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Approximations for many-visits multiple traveling salesman problems

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  • Bérczi, Kristóf
  • Mnich, Matthias
  • Vincze, Roland

Abstract

A fundamental variant of the classical traveling salesman problem (TSP) is the so-called multiple TSP (mTSP), where a set of m salesmen jointly visit all cities from a set of n cities. The mTSP models many important real-life applications, in particular for vehicle routing problems. An extensive survey by Bektas (Omega34(3), 2006) lists a variety of heuristic and exact solution procedures for the mTSP that solve particular problem instances. In this work we consider a further generalization of mTSP, the many-visits mTSP, where each city v has a request r(v) of how many times it should be visited by the salesmen. This problem opens up new real-life applications such as aircraft sequencing, while at the same time it poses several computational challenges. We provide polynomial-time algorithms for several variants of the many-visits mTSP that compute constant-factor approximate solutions.

Suggested Citation

  • Bérczi, Kristóf & Mnich, Matthias & Vincze, Roland, 2023. "Approximations for many-visits multiple traveling salesman problems," Omega, Elsevier, vol. 116(C).
    • Handle: RePEc:eee:jomega:v:116:y:2023:i:c:s0305048322002225
    DOI: 10.1016/j.omega.2022.102816
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    References listed on IDEAS

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