IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v7y2003i3d10.1023_a1027368621279.html
   My bibliography  Save this article

Solving Steiner Tree Problems in Graphs with Lagrangian Relaxation

Author

Listed:
  • Laura Bahiense

    (Universidade Federal do Rio de Janeiro, COPPE-Sistemas e Computação)

  • Francisco Barahona

    (IBM T. J. Watson Research Center)

  • Oscar Porto

    (Rua Marquês de São Vicente 225, Predio Cardeal Leme, Sala 401)

Abstract

This paper presents an algorithm to obtain near optimal solutions for the Steiner tree problem in graphs. It is based on a Lagrangian relaxation of a multi-commodity flow formulation of the problem. An extension of the subgradient algorithm, the volume algorithm, has been used to obtain lower bounds and to estimate primal solutions. It was possible to solve several difficult instances from the literature to proven optimality without branching. Computational results are reported for problems drawn from the SteinLib library.

Suggested Citation

  • Laura Bahiense & Francisco Barahona & Oscar Porto, 2003. "Solving Steiner Tree Problems in Graphs with Lagrangian Relaxation," Journal of Combinatorial Optimization, Springer, vol. 7(3), pages 259-282, September.
  • Handle: RePEc:spr:jcomop:v:7:y:2003:i:3:d:10.1023_a:1027368621279
    DOI: 10.1023/A:1027368621279
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1027368621279
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1023/A:1027368621279?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. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    2. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    3. Sunil Chopra & Edgar R. Gorres & M. R. Rao, 1992. "Solving the Steiner Tree Problem on a Graph Using Branch and Cut," INFORMS Journal on Computing, INFORMS, vol. 4(3), pages 320-335, August.
    4. Kaj Holmberg & Johan Hellstrand, 1998. "Solving the Uncapacitated Network Design Problem by a Lagrangean Heuristic and Branch-and-Bound," Operations Research, INFORMS, vol. 46(2), pages 247-259, 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. Igor Litvinchev & Socorro Rangel & Jania Saucedo, 2010. "A Lagrangian bound for many-to-many assignment problems," Journal of Combinatorial Optimization, Springer, vol. 19(3), pages 241-257, April.

    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. Louwerse, I. & Mijnarends, J. & Meuffels, I. & Huisman, D. & Fleuren, H.A., 2012. "Scheduling Movements in the Network of an Express Service Provider," Econometric Institute Research Papers EI 2012-08, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Yongjia Song & Minjiao Zhang, 2015. "Chance‐constrained multi‐terminal network design problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(4), pages 321-334, June.
    3. Alessandro Hill & Roberto Baldacci & Stefan Voß, 2022. "Optimal Steiner trees under node and edge privacy conflicts," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1509-1533, July.
    4. Keely L. Croxton & Bernard Gendron & Thomas L. Magnanti, 2007. "Variable Disaggregation in Network Flow Problems with Piecewise Linear Costs," Operations Research, INFORMS, vol. 55(1), pages 146-157, February.
    5. Hamid Farvaresh & Mohammad Sepehri, 2013. "A Branch and Bound Algorithm for Bi-level Discrete Network Design Problem," Networks and Spatial Economics, Springer, vol. 13(1), pages 67-106, March.
    6. Meuffels, W.J.M., 2015. "The design of road and air networks for express service providers," Other publications TiSEM d3266cb8-bc55-41be-adc7-4, Tilburg University, School of Economics and Management.
    7. Poorzahedy, Hossain & Rouhani, Omid M., 2007. "Hybrid meta-heuristic algorithms for solving network design problem," European Journal of Operational Research, Elsevier, vol. 182(2), pages 578-596, October.
    8. Cohn, Amy & Davey, Melinda & Schkade, Lisa & Siegel, Amanda & Wong, Caris, 2008. "Network design and flow problems with cross-arc costs," European Journal of Operational Research, Elsevier, vol. 189(3), pages 890-901, September.
    9. Ada Alvarez & José González-Velarde & Karim De-Alba, 2005. "Scatter Search for Network Design Problem," Annals of Operations Research, Springer, vol. 138(1), pages 159-178, September.
    10. Kaj Holmberg & Di Yuan, 2000. "A Lagrangian Heuristic Based Branch-and-Bound Approach for the Capacitated Network Design Problem," Operations Research, INFORMS, vol. 48(3), pages 461-481, June.
    11. C S Sung & S H Song, 2003. "Branch-and-price algorithm for a combined problem of virtual path establishment and traffic packet routing in a layered communication network," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(1), pages 72-82, January.
    12. Zetina, Carlos Armando & Contreras, Ivan & Cordeau, Jean-François, 2019. "Profit-oriented fixed-charge network design with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 1-19.
    13. Holmberg, Kaj & Joborn, Martin & Melin, Kennet, 2008. "Lagrangian based heuristics for the multicommodity network flow problem with fixed costs on paths," European Journal of Operational Research, Elsevier, vol. 188(1), pages 101-108, July.
    14. A. Ruszczynski, 1993. "Regularized Decomposition of Stochastic Programs: Algorithmic Techniques and Numerical Results," Working Papers wp93021, International Institute for Applied Systems Analysis.
    15. Ethem Çanakoğlu & İbrahim Muter & Tevfik Aytekin, 2021. "Integrating Individual and Aggregate Diversity in Top- N Recommendation," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 300-318, January.
    16. Ogbe, Emmanuel & Li, Xiang, 2017. "A new cross decomposition method for stochastic mixed-integer linear programming," European Journal of Operational Research, Elsevier, vol. 256(2), pages 487-499.
    17. Sankaran, Jayaram K., 1995. "Column generation applied to linear programs in course registration," European Journal of Operational Research, Elsevier, vol. 87(2), pages 328-342, December.
    18. Metrane, Abdelmoutalib & Soumis, François & Elhallaoui, Issmail, 2010. "Column generation decomposition with the degenerate constraints in the subproblem," European Journal of Operational Research, Elsevier, vol. 207(1), pages 37-44, November.
    19. Belanger, Nicolas & Desaulniers, Guy & Soumis, Francois & Desrosiers, Jacques, 2006. "Periodic airline fleet assignment with time windows, spacing constraints, and time dependent revenues," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1754-1766, December.
    20. François Clautiaux & Cláudio Alves & José Valério de Carvalho & Jürgen Rietz, 2011. "New Stabilization Procedures for the Cutting Stock Problem," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 530-545, November.

    More about this item

    Keywords

    Steiner trees; Lagrangian relaxation;

    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:spr:jcomop:v:7:y:2003:i:3:d:10.1023_a:1027368621279. 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.