IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v82y2022i1d10.1007_s10589-022-00355-1.html
   My bibliography  Save this article

SDP-based bounds for graph partition via extended ADMM

Author

Listed:
  • Angelika Wiegele

    (Alpen-Adria-Universität Klagenfurt)

  • Shudian Zhao

    (Alpen-Adria-Universität Klagenfurt)

Abstract

We study two NP-complete graph partition problems, k-equipartition problems and graph partition problems with knapsack constraints (GPKC). We introduce tight SDP relaxations with nonnegativity constraints to get lower bounds, the SDP relaxations are solved by an extended alternating direction method of multipliers (ADMM). In this way, we obtain high quality lower bounds for k-equipartition on large instances up to $$n =1000$$ n = 1000 vertices within as few as 5 min and for GPKC problems up to $$n=500$$ n = 500 vertices within as little as 1 h. On the other hand, interior point methods fail to solve instances from $$n=300$$ n = 300 due to memory requirements. We also design heuristics to generate upper bounds from the SDP solutions, giving us tighter upper bounds than other methods proposed in the literature with low computational expense.

Suggested Citation

  • Angelika Wiegele & Shudian Zhao, 2022. "SDP-based bounds for graph partition via extended ADMM," Computational Optimization and Applications, Springer, vol. 82(1), pages 251-291, May.
    • Handle: RePEc:spr:coopap:v:82:y:2022:i:1:d:10.1007_s10589-022-00355-1
    DOI: 10.1007/s10589-022-00355-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-022-00355-1
    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/s10589-022-00355-1?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. Dirk A. Lorenz & Quoc Tran-Dinh, 2019. "Non-stationary Douglas–Rachford and alternating direction method of multipliers: adaptive step-sizes and convergence," Computational Optimization and Applications, Springer, vol. 74(1), pages 67-92, September.
    2. David S. Johnson & Cecilia R. Aragon & Lyle A. McGeoch & Catherine Schevon, 1989. "Optimization by Simulated Annealing: An Experimental Evaluation; Part I, Graph Partitioning," Operations Research, INFORMS, vol. 37(6), pages 865-892, December.
    3. Neng Fan & Panos Pardalos, 2010. "Linear and quadratic programming approaches for the general graph partitioning problem," Journal of Global Optimization, Springer, vol. 48(1), pages 57-71, September.
    4. Bissan Ghaddar & Miguel Anjos & Frauke Liers, 2011. "A branch-and-cut algorithm based on semidefinite programming for the minimum k-partition problem," Annals of Operations Research, Springer, vol. 188(1), pages 155-174, August.
    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. Dell'Amico, Mauro & Trubian, Marco, 1998. "Solution of large weighted equicut problems," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 500-521, April.
    2. Schlereth, Christian & Stepanchuk, Tanja & Skiera, Bernd, 2010. "Optimization and analysis of the profitability of tariff structures with two-part tariffs," European Journal of Operational Research, Elsevier, vol. 206(3), pages 691-701, November.
    3. Orlin, James & Sharma, Dushyant, 2003. "The Extended Neighborhood: Definition And Characterization," Working papers 4392-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. Melissa Gama & Bruno Filipe Santos & Maria Paola Scaparra, 2016. "A multi-period shelter location-allocation model with evacuation orders for flood disasters," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 4(3), pages 299-323, September.
    5. Pirlot, Marc, 1996. "General local search methods," European Journal of Operational Research, Elsevier, vol. 92(3), pages 493-511, August.
    6. M Kumral & P A Dowd, 2005. "A simulated annealing approach to mine production scheduling," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(8), pages 922-930, August.
    7. Cheng Lu & Zhibin Deng, 2021. "A branch-and-bound algorithm for solving max-k-cut problem," Journal of Global Optimization, Springer, vol. 81(2), pages 367-389, October.
    8. Jamie Fairbrother & Adam N. Letchford & Keith Briggs, 2018. "A two-level graph partitioning problem arising in mobile wireless communications," Computational Optimization and Applications, Springer, vol. 69(3), pages 653-676, April.
    9. Noureddine Bouhmala, 2019. "Combining simulated annealing with local search heuristic for MAX-SAT," Journal of Heuristics, Springer, vol. 25(1), pages 47-69, February.
    10. Yiyo Kuo, 2014. "Design method using hybrid of line-type and circular-type routes for transit network system optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 600-613, July.
    11. Neng Fan & Panos M. Pardalos, 2012. "Multi-way clustering and biclustering by the Ratio cut and Normalized cut in graphs," Journal of Combinatorial Optimization, Springer, vol. 23(2), pages 224-251, February.
    12. Gabriel M. Portal & Marcus Ritt & Leonardo M. Borba & Luciana S. Buriol, 2016. "Simulated annealing for the machine reassignment problem," Annals of Operations Research, Springer, vol. 242(1), pages 93-114, July.
    13. Graeme J. Doole & David J. Pannell, 2008. "Optimisation of a Large, Constrained Simulation Model using Compressed Annealing," Journal of Agricultural Economics, Wiley Blackwell, vol. 59(1), pages 188-206, February.
    14. Giovanni Giallombardo & Houyuan Jiang & Giovanna Miglionico, 2016. "New Formulations for the Conflict Resolution Problem in the Scheduling of Television Commercials," Operations Research, INFORMS, vol. 64(4), pages 838-848, August.
    15. Michele Battistutta & Andrea Schaerf & Tommaso Urli, 2017. "Feature-based tuning of single-stage simulated annealing for examination timetabling," Annals of Operations Research, Springer, vol. 252(2), pages 239-254, May.
    16. Helena Ramalhinho-Lourenço & Daniel Serra, 1998. "Adaptive approach heuristics for the generalized assignment problem," Economics Working Papers 288, Department of Economics and Business, Universitat Pompeu Fabra.
    17. Jeffrey W. Ohlmann & Barrett W. Thomas, 2007. "A Compressed-Annealing Heuristic for the Traveling Salesman Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 80-90, February.
    18. Kaji, Taichi & Ohuchi, Azuma, 1999. "A simulated annealing algorithm with the random compound move for the sequential partitioning problem of directed acyclic graphs," European Journal of Operational Research, Elsevier, vol. 112(1), pages 147-157, January.
    19. Healy, Patrick & Moll, Robert, 1995. "A new extension of local search applied to the Dial-A-Ride Problem," European Journal of Operational Research, Elsevier, vol. 83(1), pages 83-104, May.
    20. Dudek, Gregor & Stadtler, Hartmut, 2005. "Negotiation-based collaborative planning between supply chains partners," European Journal of Operational Research, Elsevier, vol. 163(3), pages 668-687, June.

    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:82:y:2022:i:1:d:10.1007_s10589-022-00355-1. 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.