IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v68y2017i10d10.1057_s41274-016-0146-7.html
   My bibliography  Save this article

A greedy heuristic for the capacitated minimum spanning tree problem

Author

Listed:
  • M. Kritikos

    (Athens University of Economics and Business)

  • G. Ioannou

    (Athens University of Economics and Business)

Abstract

This paper develops a greedy heuristic for the capacitated minimum spanning tree problem (CMSTP), based on the two widely known methods of Prim and of Esau–Williams. The proposed algorithm intertwines two-stages: an enhanced combination of the Prim and Esau–Williams approaches via augmented and synthetic node selection criteria, and an increase of the feasible solution space by perturbing the input data using the law of cosines. Computational tests on benchmark problems show that the new heuristic provides extremely good performance results for the CMSTP, justifying its effectiveness and robustness. Furthermore, excluding the feasible space expansion, we show that we can still obtain good quality solutions in very short computational times.

Suggested Citation

  • M. Kritikos & G. Ioannou, 2017. "A greedy heuristic for the capacitated minimum spanning tree problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(10), pages 1223-1235, October.
    • Handle: RePEc:pal:jorsoc:v:68:y:2017:i:10:d:10.1057_s41274-016-0146-7
    DOI: 10.1057/s41274-016-0146-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/s41274-016-0146-7
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/s41274-016-0146-7?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. G Bruno & G Laporte, 2002. "A simple enhancement of the Esau–Williams heuristic for the capacitated minimum spanning tree problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(5), pages 583-586, May.
    2. İ K Altınel & T Öncan, 2005. "A new enhancement of the Clarke and Wright savings heuristic for the capacitated vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(8), pages 954-961, August.
    3. Leslie Hall, 1996. "Experience with a Cutting Plane Algorithm for the Capacitated Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 8(3), pages 219-234, August.
    4. M Battarra & T Öncan & I K Altınel & B Golden & D Vigo & E Phillips, 2012. "An evolutionary approach for tuning parametric Esau and Williams heuristics," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(3), pages 368-378, March.
    5. Cesar Rego & Frank Mathew & Fred Glover, 2010. "RAMP for the capacitated minimum spanning tree problem," Annals of Operations Research, Springer, vol. 181(1), pages 661-681, December.
    6. G. Clarke & J. W. Wright, 1964. "Scheduling of Vehicles from a Central Depot to a Number of Delivery Points," Operations Research, INFORMS, vol. 12(4), pages 568-581, August.
    7. T Öncan & İ K Altınel, 2009. "Parametric enhancements of the Esau–Williams heuristic for the capacitated minimum spanning tree problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(2), pages 259-267, February.
    8. Paessens, H., 1988. "The savings algorithm for the vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 34(3), pages 336-344, March.
    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. Xiaojun Zhu & Shaojie Tang, 2021. "A Branch-and-Bound Algorithm for Building Optimal Data Gathering Tree in Wireless Sensor Networks," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1446-1460, October.

    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. T Öncan & İ K Altınel, 2009. "Parametric enhancements of the Esau–Williams heuristic for the capacitated minimum spanning tree problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(2), pages 259-267, February.
    2. Haughton, Michael A., 1998. "The performance of route modification and demand stabilization strategies in stochastic vehicle routing," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 551-566, November.
    3. Kleprlík Jaroslav & Brázdová Markéta, 2024. "Design of Restrictive Conditions for Simultaneous Loading and Unloading of Goods with Different Temperature Regimes in Vehicle Routing Problem," LOGI – Scientific Journal on Transport and Logistics, Sciendo, vol. 15(1), pages 97-108.
    4. Loske, Dominic & Klumpp, Matthias, 2021. "Human-AI collaboration in route planning: An empirical efficiency-based analysis in retail logistics," International Journal of Production Economics, Elsevier, vol. 241(C).
    5. Javier Faulin & Pablo Sarobe & Jorge Simal, 2005. "The DSS LOGDIS Optimizes Delivery Routes for FRILAC’s Frozen Products," Interfaces, INFORMS, vol. 35(3), pages 202-214, June.
    6. A A Juan & J Faulin & J Jorba & D Riera & D Masip & B Barrios, 2011. "On the use of Monte Carlo simulation, cache and splitting techniques to improve the Clarke and Wright savings heuristics," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(6), pages 1085-1097, June.
    7. Park, Junhyuk & Kim, Byung-In, 2010. "The school bus routing problem: A review," European Journal of Operational Research, Elsevier, vol. 202(2), pages 311-319, April.
    8. Gilbert Laporte, 2009. "Fifty Years of Vehicle Routing," Transportation Science, INFORMS, vol. 43(4), pages 408-416, November.
    9. Wadi Khalid Anuar & Lai Soon Lee & Hsin-Vonn Seow & Stefan Pickl, 2022. "A Multi-Depot Dynamic Vehicle Routing Problem with Stochastic Road Capacity: An MDP Model and Dynamic Policy for Post-Decision State Rollout Algorithm in Reinforcement Learning," Mathematics, MDPI, vol. 10(15), pages 1-70, July.
    10. Zhixing Luo & Hu Qin & T. C. E. Cheng & Qinghua Wu & Andrew Lim, 2021. "A Branch-and-Price-and-Cut Algorithm for the Cable-Routing Problem in Solar Power Plants," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 452-476, May.
    11. Zachariadis, Emmanouil E. & Tarantilis, Christos D. & Kiranoudis, Chris T., 2010. "An adaptive memory methodology for the vehicle routing problem with simultaneous pick-ups and deliveries," European Journal of Operational Research, Elsevier, vol. 202(2), pages 401-411, April.
    12. Van Breedam, Alex, 2002. "A parametric analysis of heuristics for the vehicle routing problem with side-constraints," European Journal of Operational Research, Elsevier, vol. 137(2), pages 348-370, March.
    13. Vigo, Daniele, 1996. "A heuristic algorithm for the asymmetric capacitated vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 89(1), pages 108-126, February.
    14. Amberg, Anita & Domschke, Wolfgang & Vo[ss], Stefan, 2000. "Multiple center capacitated arc routing problems: A tabu search algorithm using capacitated trees," European Journal of Operational Research, Elsevier, vol. 124(2), pages 360-376, July.
    15. C D Tarantilis & C T Kiranoudis & V S Vassiliadis, 2003. "A list based threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(1), pages 65-71, January.
    16. Tarantilis, C.D. & Kiranoudis, C.T., 2007. "A flexible adaptive memory-based algorithm for real-life transportation operations: Two case studies from dairy and construction sector," European Journal of Operational Research, Elsevier, vol. 179(3), pages 806-822, June.
    17. Rieck, Julia, 2011. "Ein Framework fu?r die Gestaltung grosser, internationaler Transportnetze: Beru?cksichtigung von Netzwerkdesign und Tourenbildung," Die Unternehmung - Swiss Journal of Business Research and Practice, Nomos Verlagsgesellschaft mbH & Co. KG, vol. 65(2), pages 133-150.
    18. T Doyuran & B Çatay, 2011. "A robust enhancement to the Clarke–Wright savings algorithm," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 223-231, January.
    19. M Battarra & B Golden & D Vigo, 2008. "Tuning a parametric Clarke–Wright heuristic via a genetic algorithm," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(11), pages 1568-1572, November.
    20. A Corominas & A García-Villoria & R Pastor, 2010. "Fine-tuning a parametric Clarke and Wright heuristic by means of EAGH (empirically adjusted greedy heuristics)," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(8), pages 1309-1314, August.

    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:pal:jorsoc:v:68:y:2017:i:10:d:10.1057_s41274-016-0146-7. 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.palgrave-journals.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.