IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v29y1995i2p167-183.html
   My bibliography  Save this article

Heuristic Bounds and Test Problem Generation for the Time-Dependent Traveling Salesman Problem

Author

Listed:
  • Russ J. Vander Wiel

    (Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, Illinois 61801)

  • Nikolaos V. Sahinidis

    (Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, Illinois 61801)

Abstract

The Time-Dependent Traveling Salesman Problem (TDTSP) is a generalization of the Traveling Salesman Problem (TSP) in which the cost of travel between two cities depends on the distance between the cities and the position of the transition in the tour. There exists a number of applications of the TDTSP in the fields of distribution and scheduling. We present a new mixed-integer linear programming (MILP) formulation for the TDTSP. A directed multi-partite graph representation of this model facilitates the development of a local search heuristic which extends the well known Lin-Kernighan tour improvement heuristic to the TDTSP. A second upper bound is derived by applying a Benders-decomposition-based heuristic to the MILP formulation. The Benders master problem is further approximately solved to provide a lower bound. We also develop a method for generating TDTSP instances with known optimal solutions. Finally, computational experience with the heuristics and problem generator is presented for problems with up to 100 cities. The results demonstrate that the heuristics can achieve optimal or very good near-optimal solutions on a variety of problem classes with minimal computational effort.

Suggested Citation

  • Russ J. Vander Wiel & Nikolaos V. Sahinidis, 1995. "Heuristic Bounds and Test Problem Generation for the Time-Dependent Traveling Salesman Problem," Transportation Science, INFORMS, vol. 29(2), pages 167-183, May.
  • Handle: RePEc:inm:ortrsc:v:29:y:1995:i:2:p:167-183
    DOI: 10.1287/trsc.29.2.167
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.29.2.167
    Download Restriction: no

    File URL: https://libkey.io/10.1287/trsc.29.2.167?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kinable, Joris & Cire, Andre A. & van Hoeve, Willem-Jan, 2017. "Hybrid optimization methods for time-dependent sequencing problems," European Journal of Operational Research, Elsevier, vol. 259(3), pages 887-897.
    2. Miranda-Bront, Juan José & Méndez-Díaz, Isabel & Zabala, Paula, 2014. "Facets and valid inequalities for the time-dependent travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 236(3), pages 891-902.
    3. Russ J. Vander Wiel & Nikolaos V. Sahinidis, 1996. "An exact solution approach for the time‐dependent traveling‐salesman problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 797-820, September.

    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:inm:ortrsc:v:29:y:1995:i:2:p:167-183. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.