IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v31y2007i4p1009-1019.html
   My bibliography  Save this article

A columnar competitive model for solving multi-traveling salesman problem

Author

Listed:
  • Qu, Hong
  • Yi, Zhang
  • Tang, HuaJin

Abstract

This paper studies an optimization problem: multi-traveling salesman problem (MTSP), which is an extension of the well known TSP. A columnar competitive model (CCM) of neural networks incorporates with a winner-take-all learning rule is employed to solve the MTSP. Stability conditions of CCM for MTSP is exploited by mathematical analysis. Parameters settings of the network for guaranteeing the network converges to valid solutions are discussed in detail. Simulations are carried out to illustrate the performance of the columnar competitive model compare to the heuristic algorithms: Tabu Search.

Suggested Citation

  • Qu, Hong & Yi, Zhang & Tang, HuaJin, 2007. "A columnar competitive model for solving multi-traveling salesman problem," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 1009-1019.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:4:p:1009-1019
    DOI: 10.1016/j.chaos.2005.10.059
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905010222
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.10.059?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. Rego, Cesar, 1998. "Relaxed tours and path ejections for the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 522-538, April.
    2. R. D. Angel & W. L. Caudle & R. Noonan & A. Whinston, 1972. "Computer-Assisted School Bus Scheduling," Management Science, INFORMS, vol. 18(6), pages 279-288, February.
    3. Pirlot, Marc, 1996. "General local search methods," European Journal of Operational Research, Elsevier, vol. 92(3), pages 493-511, August.
    4. Joseph A. Svestka & Vaughn E. Huckfeldt, 1973. "Computational Experience with an M-Salesman Traveling Salesman Algorithm," Management Science, INFORMS, vol. 19(7), pages 790-799, 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. Lining Xing & Yuanyuan Liu & Haiyan Li & Chin-Chia Wu & Win-Chin Lin & Xin Chen, 2020. "A Novel Tabu Search Algorithm for Multi-AGV Routing Problem," Mathematics, MDPI, vol. 8(2), pages 1-16, February.

    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. Bektas, Tolga, 2006. "The multiple traveling salesman problem: an overview of formulations and solution procedures," Omega, Elsevier, vol. 34(3), pages 209-219, June.
    2. Mutsunori Yagiura & Toshihide Ibaraki & Fred Glover, 2004. "An Ejection Chain Approach for the Generalized Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 133-151, May.
    3. 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.
    4. Melouk, Sharif & Damodaran, Purushothaman & Chang, Ping-Yu, 2004. "Minimizing makespan for single machine batch processing with non-identical job sizes using simulated annealing," International Journal of Production Economics, Elsevier, vol. 87(2), pages 141-147, January.
    5. Ganesan, Viswanath Kumar & Sivakumar, Appa Iyer, 2006. "Scheduling in static jobshops for minimizing mean flowtime subject to minimum total deviation of job completion times," International Journal of Production Economics, Elsevier, vol. 103(2), pages 633-647, October.
    6. César Rego, 1998. "A Subpath Ejection Method for the Vehicle Routing Problem," Management Science, INFORMS, vol. 44(10), pages 1447-1459, October.
    7. Rego, César & Duarte, Renato, 2009. "A filter-and-fan approach to the job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 194(3), pages 650-662, May.
    8. Van Woensel, T. & Kerbache, L. & Peremans, H. & Vandaele, N., 2008. "Vehicle routing with dynamic travel times: A queueing approach," European Journal of Operational Research, Elsevier, vol. 186(3), pages 990-1007, May.
    9. Chen, Lijian & Chiang, Wen-Chyuan & Russell, Robert & Chen, Jun & Sun, Dengfeng, 2018. "The probabilistic vehicle routing problem with service guarantees," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 111(C), pages 149-164.
    10. Kara, Imdat & Bektas, Tolga, 2006. "Integer linear programming formulations of multiple salesman problems and its variations," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1449-1458, November.
    11. Cantarella, G.E. & Pavone, G. & Vitetta, A., 2006. "Heuristics for urban road network design: Lane layout and signal settings," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1682-1695, December.
    12. Day, Jamison M. & Daniel Wright, P. & Schoenherr, Tobias & Venkataramanan, Munirpallam & Gaudette, Kevin, 2009. "Improving routing and scheduling decisions at a distributor of industrial gasses," Omega, Elsevier, vol. 37(1), pages 227-237, February.
    13. Gary R. Waissi & Pragya Kaushal, 2020. "A polynomial matrix processing heuristic algorithm for finding high quality feasible solutions for the TSP," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 73-87, March.
    14. Ellegood, William A. & Solomon, Stanislaus & North, Jeremy & Campbell, James F., 2020. "School bus routing problem: Contemporary trends and research directions," Omega, Elsevier, vol. 95(C).
    15. Alizadeh, Somayeh & Ghazanfari, Mehdi, 2009. "Learning FCM by chaotic simulated annealing," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1182-1190.
    16. B Suman & P Kumar, 2006. "A survey of simulated annealing as a tool for single and multiobjective optimization," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(10), pages 1143-1160, October.
    17. Colin Osterman & César Rego, 2016. "A k-level data structure for large-scale traveling salesman problems," Annals of Operations Research, Springer, vol. 244(2), pages 583-601, September.
    18. Suxia Ma & Yuelin Gao & Bo Zhang & Wenlu Zuo, 2022. "A New Nonparametric Filled Function Method for Integer Programming Problems with Constraints," Mathematics, MDPI, vol. 10(5), pages 1-16, February.
    19. Bräysy, Olli & Dullaert, Wout & Nakari, Pentti, 2009. "The potential of optimization in communal routing problems: case studies from Finland," Journal of Transport Geography, Elsevier, vol. 17(6), pages 484-490.
    20. Julia Rieck & Jürgen Zimmermann & Matthias Glagow, 2007. "Tourenplanung mittelständischer Speditionsunternehmen in Stückgutkooperationen: Modellierung und heuristische Lösungsverfahren," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 17(4), pages 365-388, January.

    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:eee:chsofr:v:31:y:2007:i:4:p:1009-1019. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.