IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v65y2016i1d10.1007_s10589-016-9835-z.html
   My bibliography  Save this article

A specialized branch-and-bound algorithm for the Euclidean Steiner tree problem in n-space

Author

Listed:
  • Marcia Fampa

    (Universidade Federal do Rio de Janeiro)

  • Jon Lee

    (University of Michigan)

  • Wendel Melo

    (PESC/COPPE, Universidade Federal do Rio de Janeiro)

Abstract

We present a specialized branch-and-bound (b&b) algorithm for the Euclidean Steiner tree problem (ESTP) in $$\mathbb {R}^n$$ R n and apply it to a convex mixed-integer nonlinear programming (MINLP) formulation of the problem, presented by Fampa and Maculan. The algorithm contains procedures to avoid difficulties observed when applying a b&b algorithm for general MINLP problems to solve the ESTP. Our main emphasis is on isomorphism pruning, in order to prevent solving several equivalent subproblems corresponding to isomorphic Steiner trees. We introduce the concept of representative Steiner trees, which allows the pruning of these subproblems, as well as the implementation of procedures to fix variables and add valid inequalities. We also propose more general procedures to improve the efficiency of the b&b algorithm, which may be extended to the solution of other MINLP problems. Computational results demonstrate substantial gains compared to the standard b&b for convex MINLP.

Suggested Citation

  • Marcia Fampa & Jon Lee & Wendel Melo, 2016. "A specialized branch-and-bound algorithm for the Euclidean Steiner tree problem in n-space," Computational Optimization and Applications, Springer, vol. 65(1), pages 47-71, September.
    • Handle: RePEc:spr:coopap:v:65:y:2016:i:1:d:10.1007_s10589-016-9835-z
    DOI: 10.1007/s10589-016-9835-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-016-9835-z
    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/s10589-016-9835-z?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. Omprakash K. Gupta & A. Ravindran, 1985. "Branch and Bound Experiments in Convex Nonlinear Integer Programming," Management Science, INFORMS, vol. 31(12), pages 1533-1546, December.
    2. Nelson Maculan & Philippe Michelon & Adilson Xavier, 2000. "The Euclidean Steiner tree problem in R n : A mathematical programming formulation," Annals of Operations Research, Springer, vol. 96(1), pages 209-220, November.
    3. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2014. "Integrating nonlinear branch-and-bound and outer approximation for convex Mixed Integer Nonlinear Programming," Journal of Global Optimization, Springer, vol. 60(2), pages 373-389, October.
    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. Renan Vicente Pinto & Nelson Maculan, 2023. "A new heuristic for the Euclidean Steiner Tree Problem in $${\mathbb {R}}^n$$ R n," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 391-413, July.
    2. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2020. "An overview of MINLP algorithms and their implementation in Muriqui Optimizer," Annals of Operations Research, Springer, vol. 286(1), pages 217-241, March.
    3. Hacene Ouzia & Nelson Maculan, 2022. "Mixed integer nonlinear optimization models for the Euclidean Steiner tree problem in $$\mathbb {R}^d$$ R d," Journal of Global Optimization, Springer, vol. 83(1), pages 119-136, May.

