Four-Quadrant Division with HNN for Euclidean TSP

  • Ke-Fan Yu
  • Ke-Han Zeng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7390)


The Traveling Salesman Problem (TSP) is a renowned combinatorial optimization problem and has caught great attention of scientists from all over the world. In this study, an algorithm of Four-quadrant Division (FQD), which in each time divides a part of the map into four equivalent quadrants until the number of cities at each part of map is suitable for HNN to create tours, is applied to TSP. Also, a path relinking method is proposed to relink each part of a map to compose a global tour.


the travel salesman problem (TSP) Four-Quadrant Division (FQD) Hopfield Neural Network (HNN) path relinking 


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  1. 1.
    Aiyer, S.V.B., Niranjan, M., Fallside, F.: A theoretical Investigation into The Performance of The Hopfield Model. IEEE Transactions on Neural Network I(2), 204–215 (1990)CrossRefGoogle Scholar
  2. 2.
    Punnen, A.P.: The Traveling Salesman Problem: Application, Formulations and Variations. In: Gutin, G., Punnen, A.P. (eds.) The Traveling Salesman Problem and Its Variations, pp. 1–28. Kluwer, Norwell (2002)Google Scholar
  3. 3.
    Yang, H.Q., Yang, H.H.: An Self-organizing Neural Network with Convex-hull Expanding Property for TSP. IEEE (2005)Google Scholar
  4. 4.
  5. 5.
    Li, M.L., Zhang, Y., Zhu, M.: Solving TSP by using Lotka-Volterra Neural Networks. Neurocomputing, 0925–2312/$ - see front matter © 2009 Elsevier B.VGoogle Scholar
  6. 6.
    Pedro, M., Talavan, J.Y.: Parameter Setting of The Hopfield Network Applied to TSP. Neural Network 15, 363–373 (2002)CrossRefGoogle Scholar
  7. 7.
    Li, Y., Tang, Z., Xia, G.P., Wang, R.L., Xu, X.S.: A Fast and Reliable Approach to TSP using Positively Self-feedbacked Hopfield Networks. Hokkaido Institute of Tecnology, Japan (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ke-Fan Yu
    • 1
  • Ke-Han Zeng
    • 1
  1. 1.Department of Computer ScienceHuizhou UniversityHuizhouChina

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