Improving Hopfield Neural Network Performance and Parameters Investigation

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Warattapop Chainate
Peeraya Thapatsuwan
Somyot Kaitwanidvilai
Paisarn Muneesawang
Pupong Pongcharoen*

Abstract

 In this work, an appropriate setting of the Hopfield Network (HN) parameter was investigated and applied to the classical traveling salesman problem. The investigation on the requirement of raw data normalization was also carried out. Moreover, a modified training algorithm by embedded a heuristic called elitism for improving the performance of the conventional HN was additionally proposed. Computer experiments were implemented using various problem sizes. The results obtained from the experiments indicated that the appropriate setting of HN parameter should be specified with a low value. It was also found that the usage of raw data or normalized data did not influence on the performance of HN. Another experimental result suggested that the proposed hybrid HN did not only outperform conventional HN in terms of the equality of the results, but execution time was also faster.


 Keywords: Neural network, Meta-heuristics, Artificial intelligence, Traveling salesman, Combinatorial optimization.


 Corresponding author: E-mail: [email protected]


 

Article Details

Section
Original Research Articles

References

[1] Applegate, D., Bixby, R. and Cook, W. 1998. On the solution of traveling salesman problems.
[2] Lu, Y. 1991. Solving combinatorial optimization problems by simulated annealing, genetic algorithms, and neural networks. Master thesis, The University of Minnesota.
[3] Pham, D.T. and Karaboga, D. 2000. Intelligent optimization techniques. London: Springer-Verlag.
[4] Flood, M.M. 1955. The traveling salesman problem. Operation Research, 4, 61-75.
[5] Yu, Y., Liu, Q. and Tan, L. 2001. Solving TSP with distributed genetic algorithm and CORBA.
[6] Dorigo, M. and Gambardella, L.M. 1997. Ant colonies for the traveling salesman problem. Biosystems, 43(2), 73-81.
[7] Ghaziri, H. and Osman, I.H. 2003. A neural network algorithm for the traveling salesman problem with backhauls. Computers and Industrial Engineering, 44(2), 267-281.
[8] Modares, A., Somhom, S. and Enkawa, T. 1999. A self-organizing neural network approach for multiple traveling salesman and vehicle routing problems. International Transactions in Operational Research, 6(6), 591-606.
[9] Talaván, P.M. and Yáñez, J. 2002. Parameter setting of the Hopfield network applied to TSP. Neural Networks, 15(3), 363-373.
[10] McCulloch, W.S. and Pitts, W.H. 1943 A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5, 115-133.
[11] Osman, I.H. and Laporte, G. 1996. Metaheuristics: A bibliography. Annals of Operations Research, 63, 513-623.
[12] Garey, M.R. and Johnson, D.S. 1979. Computers and Intractability: A Guide to the Theory of NP-completeness. New York: Freeman.
[13] Nemhauser, G.L. and Wolsey, L.A. 1988 Integer and Combinatorial Optimization. John Wiley and Sons.
[14] Kohonen, T. 1982. Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43, 59-69.
[15] Aarts, E.H.L. and Korst, J.H.M. 1989. Simulated Annealing and Boltzmann Machines. John Wiley and Sons.
[16] Durbin, R. and Wilshaw, D. 1987. An analogue approach to the traveling salesman problem using elastic net method. Nature, 326, 689-691.
[17] Cochrane, E.M. and Beasley, J.E. 2003. The co-adaptive neural network approach to the Euclidean Traveling Salesman Problem. Neural Networks, 16(10), 1499-1525.
[18] Hedge, S., Sweet, J. and Levy, W. 1988. Determination of Parameters in a Hopfield/Tank Computational Network. Proceedings of 2nd IEEE International Conference on Neural Networks.
[19] Kamgar-Parsi, B. and Kamgar-Parsi, B. 1992. Dynamical stability and parameter selection in neural optimization. Proceedings of 4th IEEE International Conference on Neural Networks.
[20] Hopfield, J.J. and Tank, D.W. 1985. Neural computation of decisions in optimization problems. Biological Cybernetics, 52, 141-152.
[21] Wang, R.L., Tang, Z. and Cao, Q.P. 2002. A learning method in Hopfield neural network for combinatorial optimization problem. Neurocomputing Letters, 48, 1021-1024.
[22] Dantzig, G., Fulkerson, R. and Johnson, S. 1954. Solution of a large scale traveling salesman problem. Operation Research, 2, 393-410.
[23] Murata, T., Ishibuchi, H. and Tanaka, H. 1996. Multi-objective genetic algorithm and its applications to flow shop scheduling. Computers and Industrial Engineering, 30(4), 957-968.
[24] Montgomery, D.C. 2001. Design and Analysis of Experiments. 5th Edition, John Wiley and Sons.