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Exploring the Solution Space of the Euclidean Traveling Salesman Problem Using a Kohonen SOM Neural Network

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Artificial Intelligence and Soft Computing (ICAISC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10245))

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Abstract

In this paper we present a new approach to solving the Euclidean traveling salesman problem (ETSP) using SOM Kohonen maps with chain topology. The Kohonen learning rule is used with random parameters providing different neuron locations. Any new neuron configuration allows us to obtain a new ETSP solution. This new approach to exploring the solution space of the ETSP is easy to implement and suitable for relatively large ETSP problems. Furthermore, the approach could be combined both with other global optimization methods as genetic algorithms and with simple TSP solving heuristic procedures. The method is illustrated by simulations used for solving some TSPLIB problems.

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References

  1. Angeniol, B., Vaubois, C., Texier, J.-Y.L.: Self-organizing feature maps and the traveling salesman problem. Neural Netw. 1, 289–293 (1988)

    Article  Google Scholar 

  2. Avsar, B., Aliabadi, D.E.: Parallelized neural network system for solving Euclidean traveling salesman problem. Appl. Soft Comput. 34, 862–873 (2015)

    Article  Google Scholar 

  3. Applegate, D.L., Bixby, R.E., Chvatal, V., Cook, W.J.: The Traveling Salesman Problem: a Computational Study. Princeton University Press, Princeton (2006)

    MATH  Google Scholar 

  4. Aras, N., Oommen, B.J., Altinel, I.K.: Kohonen Network incorporating explicit statistics and its application to the traveling salesman problem. Neural Netw. 12, 1273–1284 (1999)

    Article  Google Scholar 

  5. Bai, Y., Zhang, W., Hu, H.: An efficient growing ring SOM and its application to TSP. In: Proceedings of the 9th WSEAS International Conference on Applied Mathematics, Istanbul, Turkey, May 27–29, 2006, pp. 351–355 (2006)

    Google Scholar 

  6. Bai, Y., Zhang, W., Jin, Z.: An new self-organizing maps strategy for solving the traveling salesman problem. Chaos Solitons Fractals 28, 1082–1089 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bartholdi, J.J., Platzman, L.K.: Heuristics based on spacefilling curves for combinatorial problems in Euclidean space. Manage. Sci. 34, 291–305 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bianchi, L., Knowles, J., Bowler, J.: Local search for the probabilistic traveling salesman problem: correction to the 2-p-opt and 1-shift algorithms. Eur. J. Oper. Res. 162(1), 206–219 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Budinich, M.: A self-organising neural network for the travelling salesman problem that is competitive with simulated annealing. Neural Comput. 8(2), 416–424 (1996)

    Article  Google Scholar 

  10. Budinich, M., Rosario, B.: A neural network for the travelling salesman problem with a well behaved energy function. In: Ellacott, S.W., Mason, J.C., Anderson, I.J. (eds.) Mathematics of Neural Networks: Models, Algorthms and Applications, pp. 134–139. Kluwer Academic Publishers, Boston (1997)

    Chapter  Google Scholar 

  11. 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)

    Article  Google Scholar 

  12. Durbin, R., Szeliski, R., Yuille, A.: An analysis of the elastic net approach to the traveling salesman problem. Neural Comput. 1, 348–358 (1989)

    Article  Google Scholar 

  13. Durbin, R., Willshaw, D.: An analogue approach to the travelling salesman problem using an elastic net method. Nature 326, 689–691 (1987)

    Article  Google Scholar 

  14. Favata, S., Walker, R.: A study of the application of Kohonen-type neural networks to the traveling salesman problem. Biol. Cybern. 64, 463–468 (1991)

    Article  MATH  Google Scholar 

  15. Fort, J.C.: Solving combinatorial problem via self-organizing process: an application of the Kohonen algorithm to the traveling salesman problem. Biol. Cybern. 59, 33–40 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hueter, G.J.: Solution of the traveling salesman problem with an adaptive ring. In: Proceedings of the IEEE International Conference on Neural Networks, vol. I, pp. 85–92 (1988)

