IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v256y2017i1p242-251.html
   My bibliography  Save this article

Compact mixed integer linear programming models to the minimum weighted tree reconstruction problem

Author

Listed:
  • Fortz, Bernard
  • Oliveira, Olga
  • Requejo, Cristina

Abstract

The Minimum Weighted Tree Reconstruction (MWTR) problem consists of finding a minimum length weighted tree connecting a set of terminal nodes in such a way that the length of the path between each pair of terminal nodes is greater than or equal to a given distance between the considered pair of terminal nodes. This problem has applications in several areas, namely, the inference of phylogenetic trees, the modeling of traffic networks and the analysis of internet infrastructures. In this paper, we investigate the MWTR problem and we present two compact mixed-integer linear programming models to solve the problem. Computational results using two different sets of instances, one from the phylogenetic area and another from the telecommunications area, show that the best of the two models is able to solve instances of the problem having up to 15 terminal nodes.

Suggested Citation

  • Fortz, Bernard & Oliveira, Olga & Requejo, Cristina, 2017. "Compact mixed integer linear programming models to the minimum weighted tree reconstruction problem," European Journal of Operational Research, Elsevier, vol. 256(1), pages 242-251.
    • Handle: RePEc:eee:ejores:v:256:y:2017:i:1:p:242-251
    DOI: 10.1016/j.ejor.2016.06.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221716304349
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2016.06.014?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. Catanzaro, Daniele & Aringhieri, Roberto & Di Summa, Marco & Pesenti, Raffaele, 2015. "A branch-price-and-cut algorithm for the minimum evolution problem," European Journal of Operational Research, Elsevier, vol. 244(3), pages 753-765.
    2. Gouveia, Luis, 1996. "Multicommodity flow models for spanning trees with hop constraints," European Journal of Operational Research, Elsevier, vol. 95(1), pages 178-190, November.
    3. James Corter & Amos Tversky, 1986. "Extended similarity trees," Psychometrika, Springer;The Psychometric Society, vol. 51(3), pages 429-451, September.
    4. Varone, Sacha C., 2006. "A constructive algorithm for realizing a distance matrix," European Journal of Operational Research, Elsevier, vol. 174(1), pages 102-111, October.
    5. Daniele Catanzaro & Martine Labbé & Raffaele Pesenti & Juan-José Salazar-González, 2012. "The Balanced Minimum Evolution Problem," INFORMS Journal on Computing, INFORMS, vol. 24(2), pages 276-294, May.
    6. Geert Soete, 1983. "A least squares algorithm for fitting additive trees to proximity data," Psychometrika, Springer;The Psychometric Society, vol. 48(4), pages 621-626, December.
    7. Shmuel Sattath & Amos Tversky, 1977. "Additive similarity trees," Psychometrika, Springer;The Psychometric Society, vol. 42(3), pages 319-345, September.
    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. Olga Fajarda & Cristina Requejo, 2022. "MIP model-based heuristics for the minimum weighted tree reconstruction problem," Operational Research, Springer, vol. 22(3), pages 2305-2342, July.
    2. Shehadeh, Karmel S. & Cohn, Amy E.M. & Epelman, Marina A., 2019. "Analysis of models for the Stochastic Outpatient Procedure Scheduling Problem," European Journal of Operational Research, Elsevier, vol. 279(3), pages 721-731.

