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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
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    References listed on IDEAS

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    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.
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