IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v60y2014i2p195-216.html
   My bibliography  Save this article

Modeling and solving the bi-objective minimum diameter-cost spanning tree problem

Author

Listed:
  • Andréa Santos
  • Diego Lima
  • Dario Aloise

Abstract

The bi-objective minimum diameter-cost spanning tree problem (bi-MDCST) seeks spanning trees with minimum total cost and minimum diameter. The bi-objective version generalizes the well-known bounded diameter minimum spanning tree problem. The bi-MDCST is a NP-hard problem and models several practical applications in transportation and network design. We propose a bi-objective multiflow formulation for the problem and effective multi-objective metaheuristics: a multi-objective evolutionary algorithm and a fast nondominated sorting genetic algorithm. Some guidelines on how to optimize the problem whenever a priority order can be established between the two objectives are provided. In addition, we present bi-MDCST polynomial cases and theoretical bounds on the search space. Results are reported for four representative test sets. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jglopt:v:60:y:2014:i:2:p:195-216
    DOI: 10.1007/s10898-013-0124-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-013-0124-4
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10898-013-0124-4?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. Abilio Lucena & Celso Ribeiro & Andréa Santos, 2010. "A hybrid heuristic for the diameter constrained minimum spanning tree problem," Journal of Global Optimization, Springer, vol. 46(3), pages 363-381, March.
    2. 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.
    3. 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.
    4. 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.
    5. 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. 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.
    2. 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.
    3. 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.
    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. 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.
    6. 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.
    7. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Delorme, Xavier & Gandibleux, Xavier & Degoutin, Fabien, 2010. "Evolutionary, constructive and hybrid procedures for the bi-objective set packing problem," European Journal of Operational Research, Elsevier, vol. 204(2), pages 206-217, July.
    17. Christian Artigues & Nicolas Jozefowiez & Boadu M. Sarpong, 2018. "Column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(2), pages 117-142, June.
    18. Juan Villegas & Fernando Palacios & Andrés Medaglia, 2006. "Solution methods for the bi-objective (cost-coverage) unconstrained facility location problem with an illustrative example," Annals of Operations Research, Springer, vol. 147(1), pages 109-141, October.
    19. Zhou, Gengui & Min, Hokey & Gen, Mitsuo, 2003. "A genetic algorithm approach to the bi-criteria allocation of customers to warehouses," International Journal of Production Economics, Elsevier, vol. 86(1), pages 35-45, October.
    20. Wen, Hao & Sang, Song & Qiu, Chenhui & Du, Xiangrui & Zhu, Xiao & Shi, Qian, 2019. "A new optimization method of wind turbine airfoil performance based on Bessel equation and GABP artificial neural network," Energy, Elsevier, vol. 187(C).

    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:jglopt:v:60:y:2014:i:2:p:195-216. 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.