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On the empirical scaling of running time for finding optimal solutions to the TSP

Author

Listed:
  • Zongxu Mu

    (University of British Columbia)

  • Jérémie Dubois-Lacoste

    (Université libre de Bruxelles (ULB))

  • Holger H. Hoos

    (University of British Columbia)

  • Thomas Stützle

    (Université libre de Bruxelles (ULB))

Abstract

We study the empirical scaling of the running time required by state-of-the-art exact and inexact TSP algorithms for finding optimal solutions to Euclidean TSP instances as a function of instance size. In particular, we use a recently introduced statistical approach to obtain scaling models from observed performance data and to assess the accuracy of these models. For Concorde, the long-standing state-of-the-art exact TSP solver, we compare the scaling of the running time until an optimal solution is first encountered (the finding time) and that of the overall running time, which adds to the finding time the additional time needed to complete the proof of optimality. For two state-of-the-art inexact TSP solvers, LKH and EAX, we compare the scaling of their running time for finding an optimal solution to a given instance; we also compare the resulting models to that for the scaling of Concorde’s finding time, presenting evidence that both inexact TSP solvers show significantly better scaling behaviour than Concorde.

Suggested Citation

  • Zongxu Mu & Jérémie Dubois-Lacoste & Holger H. Hoos & Thomas Stützle, 2018. "On the empirical scaling of running time for finding optimal solutions to the TSP," Journal of Heuristics, Springer, vol. 24(6), pages 879-898, December.
  • Handle: RePEc:spr:joheur:v:24:y:2018:i:6:d:10.1007_s10732-018-9374-0
    DOI: 10.1007/s10732-018-9374-0
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    References listed on IDEAS

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    1. Hoos, Holger H. & Stützle, Thomas, 2014. "On the empirical scaling of run-time for finding optimal solutions to the travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 238(1), pages 87-94.
    2. Yuichi Nagata & Shigenobu Kobayashi, 2013. "A Powerful Genetic Algorithm Using Edge Assembly Crossover for the Traveling Salesman Problem," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 346-363, May.
    3. Helsgaun, Keld, 2000. "An effective implementation of the Lin-Kernighan traveling salesman heuristic," European Journal of Operational Research, Elsevier, vol. 126(1), pages 106-130, October.
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