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A Heuristic for the Traveling Salesperson Problem with Forbidden Neighborhoods on Regular 2D and 3D Grids

In: Operations Research Proceedings 2018

Author

Listed:
  • Philipp Armbrust

    (Alpen-Adria-Universität Klagenfurt)

  • Philipp Hungerländer

    (Alpen-Adria-Universität Klagenfurt)

  • Anna Jellen

    (Alpen-Adria-Universität Klagenfurt)

Abstract

We examine an extension of the Traveling Salesperson Problem (TSP), the so called TSP with Forbidden Neighborhoods (TSPFN). The TSPFN is asking for a shortest Hamiltonian cycle of a given graph, where vertices traversed successively have a distance larger than a given radius. This problem is motivated by an application in mechanical engineering, more precisely in laser beam melting. This paper discusses a heuristic for solving the TSPFN when there don’t exist closed-form solutions and exact approaches fail. The underlying concept is based on Warnsdorff’s Rule but allows arbitrary step sizes and produces a Hamiltonian cycle instead of a Hamiltonian path. We implemented the heuristic and conducted a computational study for various neighborhoods. In particular the heuristic is able to find high quality TSPFN tours on 2D and 3D grids, i.e., it produces optimum and near-optimum solutions and shows a very good scalability also for large instances.

Suggested Citation

  • Philipp Armbrust & Philipp Hungerländer & Anna Jellen, 2019. "A Heuristic for the Traveling Salesperson Problem with Forbidden Neighborhoods on Regular 2D and 3D Grids," Operations Research Proceedings, in: Bernard Fortz & Martine Labbé (ed.), Operations Research Proceedings 2018, pages 95-101, Springer.
    • Handle: RePEc:spr:oprchp:978-3-030-18500-8_13
    DOI: 10.1007/978-3-030-18500-8_13
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