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Lower bounding procedure for the asymmetric quadratic traveling salesman problem

Author

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  • Rostami, Borzou
  • Malucelli, Federico
  • Belotti, Pietro
  • Gualandi, Stefano

Abstract

In this paper we consider the Asymmetric Quadratic Traveling Salesman Problem (AQTSP). Given a directed graph and a function that maps every pair of consecutive arcs to a cost, the problem consists in finding a cycle that visits every vertex exactly once and such that the sum of the costs is minimal. We propose an extended Linear Programming formulation that has a variable for each cycle in the graph. Since the number of cycles is exponential in the graph size, we propose a column generation approach. Moreover, we apply a particular reformulation-linearization technique on a compact representation of the problem, and compute lower bounds based on Lagrangian relaxation. We compare our new bounds with those obtained by some linearization models proposed in the literature. Computational results on some set of benchmarks used in the literature show that our lower bounding procedures are very promising.

Suggested Citation

  • Rostami, Borzou & Malucelli, Federico & Belotti, Pietro & Gualandi, Stefano, 2016. "Lower bounding procedure for the asymmetric quadratic traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 253(3), pages 584-592.
  • Handle: RePEc:eee:ejores:v:253:y:2016:i:3:p:584-592
    DOI: 10.1016/j.ejor.2016.03.031
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    References listed on IDEAS

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    Cited by:

    1. Borzou Rostami & Guy Desaulniers & Fausto Errico & Andrea Lodi, 2021. "Branch-Price-and-Cut Algorithms for the Vehicle Routing Problem with Stochastic and Correlated Travel Times," Operations Research, INFORMS, vol. 69(2), pages 436-455, March.
    2. Brad D. Woods & Abraham P. Punnen, 2020. "A class of exponential neighbourhoods for the quadratic travelling salesman problem," Journal of Combinatorial Optimization, Springer, vol. 40(2), pages 303-332, August.
    3. Brad D. Woods & Abraham P. Punnen, 0. "A class of exponential neighbourhoods for the quadratic travelling salesman problem," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-30.

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