IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v39y1992i3p399-417.html
   My bibliography  Save this article

The quadratic minimum spanning tree problem

Author

Listed:
  • Arjang Assad
  • Weixuan Xu

Abstract

This article introduces a new optimization problem that involves searching for the spanning tree of minimum cost under a quadratic cost structure. This quadratic minimum spanning tree problem is proven to be NP‐hard. A technique for generating lower bounds for this problem is discussed and incorporated into branch‐and‐bound schemes for obtaining exact solutions. Two heuristic algorithms are also developed. Computational experience with both exact and heuristic algorithms is reported.

Suggested Citation

  • Arjang Assad & Weixuan Xu, 1992. "The quadratic minimum spanning tree problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 399-417, April.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:3:p:399-417
    DOI: 10.1002/1520-6750(199204)39:33.0.CO;2-0
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(199204)39:33.0.CO;2-0
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(199204)39:33.0.CO;2-0?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
    ---><---

    References listed on IDEAS

    as
    1. Kusiak, Andrew & Heragu, Sunderesh S., 1987. "The facility layout problem," European Journal of Operational Research, Elsevier, vol. 29(3), pages 229-251, June.
    2. A. Charnes & W. W. Cooper, 1963. "Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints," Operations Research, INFORMS, vol. 11(1), pages 18-39, February.
    3. Robin Segerblom Liggett, 1981. "The Quadratic Assignment Problem: An Experimental Evaluation of Solution Strategies," Management Science, INFORMS, vol. 27(4), pages 442-458, April.
    4. Burkard, Rainer E., 1984. "Quadratic assignment problems," European Journal of Operational Research, Elsevier, vol. 15(3), pages 283-289, March.
    5. Kaku, Bharat K & Thompson, Gerald L., 1986. "An exact algorithm for the general quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 23(3), pages 382-390, March.
    6. Connolly, David T., 1990. "An improved annealing scheme for the QAP," European Journal of Operational Research, Elsevier, vol. 46(1), pages 93-100, 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. Christoph Buchheim & Emiliano Traversi, 2018. "Quadratic Combinatorial Optimization Using Separable Underestimators," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 424-437, August.
    2. de Meijer, Frank, 2023. "Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization," Other publications TiSEM b1f1088c-95fe-4b8a-9e15-c, Tilburg University, School of Economics and Management.
    3. Abraham P. Punnen & Ruonan Zhang, 2011. "Quadratic bottleneck problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 153-164, March.
    4. Ante Ćustić & Abraham P. Punnen, 2018. "A characterization of linearizable instances of the quadratic minimum spanning tree problem," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 436-453, February.
    5. Pereira, Dilson Lucas & Salles da Cunha, Alexandre, 2020. "Dynamic intersection of multiple implicit Dantzig–Wolfe decompositions applied to the adjacent only quadratic minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 284(2), pages 413-426.

    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. Ravi Kumar, K. & Hadjinicola, George C. & Lin, Ting-li, 1995. "A heuristic procedure for the single-row facility layout problem," European Journal of Operational Research, Elsevier, vol. 87(1), pages 65-73, November.
    2. Loiola, Eliane Maria & de Abreu, Nair Maria Maia & Boaventura-Netto, Paulo Oswaldo & Hahn, Peter & Querido, Tania, 2007. "A survey for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 176(2), pages 657-690, January.
    3. Bolte, Andreas & Thonemann, Ulrich Wilhelm, 1996. "Optimizing simulated annealing schedules with genetic programming," European Journal of Operational Research, Elsevier, vol. 92(2), pages 402-416, July.
    4. Vittorio Maniezzo, 1999. "Exact and Approximate Nondeterministic Tree-Search Procedures for the Quadratic Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 11(4), pages 358-369, November.
    5. Tian, Peng & Ma, Jian & Zhang, Dong-Mo, 1999. "Application of the simulated annealing algorithm to the combinatorial optimisation problem with permutation property: An investigation of generation mechanism," European Journal of Operational Research, Elsevier, vol. 118(1), pages 81-94, October.
    6. Jerzy Grobelny & Rafal Michalski, 2017. "A novel version of simulated annealing based on linguistic patterns for solving facility layout problems," WORking papers in Management Science (WORMS) WORMS/17/07, Department of Operations Research and Business Intelligence, Wroclaw University of Science and Technology.
    7. Jerzy Grobelny & Rafał Michalski, 2020. "Effects of scatter plot initial solutions on regular grid facility layout algorithms in typical production models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(2), pages 601-632, June.
    8. Maniezzo, Vittorio & Dorigo, Marco & Colorni, Alberto, 1995. "Algodesk: An experimental comparison of eight evolutionary heuristics applied to the Quadratic Assignment Problem," European Journal of Operational Research, Elsevier, vol. 81(1), pages 188-204, February.
    9. Solimanpur, M. & Vrat, P. & Shankar, R., 2004. "Ant colony optimization algorithm to the inter-cell layout problem in cellular manufacturing," European Journal of Operational Research, Elsevier, vol. 157(3), pages 592-606, September.
    10. Matai, Rajesh, 2015. "Solving multi objective facility layout problem by modified simulated annealing," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 302-311.
    11. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    12. Torki, Abdolhamid & Yajima, Yatsutoshi & Enkawa, Takao, 1996. "A low-rank bilinear programming approach for sub-optimal solution of the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 94(2), pages 384-391, October.
    13. Lin, Jin-Ling & Foote, Bobbie & Pulat, Simin & Chang, Chir-Ho & Cheung, John Y., 1996. "Solving the failure-to-fit problem for plant layout: By changing department shapes and sizes," European Journal of Operational Research, Elsevier, vol. 89(1), pages 135-146, February.
    14. Hang Li & Zhe Zhang & Xianggen Yin & Buhan Zhang, 2020. "Preventive Security-Constrained Optimal Power Flow with Probabilistic Guarantees," Energies, MDPI, vol. 13(9), pages 1-13, May.
    15. Ioannou, George, 2006. "Time-phased creation of hybrid manufacturing systems," International Journal of Production Economics, Elsevier, vol. 102(2), pages 183-198, August.
    16. Wu, Desheng (Dash) & Lee, Chi-Guhn, 2010. "Stochastic DEA with ordinal data applied to a multi-attribute pricing problem," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1679-1688, December.
    17. Zeinal Hamadani, Ali & Abouei Ardakan, Mostafa & Rezvan, Taghi & Honarmandian, Mohammad Mehran, 2013. "Location-allocation problem for intra-transportation system in a big company by using meta-heuristic algorithm," Socio-Economic Planning Sciences, Elsevier, vol. 47(4), pages 309-317.
    18. Giada Spaccapanico Proietti & Mariagiulia Matteucci & Stefania Mignani & Bernard P. Veldkamp, 2024. "Chance-Constrained Automated Test Assembly," Journal of Educational and Behavioral Statistics, , vol. 49(1), pages 92-120, February.
    19. Luca Maria Gambardella & Marco Dorigo, 2000. "An Ant Colony System Hybridized with a New Local Search for the Sequential Ordering Problem," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 237-255, August.
    20. Guigues, Vincent & Juditsky, Anatoli & Nemirovski, Arkadi, 2021. "Constant Depth Decision Rules for multistage optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 295(1), pages 223-232.

    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:wly:navres:v:39:y:1992:i:3:p:399-417. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.