IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v30y2022i4d10.1007_s10100-021-00784-z.html
   My bibliography  Save this article

Equivalent cyclic polygon of a euclidean travelling salesman problem tour and modified formulation

Author

Listed:
  • A. Herraiz

    (Universidad Politécnica de Madrid)

  • M. Gutierrez

    (Universidad Politécnica de Madrid)

  • M. Ortega-Mier

    (Universidad Politécnica de Madrid)

Abstract

We define a geometric transformation of Euclidean Travelling Salesman Problem (TSP) tours that leads to a new formulation of the TSP. For every Euclidean TSP n-city tour, it is possible to construct an inscribed n-polygon (Equivalent Cyclic Polygon, ECP) such that the lengths of the edges are equal to the corresponding TSP tour links and follow the same sequence order. The analysis of the ECP elicits the possibility of defining a new objective function in terms of angles instead of distances. This modification opens the way to identify characterizing geometric parameters of the TSP as well as to explore new heuristics based on the inclusion of additional constraints. The experimentation with a set of cases shows promising results compared to the traditional compact formulations. The behavior of the ECP-based TSP formulations is better when the nodes of the TSP are randomly or evenly distributed.

Suggested Citation

  • A. Herraiz & M. Gutierrez & M. Ortega-Mier, 2022. "Equivalent cyclic polygon of a euclidean travelling salesman problem tour and modified formulation," 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. 30(4), pages 1427-1450, December.
    • Handle: RePEc:spr:cejnor:v:30:y:2022:i:4:d:10.1007_s10100-021-00784-z
    DOI: 10.1007/s10100-021-00784-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10100-021-00784-z
    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/s10100-021-00784-z?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. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    2. S. P. Anbuudayasankar & K. Ganesh & Sanjay Mohapatra, 2014. "Models for Practical Routing Problems in Logistics," Springer Books, Springer, edition 127, number 978-3-319-05035-5, September.
    3. Laporte, Gilbert, 1992. "The traveling salesman problem: An overview of exact and approximate algorithms," European Journal of Operational Research, Elsevier, vol. 59(2), pages 231-247, June.
    4. John P. Norback & Robert F. Love, 1977. "Geometric Approaches to Solving the Traveling Salesman Problem," Management Science, INFORMS, vol. 23(11), pages 1208-1223, July.
    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. Tang, Lixin & Liu, Jiyin & Rong, Aiying & Yang, Zihou, 2000. "A multiple traveling salesman problem model for hot rolling scheduling in Shanghai Baoshan Iron & Steel Complex," European Journal of Operational Research, Elsevier, vol. 124(2), pages 267-282, July.
    2. A. S. Santos & A. M. Madureira & M. L. R. Varela, 2018. "The Influence of Problem Specific Neighborhood Structures in Metaheuristics Performance," Journal of Mathematics, Hindawi, vol. 2018, pages 1-14, July.
    3. Duygu Pamukcu & Burcu Balcik, 2020. "A multi-cover routing problem for planning rapid needs assessment under different information-sharing settings," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(1), pages 1-42, March.
    4. Zhouchun Huang & Qipeng Phil Zheng & Eduardo Pasiliao & Vladimir Boginski & Tao Zhang, 2019. "A cutting plane method for risk-constrained traveling salesman problem with random arc costs," Journal of Global Optimization, Springer, vol. 74(4), pages 839-859, August.
    5. Burger, M. & Su, Z. & De Schutter, B., 2018. "A node current-based 2-index formulation for the fixed-destination multi-depot travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 265(2), pages 463-477.
    6. Schuijbroek, J. & Hampshire, R.C. & van Hoeve, W.-J., 2017. "Inventory rebalancing and vehicle routing in bike sharing systems," European Journal of Operational Research, Elsevier, vol. 257(3), pages 992-1004.
    7. Bassetto, Tatiana & Mason, Francesco, 2011. "Heuristic algorithms for the 2-period balanced Travelling Salesman Problem in Euclidean graphs," European Journal of Operational Research, Elsevier, vol. 208(3), pages 253-262, February.
    8. G Laporte, 2010. "A concise guide to the Traveling Salesman Problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(1), pages 35-40, January.
    9. Rostami, Borzou & Malucelli, Federico & Belotti, Pietro & Gualandi, Stefano, 2016. "Lower bounding procedure for the asymmetric quadratic traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 253(3), pages 584-592.
    10. Neves-Moreira, Fábio & Almada-Lobo, Bernardo & Guimarães, Luís & Amorim, Pedro, 2022. "The multi-product inventory-routing problem with pickups and deliveries: Mitigating fluctuating demand via rolling horizon heuristics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
    11. Furini, Fabio & Persiani, Carlo Alfredo & Toth, Paolo, 2016. "The Time Dependent Traveling Salesman Planning Problem in Controlled Airspace," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 38-55.
    12. Almoustafa, Samira & Hanafi, Said & Mladenović, Nenad, 2013. "New exact method for large asymmetric distance-constrained vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 226(3), pages 386-394.
    13. Og[breve]uz, Ceyda & Sibel Salman, F. & Bilgintürk YalçIn, Zehra, 2010. "Order acceptance and scheduling decisions in make-to-order systems," International Journal of Production Economics, Elsevier, vol. 125(1), pages 200-211, May.
    14. Castellano, Davide & Gallo, Mosè & Grassi, Andrea & Santillo, Liberatina C., 2019. "The effect of GHG emissions on production, inventory replenishment and routing decisions in a single vendor-multiple buyers supply chain," International Journal of Production Economics, Elsevier, vol. 218(C), pages 30-42.
    15. Santos, Lui­s & Coutinho-Rodrigues, João & Current, John R., 2008. "Implementing a multi-vehicle multi-route spatial decision support system for efficient trash collection in Portugal," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(6), pages 922-934, July.
    16. Rahma Lahyani & Leandro C. Coelho & Jacques Renaud, 2018. "Alternative formulations and improved bounds for the multi-depot fleet size and mix vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 125-157, January.
    17. Kafle, Nabin & Zou, Bo & Lin, Jane, 2017. "Design and modeling of a crowdsource-enabled system for urban parcel relay and delivery," Transportation Research Part B: Methodological, Elsevier, vol. 99(C), pages 62-82.
    18. Anja Fischer & Frank Fischer, 2015. "An extended approach for lifting clique tree inequalities," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 489-519, October.
    19. Martinhon, Carlos & Lucena, Abilio & Maculan, Nelson, 2004. "Stronger K-tree relaxations for the vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 158(1), pages 56-71, October.
    20. 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.

    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:cejnor:v:30:y:2022:i:4:d:10.1007_s10100-021-00784-z. 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.