IDEAS home Printed from https://ideas.repec.org/p/cor/louvrp/2698.html
   My bibliography  Save this paper

A branch-price-and-cut algorithm for the minimum evolution problem

Author

Listed:
  • CATANZARO, Daniele
  • ARINGHIERI, Roberto
  • DI SUMMA, Marco
  • PESENTI, Raffaele

Abstract

We investigate the Minimum Evolution Problem (MEP), an NP-hard network design problem arising from computational biology. The MEP consists in finding a weighted unrooted binary tree having n leaves, minimal length, and such that the sum of the edge weights belonging to the unique path between each pair of leaves is greater than or equal to a prescribed value. We study the polyhedral combinatorics of the MEP and investigate its relationships with the Balanced Minimum Evolution Problem. We develop an exact solution approach for the MEP based on a nontrivial combination of a parallel branch-price-and-cut scheme and a non-isomorphic enumeration of all possible solutions to the problem. Computational experiments show that the new solution approach outperforms the best mixed integer linear programming formulation for the MEP currently described in the literature. Our results give a perspective on the combinatorics of the MEP and suggest new directions for the development of future exact solution approaches that may turn out useful in practical applications. We also show that the MEP is statistically consistent.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • CATANZARO, Daniele & ARINGHIERI, Roberto & DI SUMMA, Marco & PESENTI, Raffaele, 2015. "A branch-price-and-cut algorithm for the minimum evolution problem," LIDAM Reprints CORE 2698, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2698
    Note: In : European Journal of Operational Research, 244 (3) 2015, p. 753-765
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Shmuel Sattath & Amos Tversky, 1977. "Additive similarity trees," Psychometrika, Springer;The Psychometric Society, vol. 42(3), pages 319-345, September.
    2. 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.
    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. 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.
    2. 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).
    3. 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).
    4. 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.
    5. 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.
    6. 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).
    7. 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).
    8. 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).

    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. 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.
    3. 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.
    4. Nudelman, Gabriel & Shiloh, Shoshana, 2015. "Mapping health behaviors: Constructing and validating a common-sense taxonomy of health behaviors," Social Science & Medicine, Elsevier, vol. 146(C), pages 1-10.
    5. J. Carroll & Linda Clark & Wayne DeSarbo, 1984. "The representation of three-way proximity data by single and multiple tree structure models," Journal of Classification, Springer;The Classification Society, vol. 1(1), pages 25-74, December.
    6. 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).
    7. Lant, Theresa & Shapira, Zur, 2008. "Managerial reasoning about aspirations and expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 66(1), pages 60-73, April.
    8. 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).
    9. Cotta, Carlos, 2006. "Scatter search with path relinking for phylogenetic inference," European Journal of Operational Research, Elsevier, vol. 169(2), pages 520-532, March.
    10. 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.
    11. 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.
    12. 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).
    13. 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.
    14. Wayne DeSarbo & Ajay Manrai & Raymond Burke, 1990. "A nonspatial methodology for the analysis of two-way proximity data incorporating the distance-density hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 55(2), pages 229-253, June.
    15. 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.
    16. N. Sriram & Scott Lewis, 1993. "Constructing optimal ultrametrics," Journal of Classification, Springer;The Classification Society, vol. 10(2), pages 241-268, December.
    17. Berry, V & Gascuel, O & Caraux, G, 2000. "Choosing the tree which actually best explains the data: another look at the bootstrap in phylogenetic reconstruction," Computational Statistics & Data Analysis, Elsevier, vol. 32(3-4), pages 273-283, January.
    18. Tudor Ionescu & Géraldine Polaillon & Frédéric Boulanger, 2010. "Minimum Tree Cost Quartet Puzzling," Journal of Classification, Springer;The Classification Society, vol. 27(2), pages 136-157, September.
    19. Wayne DeSarbo & Vijay Mahajan, 1984. "Constrained classification: The use of a priori information in cluster analysis," Psychometrika, Springer;The Psychometric Society, vol. 49(2), pages 187-215, June.
    20. Michel Wedel & Wayne DeSarbo, 1998. "Mixtures of (constrained) ultrametric trees," Psychometrika, Springer;The Psychometric Society, vol. 63(4), pages 419-443, December.

    More about this item

    Statistics

    Access and download statistics

    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:cor:louvrp:2698. 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: Alain GILLIS (email available below). General contact details of provider: https://edirc.repec.org/data/coreebe.html .

    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.