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A Market-based Solution to the Multiple Traveling Salesmen Problem

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Abstract

This paper describes a market-based solution to the problem of assigning mobile agents to tasks. The problem is formulated as the multiple depots, multiple traveling salesmen problem (MTSP), where agents and tasks operate in a market to achieve near-optimal solutions. We consider both the classical MTSP, in which the sum of all tour lengths is minimized, and the Min-Max MTSP, in which the longest tour is minimized. We compare the market-based solution with direct enumeration in small scenarios, and show that the results are nearly optimal. For the classical MTSP, we compare our results to linear programming, and show that the results are within 1 % of the best cost found by linear programming in more than 90 % of the runs, with a significant reduction in runtime. For the Min-Max case, we compare our method with Carlsson’s algorithm and show an improvement of 5 % to 40 % in cost, albeit at an increase in runtime. Finally, we demonstrate the ability of the market-based solution to deal with changes in the scenario, e.g., agents leaving and entering the market. We show that the market paradigm is ideal for dealing with these changes during runtime, without the need to restart the algorithm, and that the solution reacts to the new scenarios in a quick and near-optimal way.

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Authors and Affiliations

  1. School of Aerospace Systems, University of Cincinnati, 2851 Woodside Dr, Cincinnati, OH, 45221, USA

    Elad Kivelevitch

  2. School of Aerospace Systems, University of Cincinnati, Cincinnati, OH, 45221-0070, USA

    Kelly Cohen

  3. Department of Mechanical, Industrial and Manufacturing Engineering (MIME), University of Toledo, Toledo, Ohio, 43606-3390, USA

    Manish Kumar

Authors
  1. Elad Kivelevitch
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  2. Kelly Cohen
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  3. Manish Kumar
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Correspondence to Elad Kivelevitch.

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Kivelevitch, E., Cohen, K. & Kumar, M. A Market-based Solution to the Multiple Traveling Salesmen Problem. J Intell Robot Syst 72, 21–40 (2013). https://doi.org/10.1007/s10846-012-9805-3

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  • DOI: https://doi.org/10.1007/s10846-012-9805-3

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