    Google Scholar 

  17. Karp, R.M., Steele, J.M.: Probabilistic analysis of heuristics. In: Lawlwr, E.L., Lenstra, J.K., Rinnooy Kan, A.G.H., Shmoys, D.B. (eds.) The Traveling Salesmen Problem: A Guided Tour of Combinatorial Optimization. Wiley, Chichister, New York, Brisbane, Toronto, Singapore (1985)

    Google Scholar 

  18. Kohonen, T.: The self-organizing map. Proc. IEEE 78(9), 1464–1480 (1990)

    Article  Google Scholar 

  19. Kohonen, T.: Self-organizing Map. Springer, New York (2001)

    Book  MATH  Google Scholar 

  20. Lawler, E., Lenstra, J., Rinnooy, K.A.: The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. Wiley, New York (1985)

    MATH  Google Scholar 

  21. 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)

    Article  Google Scholar 

  22. La Maire, B.F.J., Mladenov, V.M.: Comparison of neural networks for solving the travelling salesman problem. In: IEEE Proceedings of the NEUREL 2012 (2012). doi:10.1109/NEUREL.2012.6419953

  23. Matsuyama, Y.: Self-organizing neural networks and various euclidean traveling salesman problems. Syst. Comput. Jpn. 2, 101–112 (1992)

    Article  Google Scholar 

  24. Papadimitriou, C.H.: The Euclidean traveling salesman problem is NP-complete. Theor. Comput. Sci. 4, 237–244 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  25. Platzman, L.K., Bartholdi, J.J.: Spacefilling curves and the planar traveling salesman problem. J. ACM 36, 719–737 (1989)

    Article  MATH  Google Scholar 

  26. Reinelt, G.: TSPLIB - a traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)

    Article  MATH  Google Scholar 

  27. Ritter, H., Martinetz, T., Schulten, K.: Neural Computation and Self Organizing Maps: An Introduction. Addison-Wesley, New York (1992)

    MATH  Google Scholar 

  28. Saadatmand-Tarzjan, M., Khademi, M., Akbarzadeh-T, M.R., Moghaddam, H.A.: A novel constructive-optimizer neural network for the traveling salesman problem. IEEE Trans. Syst. Man Cybern. Part B Cybern. 37(4), 754–770 (2007)

    Article  Google Scholar 

  29. Steele, J.M.: Efficacy of spacefilling heuristics in euclidean combinatorial optimization. Oper. Res. Lett. 8, 237–239 (1989)

    Article  MathSciNet  Google Scholar 

  30. Vieira, F.C., Dria Neto, A.D., Costa, J.A.: An efficient approach to the travelling salesman problem using self-organizing maps. Int. J. Neural Syst. 13(2), 59–66 (2003)

    Article  Google Scholar 

  31. Xu, X., Jia, Z., Ma, J., Wang, J.: A self-organizing map algorithm for the traveling salesman problem. In: IEEE Proceedings of the Fourth International Conference on Natural Computation, pp. 431–435 (2008). doi:10.1109/ICNC.2008.569

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Authors and Affiliations

  1. Department of Computer Engineering, Faculty of Electronics, Wrocław University of Science and Technology, Wrocław, Poland

    Ewa Skubalska-Rafajłowicz

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  1. Ewa Skubalska-Rafajłowicz
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Correspondence to Ewa Skubalska-Rafajłowicz .

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Częstochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Częstochowa, Poland

    Marcin Korytkowski

  3. Częstochowa University of Technology, Częstochowa, Poland

    Rafał Scherer

  4. AGH University of Science and Technology, Kraków, Poland

    Ryszard Tadeusiewicz

  5. University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  6. University of Louisville, Louisville, Kentucky, USA

    Jacek M. Zurada

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Skubalska-Rafajłowicz, E. (2017). Exploring the Solution Space of the Euclidean Traveling Salesman Problem Using a Kohonen SOM Neural Network. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2017. Lecture Notes in Computer Science(), vol 10245. Springer, Cham. https://doi.org/10.1007/978-3-319-59063-9_15

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  • DOI: https://doi.org/10.1007/978-3-319-59063-9_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59062-2

  • Online ISBN: 978-3-319-59063-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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