    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. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2020. "An overview of MINLP algorithms and their implementation in Muriqui Optimizer," Annals of Operations Research, Springer, vol. 286(1), pages 217-241, March.
    2. Renan Vicente Pinto & Nelson Maculan, 2023. "A new heuristic for the Euclidean Steiner Tree Problem in $${\mathbb {R}}^n$$ R n," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 391-413, July.
    3. Tommy Andersson & Christer Andersson, 2009. "Solving House Allocation Problems with Risk-Averse Agents," Computational Economics, Springer;Society for Computational Economics, vol. 33(4), pages 389-401, May.
    4. Terzi, Mourad & Ouazene, Yassine & Yalaoui, Alice & Yalaoui, Farouk, 2023. "Lot-sizing and pricing decisions under attraction demand models and multi-channel environment: New efficient formulations," Operations Research Perspectives, Elsevier, vol. 10(C).
    5. Xiaoguang Chen & Hayri Önal, 2014. "An Economic Analysis of the Future U.S. Biofuel Industry, Facility Location, and Supply Chain Network," Transportation Science, INFORMS, vol. 48(4), pages 575-591, November.
    6. David E. Bernal & Zedong Peng & Jan Kronqvist & Ignacio E. Grossmann, 2022. "Alternative regularizations for Outer-Approximation algorithms for convex MINLP," Journal of Global Optimization, Springer, vol. 84(4), pages 807-842, December.
    7. Andreas Lundell & Jan Kronqvist & Tapio Westerlund, 2022. "The supporting hyperplane optimization toolkit for convex MINLP," Journal of Global Optimization, Springer, vol. 84(1), pages 1-41, September.
    8. Zhang, Zijun & Zeng, Yaohui & Kusiak, Andrew, 2012. "Minimizing pump energy in a wastewater processing plant," Energy, Elsevier, vol. 47(1), pages 505-514.
    9. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2014. "Integrating nonlinear branch-and-bound and outer approximation for convex Mixed Integer Nonlinear Programming," Journal of Global Optimization, Springer, vol. 60(2), pages 373-389, October.
    10. Zheng, Zhuang & Pan, Jia & Huang, Gongsheng & Luo, Xiaowei, 2022. "A bottom-up intra-hour proactive scheduling of thermal appliances for household peak avoiding based on model predictive control," Applied Energy, Elsevier, vol. 323(C).
    11. Andrew Allman & Qi Zhang, 2021. "Branch-and-price for a class of nonconvex mixed-integer nonlinear programs," Journal of Global Optimization, Springer, vol. 81(4), pages 861-880, December.
    12. Kuthambalayan, Thyagaraj S. & Mehta, Peeyush & Shanker, Kripa, 2014. "Integrating operations and marketing decisions using delayed differentiation of products and guaranteed delivery time under stochastic demand," European Journal of Operational Research, Elsevier, vol. 237(2), pages 617-627.
    13. Hacene Ouzia & Nelson Maculan, 2022. "Mixed integer nonlinear optimization models for the Euclidean Steiner tree problem in $$\mathbb {R}^d$$ R d," Journal of Global Optimization, Springer, vol. 83(1), pages 119-136, May.
    14. Meenarli Sharma & Prashant Palkar & Ashutosh Mahajan, 2022. "Linearization and parallelization schemes for convex mixed-integer nonlinear optimization," Computational Optimization and Applications, Springer, vol. 81(2), pages 423-478, March.
    15. Sangwon Moon, 1989. "Application of generalized benders decomposition to a nonlinear distribution system design problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(3), pages 283-295, June.
    16. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2022. "Two linear approximation algorithms for convex mixed integer nonlinear programming," Annals of Operations Research, Springer, vol. 316(2), pages 1471-1491, September.
    17. Kumar Abhishek & Sven Leyffer & Jeff Linderoth, 2010. "FilMINT: An Outer Approximation-Based Solver for Convex Mixed-Integer Nonlinear Programs," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 555-567, November.
    18. Shyamal Gondkar & Sivakumar Sreeramagiri & Edwin Zondervan, 2012. "Methodology for Assessment and Optimization of Industrial Eco-Systems," Challenges, MDPI, vol. 3(1), pages 1-21, June.
    19. Francisco Trespalacios & Ignacio E. Grossmann, 2016. "Cutting Plane Algorithm for Convex Generalized Disjunctive Programs," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 209-222, May.
    20. Luca Mencarelli & Youcef Sahraoui & Leo Liberti, 2017. "A multiplicative weights update algorithm for MINLP," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 31-86, March.

    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:65:y:2016:i:1:d:10.1007_s10589-016-9835-z. 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.