, Sune Lauth & Nielsen, Lars Relund, 2022. "Warm-starting lower bound set computations for branch-and-bound algorithms for multi objective integer linear programs," European Journal of Operational Research, Elsevier, vol. 302(3), pages 909-924.
    6. Markus Leitner & Ivana Ljubić & Markus Sinnl, 2015. "A Computational Study of Exact Approaches for the Bi-Objective Prize-Collecting Steiner Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 118-134, February.
    7. Natashia Boland & Hadi Charkhgard & Martin Savelsbergh, 2015. "A Criterion Space Search Algorithm for Biobjective Integer Programming: The Balanced Box Method," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 735-754, November.
    8. Alonso, Sergio & Domínguez-Ríos, Miguel Ángel & Colebrook, Marcos & Sedeo-Noda, Antonio, 2009. "Optimality conditions in preference-based spanning tree problems," European Journal of Operational Research, Elsevier, vol. 198(1), pages 232-240, October.
    9. Pedro Correia & Luís Paquete & José Rui Figueira, 2021. "Finding multi-objective supported efficient spanning trees," Computational Optimization and Applications, Springer, vol. 78(2), pages 491-528, March.
    10. Satya Tamby & Daniel Vanderpooten, 2021. "Enumeration of the Nondominated Set of Multiobjective Discrete Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 72-85, January.
    11. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    12. Lacour, Renaud, 2014. "Approches de résolution exacte et approchée en optimisation combinatoire multi-objectif, application au problème de l'arbre couvrant de poids minimal," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/14806 edited by Vanderpooten, Daniel.
    13. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
    14. Cristina Requejo & Eulália Santos, 2020. "Efficient lower and upper bounds for the weight-constrained minimum spanning tree problem using simple Lagrangian based algorithms," Operational Research, Springer, vol. 20(4), pages 2467-2495, December.
    15. Boland, Natashia & Charkhgard, Hadi & Savelsbergh, Martin, 2017. "The Quadrant Shrinking Method: A simple and efficient algorithm for solving tri-objective integer programs," European Journal of Operational Research, Elsevier, vol. 260(3), pages 873-885.
    16. Perny, Patrice & Spanjaard, Olivier, 2005. "A preference-based approach to spanning trees and shortest paths problems***," European Journal of Operational Research, Elsevier, vol. 162(3), pages 584-601, May.
    17. Cacchiani, Valentina & D’Ambrosio, Claudia, 2017. "A branch-and-bound based heuristic algorithm for convex multi-objective MINLPs," European Journal of Operational Research, Elsevier, vol. 260(3), pages 920-933.
    18. Francis Sourd & Olivier Spanjaard, 2008. "A Multiobjective Branch-and-Bound Framework: Application to the Biobjective Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 472-484, August.
    19. Seyyed Amir Babak Rasmi & Ali Fattahi & Metin Türkay, 2021. "SASS: slicing with adaptive steps search method for finding the non-dominated points of tri-objective mixed-integer linear programming problems," Annals of Operations Research, Springer, vol. 296(1), pages 841-876, January.
    20. David Bergman & Merve Bodur & Carlos Cardonha & Andre A. Cire, 2022. "Network Models for Multiobjective Discrete Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 990-1005, March.

    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:spr:coopap:v:75:y:2020:i:2:d:10.1007_s10589-019-00154-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.