A New Neural Network Approach to the Traveling Salesman Problem

  • Paulo Henrique Siqueira
  • Sérgio Scheer
  • Maria Teresinha Arns Steiner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3971)


This paper presents a technique that uses the Wang Recurrent Neural Network with the "Winner Takes All" principle to solve the Traveling Salesman Problem (TSP). When the Wang Neural Network presents solutions for the Assignment Problem with all constraints satisfied, the "Winner Takes All" principle is applied to the values in the Neural Network’s decision variables, with the additional constraint that the new solution must form a feasible route for the TSP. The results from this new technique are compared to other heuristics, with data from the TSPLIB (TSP Library). The 2-opt local search technique is applied to the final solutions of the proposed technique and shows a considerable improvement of the results.


Neural Network Assignment Problem Travel Salesman Problem Travel Salesman Problem Recurrent Neural Network 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ahuja, R.K., Mangnanti, T.L., Orlin, J.B.: Network Flows. Prentice Hall, New Jersey (1993)Google Scholar
  2. 2.
    Laporte, G.: The Vehicle Roting Problem: An Overview of Exact and Approximate Algorithms. European Journal of Operational Research 59(2), 345–358 (1992)MATHCrossRefGoogle Scholar
  3. 3.
    Onwubolu, G.C., Clerc, M.: Optimal Path for Automated Drilling Operations by a New Heuristic Approach Using Particle Swarm Optimization. International Journal of Production Research 42(3), 473–491 (2004)MATHCrossRefGoogle Scholar
  4. 4.
    Affenzeller, M., Wanger, S.: A Self-Adaptive Model for Selective Pressure Handling within the Theory of Genetic Algorithms. In: Moreno-Díaz Jr., R., Pichler, F. (eds.) EUROCAST 2003. LNCS, vol. 2809, pp. 384–393. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Budinich, M.: A Self-Organizing Neural Network for the Traveling Salesman Problem That Is Competitive with Simulated Annealing. Neural Computing 8, 416–424 (1996)CrossRefGoogle Scholar
  6. 6.
    Liu, G., He, Y., Fang, Y., Oiu, Y.: A Novel Adaptive Search Strategy of Intensification and Diversification in Tabu Search. In: Proceedings of the IEEE International Conference on Neural Networks and Signal Processing – ICNNSP 2003, vol. 1, pp. 428–431. IEEE, Los Alamitos (2003)CrossRefGoogle Scholar
  7. 7.
    Bianchi, L., Knowles, J., Bowler, J.: Local Search for the Probabilistic Traveling Salesman Problem: Correction to the 2-P-Opt and 1-Shift Algorithms. European Journal of Operational Research 162(1), 206–219 (2005)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Chu, S.C., Roddick, J.F., Pan, J.S.: Ant Colony System with Communication Strategies. Information Sciences 167(1-4), 63–76 (2004)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Leung, K.S., Jin, H.D., Xu, Z.B.: An Expanding Self-Organizing Neural Network for the Traveling Salesman Problem. Neurocomputing 62, 267–292 (2004)CrossRefGoogle Scholar
  10. 10.
    Wang, R.L., Tang, Z., Cao, Q.P.: A Learning Method iIn Hopfield Neural Network for Combinatorial Optimization Problem. Neurocomputing 48(4), 1021–1024 (2002)MATHCrossRefGoogle Scholar
  11. 11.
    Wang, J.: Primal and Dual Neural Networks for Shortest-path Routing. IEEE Transactions on Systems: Man and Cybernetics - Part A: Systems and Humans 28(6), 864–869 (1998)CrossRefGoogle Scholar
  12. 12.
    Xia, Y., Wang, J.: A Discrete-time Recurrent Neural Network for Shortest-path Routing. IEEE Transactions on Automatic Control 45(11), 2129–2135 (2000)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Wang, J.: Analog Neural Network for Solving the Assignment Problem. Electronic Letters 28(11), 1047–1050 (1992)CrossRefGoogle Scholar
  14. 14.
    Hung, D.L., Wang, J.: Digital Hardware Realization of a Recurrent Neural Network for Solving the Assignment Problem. Neurocomputing 51, 447–461 (2003)CrossRefGoogle Scholar
  15. 15.
    Siqueira, P.H., Scheer, S., Steiner, M.T.A.: Application of the “Winner Takes All” Principle in Wang’s Recurrent Neural Network for the Assignment Problem. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 731–738. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    Reinelt, G.: TSPLIB – A Traveling Salesman Problem Library. ORSA Journal on Computing 3(4), 376–384 (1991)MATHGoogle Scholar
  17. 17.
    Wang, J.: Primal and Dual Assignment Networks. IEEE Transactions on Neural Networks 8(3), 784–790 (1997)CrossRefGoogle Scholar
  18. 18.
    Aras, N., Oommen, B.J., Altinel, I.K.: The Kohonen Network Incorporating Explicit Statistics and Its Application to the Traveling Salesman Problem. Neural Networks 12(9), 1273–1284 (1999)CrossRefGoogle Scholar
  19. 19.
    Jin, H.D., Leung, K.S., Wong, M.L., Xu, Z.B.: An Efficient Self-Organizing Map Designed by Genetic Algorithms for the Traveling Salesman Problem. IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics 33(6), 877–887 (2003)CrossRefGoogle Scholar
  20. 20.
    Vieira, F.C., Doria Neto, A.D., Costa, J.A.: An Efficient Approach to the Travelling Salesman Problem Using Self-Organizing Maps. International Journal of Neural Systems 13(2), 59–66 (2003)CrossRefGoogle Scholar
  21. 21.
    Cochrane, E.M., Beasley, J.E.: The Co-Adaptive Neural Network Approach to the Euclidean Travelling Salesman Problem. Neural Networks 16(10), 1499–1525 (2003)CrossRefGoogle Scholar
  22. 22.
    Glover, F., Gutin, G., Yeo, A., Zverovich, A.: Construction Heuristics for the Asymmetric TSP. European Journal of Operational Research 129(3), 555–568 (2001)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Paulo Henrique Siqueira
    • 1
  • Sérgio Scheer
    • 2
  • Maria Teresinha Arns Steiner
    • 3
  1. 1.Department of DrawingFederal University of ParanáCuritibaBrazil
  2. 2.Department of Civil ConstructionFederal University of ParanáCuritibaBrazil
  3. 3.Department of MathematicsFederal University of ParanáCuritibaBrazil

Personalised recommendations