IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v40y2020i3d10.1007_s10878-020-00605-0.html
   My bibliography  Save this article

A rapid learning automata-based approach for generalized minimum spanning tree problem

Author

Listed:
  • Masoumeh Zojaji

    (Islamic Azad University)

  • Mohammad Reza Mollakhalili Meybodi

    (Islamic Azad University)

  • Kamal Mirzaie

    (Islamic Azad University)

Abstract

Generalized minimum spanning tree problem, which has several real-world applications like telecommunication network designing, is related to combinatorial optimization problems. This problem belongs to the NP-hard class and is a minimum tree on a clustered graph spanning one node from each cluster. Although exact and metaheuristic algorithms have been applied to solve the problems successfully, obtaining an optimal solution using these approaches and other optimization tools has been a challenge. In this paper, an attempt is made to achieve a sub-optimal solution using a network of learning automata (LA). This algorithm assigns an LA to every cluster so that the number of actions is the same as that of nodes in the corresponding cluster. At each iteration, LAs select one node from their clusters. Then, the weight of the constructed generalized spanning tree is considered as a criterion for rewarding or penalizing the selected actions. The experimental results on a set of 20 benchmarks of TSPLIB demonstrate that the proposed approach is significantly faster than the other mentioned algorithms. The results indicate that the new algorithm is competitive in terms of solution quality.

Suggested Citation

  • Masoumeh Zojaji & Mohammad Reza Mollakhalili Meybodi & Kamal Mirzaie, 2020. "A rapid learning automata-based approach for generalized minimum spanning tree problem," Journal of Combinatorial Optimization, Springer, vol. 40(3), pages 636-659, October.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:3:d:10.1007_s10878-020-00605-0
    DOI: 10.1007/s10878-020-00605-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-020-00605-0
    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/s10878-020-00605-0?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
    ---><---

    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. Moshe Dror & Mohamed Haouari, 2000. "Generalized Steiner Problems and Other Variants," Journal of Combinatorial Optimization, Springer, vol. 4(4), pages 415-436, December.
    2. Pop, Petrica C. & Kern, W. & Still, G., 2006. "A new relaxation method for the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 170(3), pages 900-908, May.
    3. Bruce Golden & S. Raghavan & Daliborka Stanojević, 2005. "Heuristic Search for the Generalized Minimum Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 17(3), pages 290-304, August.
    4. Haouari, Mohamed & Chaouachi, Jouhaina Siala, 2006. "Upper and lower bounding strategies for the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 171(2), pages 632-647, June.
    5. Moradabadi, Behnaz & Meybodi, Mohammad Reza, 2017. "A novel time series link prediction method: Learning automata approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 422-432.
    6. Öncan, Temel & Cordeau, Jean-François & Laporte, Gilbert, 2008. "A tabu search heuristic for the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 191(2), pages 306-319, December.
    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. Masoumeh Zojaji & Mohammad Reza Mollakhalili Meybodi & Kamal Mirzaie, 0. "A rapid learning automata-based approach for generalized minimum spanning tree problem," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-24.
    2. Pop, Petrică C., 2020. "The generalized minimum spanning tree problem: An overview of formulations, solution procedures and latest advances," European Journal of Operational Research, Elsevier, vol. 283(1), pages 1-15.
    3. Pop, Petrică C. & Matei, Oliviu & Sabo, Cosmin & Petrovan, Adrian, 2018. "A two-level solution approach for solving the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 265(2), pages 478-487.
    4. Markus Leitner, 2016. "Integer programming models and branch-and-cut approaches to generalized {0,1,2}-survivable network design problems," Computational Optimization and Applications, Springer, vol. 65(1), pages 73-92, September.
    5. F. Carrabs & R. Cerulli & R. Pentangelo & A. Raiconi, 2018. "A two-level metaheuristic for the all colors shortest path problem," Computational Optimization and Applications, Springer, vol. 71(2), pages 525-551, November.
    6. Öncan, Temel & Cordeau, Jean-François & Laporte, Gilbert, 2008. "A tabu search heuristic for the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 191(2), pages 306-319, December.
    7. Mehmet Berkehan Akçay & Hüseyin Akcan & Cem Evrendilek, 2018. "All Colors Shortest Path problem on trees," Journal of Heuristics, Springer, vol. 24(4), pages 617-644, August.
    8. Feremans, Corinne & Labbe, Martine & Laporte, Gilbert, 2003. "Generalized network design problems," European Journal of Operational Research, Elsevier, vol. 148(1), pages 1-13, July.
    9. Pop, Petrică C. & Cosma, Ovidiu & Sabo, Cosmin & Sitar, Corina Pop, 2024. "A comprehensive survey on the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 314(3), pages 819-835.
    10. Phuoc Hoang Le & Tri-Dung Nguyen & Tolga Bektaş, 2016. "Generalized minimum spanning tree games," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 4(2), pages 167-188, May.
    11. Volgenant, A., 2004. "Solving the k-cardinality assignment problem by transformation," European Journal of Operational Research, Elsevier, vol. 157(2), pages 322-331, September.
    12. Mehdi El Krari & Belaïd Ahiod & Youssef Bouazza El Benani, 2021. "A pre-processing reduction method for the generalized travelling salesman problem," Operational Research, Springer, vol. 21(4), pages 2543-2591, December.
    13. Karapetyan, D. & Gutin, G., 2011. "Lin-Kernighan heuristic adaptations for the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 208(3), pages 221-232, February.
    14. Bergantiños, G. & Gómez-Rúa, M. & Llorca, N. & Pulido, M. & Sánchez-Soriano, J., 2014. "A new rule for source connection problems," European Journal of Operational Research, Elsevier, vol. 234(3), pages 780-788.
    15. Hansen, Jared M. & Raut, Sumit & Swami, Sanjeev, 2010. "Retail Shelf Allocation: A Comparative Analysis of Heuristic and Meta-Heuristic Approaches," Journal of Retailing, Elsevier, vol. 86(1), pages 94-105.
    16. W Zahrouni & H Kamoun, 2011. "Transforming part-sequencing problems in a robotic cell into a GTSP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 114-123, January.
    17. Pop, Petrica C. & Kern, W. & Still, G., 2006. "A new relaxation method for the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 170(3), pages 900-908, May.
    18. Zhang-Hua Fu & Jin-Kao Hao, 2015. "Dynamic Programming Driven Memetic Search for the Steiner Tree Problem with Revenues, Budget, and Hop Constraints," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 221-237, May.
    19. Contreras, Ivan & Fernández, Elena & Marín, Alfredo, 2010. "The Tree of Hubs Location Problem," European Journal of Operational Research, Elsevier, vol. 202(2), pages 390-400, April.
    20. Snyder, Lawrence V. & Daskin, Mark S., 2006. "A random-key genetic algorithm for the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 174(1), pages 38-53, October.

    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:40:y:2020:i:3:d:10.1007_s10878-020-00605-0. 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.