IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v78y2021i2d10.1007_s10589-020-00251-6.html
   My bibliography  Save this article

Finding multi-objective supported efficient spanning trees

Author

Listed:
  • Pedro Correia

    (University of Coimbra)

  • Luís Paquete

    (University of Coimbra)

  • José Rui Figueira

    (Universidade de Lisboa)

Abstract

This article introduces a new algorithm for computing the set of supported non-dominated points in the objective space and all the corresponding efficient solutions in the decision space for the multi-objective spanning tree (MOST) problem. This algorithm is based on the connectedness property of the set of efficient supported solutions and uses a decomposition of the weight set in the weighting space defined for a parametric version of the MOST problem. This decomposition is performed through a space reduction approach until an indifference region for each supported non-dominated point is obtained. An adjacency relation defined in the decision space is used to compute all the supported efficient spanning trees associated to the same non-dominated supported point as well as to define the indifference region of the next points. An in-depth computational analysis of this approach for different types of networks with three objectives is also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:78:y:2021:i:2:d:10.1007_s10589-020-00251-6
    DOI: 10.1007/s10589-020-00251-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-020-00251-6
    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/s10589-020-00251-6?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. Alves, Maria João & Costa, João Paulo, 2016. "Graphical exploration of the weight space in three-objective mixed integer linear programs," European Journal of Operational Research, Elsevier, vol. 248(1), pages 72-83.
    2. José Figueira & Luís Paquete & Marco Simões & Daniel Vanderpooten, 2013. "Algorithmic improvements on dynamic programming for the bi-objective {0,1} knapsack problem," Computational Optimization and Applications, Springer, vol. 56(1), pages 97-111, September.
    3. 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.
    4. Ehrgott, Matthias & Klamroth, Kathrin, 1997. "Connectedness of efficient solutions in multiple criteria combinatorial optimization," European Journal of Operational Research, Elsevier, vol. 97(1), pages 159-166, February.
    5. Jochen Gorski & Kathrin Klamroth & Stefan Ruzika, 2011. "Connectedness of Efficient Solutions in Multiple Objective Combinatorial Optimization," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 475-497, September.
    6. 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.
    7. 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. Stephan Helfrich & Kathrin Prinz & Stefan Ruzika, 2024. "The Weighted p-Norm Weight Set Decomposition for Multiobjective Discrete Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1187-1216, September.
    2. Stephan Helfrich & Tyler Perini & Pascal Halffmann & Natashia Boland & Stefan Ruzika, 2023. "Analysis of the weighted Tchebycheff weight set decomposition for multiobjective discrete optimization problems," Journal of Global Optimization, Springer, vol. 86(2), pages 417-440, June.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    6. 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.
    7. 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.
    8. 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.
    9. Michael Stiglmayr & José Figueira & Kathrin Klamroth, 2014. "On the multicriteria allocation problem," Annals of Operations Research, Springer, vol. 222(1), pages 535-549, November.
    10. 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.
    11. 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.
    12. 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.
    13. Pascal Halffmann & Tobias Dietz & Anthony Przybylski & Stefan Ruzika, 2020. "An inner approximation method to compute the weight set decomposition of a triobjective mixed-integer problem," Journal of Global Optimization, Springer, vol. 77(4), pages 715-742, August.
    14. 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.
    15. Rong, Aiying & Figueira, José Rui, 2014. "Dynamic programming algorithms for the bi-objective integer knapsack problem," European Journal of Operational Research, Elsevier, vol. 236(1), pages 85-99.
    16. Michael Stiglmayr & José Rui Figueira & Kathrin Klamroth & Luís Paquete & Britta Schulze, 2022. "Decision space robustness for multi-objective integer linear programming," Annals of Operations Research, Springer, vol. 319(2), pages 1769-1791, December.
    17. 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.
    18. Audrey Cerqueus & Xavier Gandibleux & Anthony Przybylski & Frédéric Saubion, 2017. "On branching heuristics for the bi-objective 0/1 unidimensional knapsack problem," Journal of Heuristics, Springer, vol. 23(5), pages 285-319, October.
    19. Sune Lauth Gadegaard & Lars Relund Nielsen & Matthias Ehrgott, 2019. "Bi-objective Branch-and-Cut Algorithms Based on LP Relaxation and Bound Sets," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 790-804, October.
    20. 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.

    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:78:y:2021:i:2:d:10.1007_s10589-020-00251-6. 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.