    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. Olga Fajarda & Cristina Requejo, 2022. "MIP model-based heuristics for the minimum weighted tree reconstruction problem," Operational Research, Springer, vol. 22(3), pages 2305-2342, July.
    2. J. Carroll & James Corter, 1995. "A graph-theoretic method for organizing overlapping clusters into trees, multiple trees, or extended trees," Journal of Classification, Springer;The Classification Society, vol. 12(2), pages 283-313, September.
    3. Catanzaro, Daniele & Frohn, Martin & Gascuel, Olivier & Pesenti, Raffaele, 2023. "A Massively Parallel Exact Solution Algorithm for the Balanced Minimum Evolution Problem," LIDAM Discussion Papers CORE 2023001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Lant, Theresa & Shapira, Zur, 2008. "Managerial reasoning about aspirations and expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 66(1), pages 60-73, April.
    5. Catanzaro, Daniele & Frohn, Martin & Pesenti, Raffaele, 2021. "A Massively Parallel Exact Solution Algorithm for the Balanced Minimum Evolution Problem," LIDAM Discussion Papers CORE 2021023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Catanzaro, Daniele & Frohn, Martin & Gascuel, Olivier & Pesenti, Raffaele, 2022. "A tutorial on the balanced minimum evolution problem," European Journal of Operational Research, Elsevier, vol. 300(1), pages 1-19.
    7. A. Penttinen & W. Krzanowski & J. Kettenring & F. Rohlf & William Day & B. Weir & John Kececioglu & N. Ohsumi & Peter Willett, 1993. "Book reviews," Journal of Classification, Springer;The Classification Society, vol. 10(1), pages 125-156, January.
    8. Wedel, Michel & DeSarbo, Wayne S., 1996. "Semiparametric estimation of (constrained) ultrametric trees," Research Report 96B34, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    9. Geert Soete, 1986. "Optimal variable weighting for ultrametric and additive tree clustering," Quality & Quantity: International Journal of Methodology, Springer, vol. 20(2), pages 169-180, June.
    10. K. Klauer & J. Carroll, 1989. "A mathematical programming approach to fitting general graphs," Journal of Classification, Springer;The Classification Society, vol. 6(1), pages 247-270, December.
    11. Catanzaro, Daniele & Frohn, Martin & Gascuel, Olivier & Pesenti, Raffaele, 2021. "A Tutorial on the Balanced Minimum Evolution Problem," LIDAM Discussion Papers CORE 20210, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Robert Coles & Gerard P. Hodgkinson, 2008. "A Psychometric Study of Information Technology Risks in the Workplace," Risk Analysis, John Wiley & Sons, vol. 28(1), pages 81-93, February.
    13. repec:dgr:rugsom:96b34 is not listed on IDEAS
    14. J. Hutchinson & Amitabh Mungale, 1997. "Pairwise partitioning: A nonmetric algorithm for identifying feature-based similarity structures," Psychometrika, Springer;The Psychometric Society, vol. 62(1), pages 85-117, March.
    15. Catanzaro, Daniele & Aringhieri, Roberto & Di Summa, Marco & Pesenti, Raffaele, 2015. "A branch-price-and-cut algorithm for the minimum evolution problem," European Journal of Operational Research, Elsevier, vol. 244(3), pages 753-765.
    16. Varone, Sacha C., 2006. "A constructive algorithm for realizing a distance matrix," European Journal of Operational Research, Elsevier, vol. 174(1), pages 102-111, October.
    17. Gasparin, Andrea & Camerota Verdù, Federico Julian & Catanzaro, Daniele, 2023. "An evolution strategy approach for the Balanced Minimum Evolution Problem," LIDAM Discussion Papers CORE 2023021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Catanzaro, Daniele & Frohn, Martin & Pesenti, Raffaele, 2021. "On Numerical Stability and Statistical Consistency of the Balanced Minimum Evolution Problem," LIDAM Discussion Papers CORE 2021026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. Wayne DeSarbo & Michael Johnson & Ajay Manrai & Lalita Manrai & Elizabeth Edwards, 1992. "Tscale: A new multidimensional scaling procedure based on tversky's contrast model," Psychometrika, Springer;The Psychometric Society, vol. 57(1), pages 43-69, March.
    20. Olivier Gascuel & Denise Levy, 1996. "A reduction algorithm for approximating a (nonmetric) dissimilarity by a tree distance," Journal of Classification, Springer;The Classification Society, vol. 13(1), pages 129-155, March.
    21. Theresa Lant & Zur Shapira, 2009. "Managerial Reasoning about Aspirations and Expectations," Discussion Paper Series dp498, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

    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:256:y:2017:i:1:p:242-251. 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.