IDEAS home Printed from https://ideas.repec.org/p/cor/louvco/2021023.html
   My bibliography  Save this paper

A Massively Parallel Exact Solution Algorithm for the Balanced Minimum Evolution Problem

Author

Listed:
  • Catanzaro, Daniele

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Frohn, Martin

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Pesenti, Raffaele

Abstract

The Balanced Minimum Evolution Problem (BMEP) is an [APX]-hard nonlinear network design problem that consists of finding a phylogeny that minimizes the cross-entropy of the molecular sequences extracted from a given set of taxa. By combining massive parallelism with recent theoretical advances on the polyhedral combinatorics of the problem and new insights on the relationships between the BMEP and information entropy, we design a new exact solution algorithm that proves to be up to an order of magnitude faster than the current state-of-the-art sequential-version on generic instances and able to solve up to 25% more taxa within the same time limit. We also investigate some issues related to numerical stability and statistical consistency of the BMEP, arising in particular when dealing with large instances. We show, as a negative finding, that no rescaling technique may ensure numerical stability, by guaranteeing at the same time the statistical consistency of the optimal solution to the problem.

Suggested Citation

  • 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).
    • Handle: RePEc:cor:louvco:2021023
    as

    Download full text from publisher

    File URL: https://dial.uclouvain.be/pr/boreal/en/object/boreal%3A254728/datastream/PDF_01/view
    Download Restriction: no
    ---><---

    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. Li, Shasha & Tu, Jianhua & Yu, Chenyan, 2016. "The generalized 3-connectivity of star graphs and bubble-sort graphs," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 41-46.
    3. Catanzaro, Daniele & Pesenti, Raffaele & Wolsey, Laurence, 2020. "On the balanced minimum evolution polytope," LIDAM Reprints CORE 3096, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Daniele Catanzaro & Raffaele Pesenti, 2019. "Enumerating vertices of the balanced minimum evolution polytope," LIDAM Reprints CORE 3005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Daniele CATANZARO & Roberto ARINGHIERI & Mardo DI SUMMA & Raffaele PESENTI, 2015. "A branch-price-and-cut algorithm for the minimum evolution problem," LIDAM Reprints CORE 2767, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Catanzaro, Daniele & Frohn, Martin & Pesenti, Raffaele, 2020. "An information theory perspective on the balanced minimum evolution problem," LIDAM Reprints CORE 3097, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

    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. 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).
    2. 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).
    3. 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.
    4. 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).
    5. 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).
    6. 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.
    7. 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.
    8. Li, Yinkui & Wei, Liqun, 2023. "Note for the conjecture on the generalized 4-connectivity of total graphs of the complete bipartite graph," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    9. Hong Chang & Xueliang Li & Colton Magnant & Zhongmei Qin, 2018. "The $$(k,\ell )$$ ( k , ℓ ) -proper index of graphs," Journal of Combinatorial Optimization, Springer, vol. 36(2), pages 458-471, August.
    10. Li, Shasha & Zhao, Yan & Li, Fengwei & Gu, Ruijuan, 2019. "The generalized 3-connectivity of the Mycielskian of a graph," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 882-890.
    11. Zhang, Guozhen & Wang, Dajin, 2019. "Structure connectivity and substructure connectivity of bubble-sort star graph networks," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    12. Zhao, Shu-Li & Hao, Rong-Xia & Wei, Chao, 2022. "Internally disjoint trees in the line graph and total graph of the complete bipartite graph," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    13. Li, Hengzhe & Ma, Yingbin & Yang, Weihua & Wang, Yifei, 2017. "The generalized 3-connectivity of graph products," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 77-83.
    14. Gao, Hui & Lv, Benjian & Wang, Kaishun, 2018. "Two lower bounds for generalized 3-connectivity of Cartesian product graphs," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 305-313.
    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. Li, Hengzhe & Wang, Jiajia, 2018. "The λ3-connectivity and κ3-connectivity of recursive circulants," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 750-757.
    17. Zhao, Shu-Li & Hao, Rong-Xia, 2019. "The generalized 4-connectivity of exchanged hypercubes," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 342-353.
    18. Mao, Yaping, 2017. "Constructing edge-disjoint Steiner paths in lexicographic product networks," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 1-10.

    More about this item

    Keywords

    Combinatorial optimization ; network design ; balanced minimum evolution ; implicit enumeration algorithms ; parallel computing ; numerical stability;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:louvco:2021023. 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.