Self-Organizing Map for the Curvature-Constrained Traveling Salesman Problem

  • Jan FaiglEmail author
  • Petr Váňa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9887)


In this paper, we consider a challenging variant of the traveling salesman problem (TSP) where it is requested to determine the shortest closed curvature-constrained path to visit a set of given locations. The problem is called the Dubins traveling salesman problem in literature and its main difficulty arises from the fact that it is necessary to determine the sequence of visits to the locations together with particular headings of the vehicle at the locations. We propose to apply principles of unsupervised learning of the self-organizing map to simultaneously determine the sequence of the visits together with the headings. A feasibility of the proposed approach is supported by an extensive evaluation and comparison to existing solutions. The presented results indicate that the proposed approach provides competitive solutions to existing heuristics, especially in dense problems, where the optimal sequence of the visits cannot be determined as a solution of the Euclidean TSP.



The presented work has been supported by the Czech Science Foundation (GAČR) under research project No. 16-24206S.

Computational resources were provided by the MetaCentrum under the program LM2010005 and the CERIT-SC under the program Centre CERIT Scientific Cloud, part of the Operational Program Research and Development for Innovations, Reg. No. CZ.1.05/3.2.00/08.0144.


  1. 1.
    Angéniol, B., de la Vaubois, C., Texier, J.Y.L.: Self-organizing feature maps and the travelling salesman problem. Neural Netw. 1, 289–293 (1988)CrossRefGoogle Scholar
  2. 2.
    Applegate, D., Bixby, R., Chvátal, V., Cook, W.: Concorde tsp solver (2003). [cited 22 Jan 2016]Google Scholar
  3. 3.
    Cochrane, E.M., Beasley, J.E.: The co-adaptive neural network approach to the Euclidean travelling salesman problem. Neural Netw. 16(10), 1499–1525 (2003)CrossRefGoogle Scholar
  4. 4.
    Cook, W.: In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation. Princeton University Press (2012)Google Scholar
  5. 5.
    Dubins, L.E.: On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. Am. J. Math. 79, 497–516 (1957)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Faigl, J., Přeučil, L.: Self-organizing map for the multi-goal path planning with polygonal goals. In: Honkela, T. (ed.) ICANN 2011, Part I. LNCS, vol. 6791, pp. 85–92. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Goaoc, X., Kim, H.S., Lazard, S.: Bounded-curvature shortest paths through a sequence of points using convex optimization. SIAM J. Comput. 42(2), 662–684 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Le Ny, J., Feron, E., Frazzoli, E.: On the dubins traveling salesman problem. IEEE Trans. Autom. Control 57(1), 265–270 (2012)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Oberlin, P., Rathinam, S., Darbha, S.: Today’s traveling salesman problem. IEEE Robot. Autom. Mag. 17(4), 70–77 (2010)CrossRefGoogle Scholar
  10. 10.
    Obermeyer, K.J., Oberlin, P., Darbha, S.: Sampling-based path planning for a visual reconnaissance unmanned air vehicle. J. Guidance Control Dynamics 35(2), 619–631 (2012)CrossRefGoogle Scholar
  11. 11.
    Savla, K., Frazzoli, E., Bullo, F.: Traveling salesperson problems for the Dubins vehicle. IEEE Trans. Autom. Control 53(6), 1378–1391 (2008)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Savla, K., Frazzoli, E., Bullo, F.: On the point-to-point and traveling salesperson problems for Dubins’ vehicle. In: Proceedings of the American Control Conference, pp. 786–791. IEEE (2005)Google Scholar
  13. 13.
    Somhom, S., Modares, A., Enkawa, T.: A self-organising model for the travelling salesman problem. J. Oper. Res. Soc. 48, 919–928 (1997)CrossRefzbMATHGoogle Scholar
  14. 14.
    Váňa, P., Faigl, J.: On the dubins traveling salesman problem with neighborhoods. In: International Conference on Intelligent Robots and Systems, pp. 4029–4034 (2015)Google Scholar
  15. 15.
    Yu, X., Hung, J.: A genetic algorithm for the dubins traveling salesman problem. In: IEEE International Symposium on Industrial Electronics, pp. 1256–1261 (2012)Google Scholar
  16. 16.
    Zhang, X., Chen, J., Xin, B., Peng, Z.: A memetic algorithm for path planning of curvature-constrained UAVs performing surveillance of multiple ground targets. Chin. J. Aeronaut. 27(3), 622–633 (2014)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceCzech Technical University in PraguePrague 6Czech Republic

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