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Lower and Upper Bounds for a Symmetric Multiple Depot, Multiple Travelling Salesman Problem

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  • Rathinam, Sivakumar
  • Sengupta, Raja

Abstract

This paper extends the well known Held-Karp's lower bound available for a single Travelling Salesman Problem to the multiple depot case. The LP-relaxation of a symmetric multiple vehicle, multiple depot problem is shown to be lower bounded by an infinite family of bounds. Each lower bound can be computed in a tractable way using a matroid intersection algorithm. When the costs of travelling between any two locations satisfy triangle inequality, it is shown that there exists a 2-approximation algorithm for solving the multiple depot, multiple TSP. These results are useful in solving the following path planning problem of UAVs: Given a set of UAVs, their starting locations, a set of final UAV locations, a set of destinations to visit and the cost of travelling between any two locations, find a path for each UAV such that each destination is visited once by any one UAV and the total cost travelled by all the UAVs is minimum.

Suggested Citation

  • Rathinam, Sivakumar & Sengupta, Raja, 2006. "Lower and Upper Bounds for a Symmetric Multiple Depot, Multiple Travelling Salesman Problem," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt4z68041r, Institute of Transportation Studies, UC Berkeley.
    • Handle: RePEc:cdl:itsrrp:qt4z68041r
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    References listed on IDEAS

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    1. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
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    1. Bérczi, Kristóf & Mnich, Matthias & Vincze, Roland, 2023. "Approximations for many-visits multiple traveling salesman problems," Omega, Elsevier, vol. 116(C).
    2. José Alejandro Cornejo-Acosta & Jesús García-Díaz & Julio César Pérez-Sansalvador & Carlos Segura, 2023. "Compact Integer Programs for Depot-Free Multiple Traveling Salesperson Problems," Mathematics, MDPI, vol. 11(13), pages 1-25, July.

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