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Solving the Multiple Traveling Salesperson Problem on Regular Grids in Linear Time

In: Operations Research Proceedings 2019

Author

Listed:
  • Philipp Hungerländer

    (University of Klagenfurt)

  • Anna Jellen

    (University of Klagenfurt)

  • Stefan Jessenitschnig

    (University of Klagenfurt)

  • Lisa Knoblinger

    (University of Klagenfurt)

  • Manuel Lackenbucher

    (University of Klagenfurt)

  • Kerstin Maier

    (University of Klagenfurt)

Abstract

In this work we analyze the multiple Traveling Salesperson Problem (mTSP) on regular grids. While the general mTSP is known to be NP-hard, the special structure of regular grids can be exploited to explicitly determine optimal solutions in linear time. Our research is motivated by several real-world applications, for example delivering goods with swarms of unmanned aerial vehicles (UAV) or search and rescue operations. In order to obtain regular grid structures, we divide large search areas in several equal-sized squares, where we choose the square size as large as the sensor range of a UAV. First, we use an Integer Linear Program (ILP) to formally describe our considered mTSP variant on regular grids that aims to minimize the total tour length of all salespersons, which corresponds to minimizing the average search time for a missing person. With the help of combinatorial counting arguments and the establishment of explicit construction schemes, we are able to determine optimal mTSP solutions for specific grid sizes with two salespersons, where the depot is located in one of the four corners.

Suggested Citation

  • Philipp Hungerländer & Anna Jellen & Stefan Jessenitschnig & Lisa Knoblinger & Manuel Lackenbucher & Kerstin Maier, 2020. "Solving the Multiple Traveling Salesperson Problem on Regular Grids in Linear Time," Operations Research Proceedings, in: Janis S. Neufeld & Udo Buscher & Rainer Lasch & Dominik Möst & Jörn Schönberger (ed.), Operations Research Proceedings 2019, pages 215-221, Springer.
    • Handle: RePEc:spr:oprchp:978-3-030-48439-2_26
    DOI: 10.1007/978-3-030-48439-2_26
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