IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v34y2017i3d10.1007_s10878-017-0119-z.html
   My bibliography  Save this article

The traveling salesman problem on grids with forbidden neighborhoods

Author

Listed:
  • Anja Fischer

    (University of Göttingen)

  • Philipp Hungerländer

    (Alpen-Adria Universität Klagenfurt)

Abstract

We introduce the traveling salesman problem with forbidden neighborhoods (TSPFN). This is an extension of the Euclidean TSP in the plane where direct connections between points that are too close are forbidden. The TSPFN is motivated by an application in laser beam melting. In the production of a workpiece in several layers using this method one hopes to reduce the internal stresses of the workpiece by excluding the heating of positions that are too close. The points in this application are often arranged in some regular (grid) structure. In this paper we study optimal solutions of TSPFN instances where the points in the Euclidean plane are the points of a regular grid. Indeed, we explicitly determine the optimal values for the TSPFN and its associated path version on rectangular regular grids for different minimal distances of the points visited consecutively. For establishing lower bounds on the optimal values we use combinatorial counting arguments depending on the parities of the grid dimensions. Furthermore we provide construction schemes for optimal TSPFN tours for the considered cases.

Suggested Citation

  • Anja Fischer & Philipp Hungerländer, 2017. "The traveling salesman problem on grids with forbidden neighborhoods," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 891-915, October.
    • Handle: RePEc:spr:jcomop:v:34:y:2017:i:3:d:10.1007_s10878-017-0119-z
    DOI: 10.1007/s10878-017-0119-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-017-0119-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/s10878-017-0119-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.
    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. 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.
    2. 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).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Sven Mallach, 2021. "Inductive linearization for binary quadratic programs with linear constraints," 4OR, Springer, vol. 19(4), pages 549-570, December.
    13. Sebastian Henn & André Scholz & Meike Stuhlmann & Gerhard Wäscher, 2015. "A New Mathematical Programming Formulation for the Single-Picker Routing Problem in a Single-Block Layout," FEMM Working Papers 150005, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    14. Moreno, Alfredo & Munari, Pedro & Alem, Douglas, 2019. "A branch-and-Benders-cut algorithm for the Crew Scheduling and Routing Problem in road restoration," European Journal of Operational Research, Elsevier, vol. 275(1), pages 16-34.
    15. Akbari, Sina & Escobedo, Adolfo R., 2023. "Beyond kemeny rank aggregation: A parameterizable-penalty framework for robust ranking aggregation with ties," Omega, Elsevier, vol. 119(C).
    16. Yuzhu Wang & Akihiro Tanaka & Akiko Yoshise, 2021. "Polyhedral approximations of the semidefinite cone and their application," Computational Optimization and Applications, Springer, vol. 78(3), pages 893-913, April.
    17. Ghosh, Diptesh & Sumanta Basu, 2011. "Diversified Local Search for the Traveling Salesman Problem," IIMA Working Papers WP2011-01-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
    18. Bakker, Steffen J. & Wang, Akang & Gounaris, Chrysanthos E., 2021. "Vehicle routing with endogenous learning: Application to offshore plug and abandonment campaign planning," European Journal of Operational Research, Elsevier, vol. 289(1), pages 93-106.
    19. Klocker, Benedikt & Fleischner, Herbert & Raidl, Günther R., 2020. "A lower bound for the smallest uniquely hamiltonian planar graph with minimum degree three," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    20. Manfred Padberg, 2005. "Classical Cuts for Mixed-Integer Programming and Branch-and-Cut," Annals of Operations Research, Springer, vol. 139(1), pages 321-352, 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:34:y:2017:i:3:d:10.1007_s10878-017-0119-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.