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Exact algorithms for the Equitable Traveling Salesman Problem

Author

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  • Kinable, Joris
  • Smeulders, Bart
  • Delcour, Eline
  • Spieksma, Frits C.R.

Abstract

Given a weighted graph G=(V,E), the Equitable Traveling Salesman Problem (ETSP) asks for two perfect matchings in G such that (1) the two matchings together form a Hamiltonian cycle in G and (2) the absolute difference in costs between the two matchings is minimized. The problem is shown to be NP-Hard, even when the graph G is complete. We present two integer programming models to solve the ETSP problem and compare the strength of these formulations. One model is solved through branch-and-cut, whereas the other model is solved through a branch-and-price framework. A simple local search heuristic is also implemented. We conduct computational experiments on different types of instances, often derived from the TSPLib. It turns out that the behavior of the different approaches varies with the type of instances. For small and medium sized instances, branch-and-bound and branch-and-price produce comparable results. However, for larger instances branch-and-bound outperforms branch-and-price.

Suggested Citation

  • Kinable, Joris & Smeulders, Bart & Delcour, Eline & Spieksma, Frits C.R., 2017. "Exact algorithms for the Equitable Traveling Salesman Problem," European Journal of Operational Research, Elsevier, vol. 261(2), pages 475-485.
  • Handle: RePEc:eee:ejores:v:261:y:2017:i:2:p:475-485
    DOI: 10.1016/j.ejor.2017.02.017
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    References listed on IDEAS

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    1. Gouveia, Luis & Vo[ss], Stefan, 1995. "A classification of formulations for the (time-dependent) traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 83(1), pages 69-82, May.
    2. Bassetto, Tatiana & Mason, Francesco, 2011. "Heuristic algorithms for the 2-period balanced Travelling Salesman Problem in Euclidean graphs," European Journal of Operational Research, Elsevier, vol. 208(3), pages 253-262, February.
    3. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    4. G. A. Croes, 1958. "A Method for Solving Traveling-Salesman Problems," Operations Research, INFORMS, vol. 6(6), pages 791-812, December.
    5. K. Aardal & R. E. Bixby & C. A. J. Hurkens & A. K. Lenstra & J. W. Smeltink, 2000. "Market Split and Basis Reduction: Towards a Solution of the Cornuéjols-Dawande Instances," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 192-202, August.
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