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Single-commodity flow-based formulations and accelerated benders algorithms for the high-multiplicity asymmetric traveling salesman problem and its extensions

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Journal of the Operational Research Society

Abstract

In this paper, we present a single-commodity flow-based formulation for the high-multiplicity asymmetric traveling salesman problem (HMATSP), which is an extension of the asymmetric traveling salesman problem (ATSP) wherein a city can be visited multiple times. We show that even though this formulation is not as tight as the best known formulation for the HMATSP, it is faster and easier to use for direct solution by CPLEX and can be used to model several variants or extensions of the HMATSP that have not been studied in the literature. Furthermore, we propose effective accelerated Benders algorithms that are demonstrated to solve instances of the HMATSP and its extensions, which are derived from the well-known ATSP libraries and involve up to 1001 cities, within an hour of CPU time. These are the largest-sized HMATSP instances solved to optimality in the literature.

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Authors and Affiliations

  1. Departamento de Ingenieria Industrial, Universidad de Concepcion, Edmundo Larenas 219, Concepcion, Chile

    Maichel M. Aguayo

  2. Grado Department of Industrial and Systems Engineering, Virginia Tech., Blacksburg, VA, 24060, USA

    Subhash C. Sarin & Hanif D. Sherali

Authors
  1. Maichel M. Aguayo
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  2. Subhash C. Sarin
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  3. Hanif D. Sherali
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Correspondence to Subhash C. Sarin.

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Aguayo, M.M., Sarin, S.C. & Sherali, H.D. Single-commodity flow-based formulations and accelerated benders algorithms for the high-multiplicity asymmetric traveling salesman problem and its extensions. J Oper Res Soc (2017). https://doi.org/10.1057/s41274-017-0261-0

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