Abstract
In the Hopfield network a solution of an optimization problem is obtained after the network is relaxed to an equilibrium state. This paper shows that the performance of the Hopfield network can be improved by using a relaxation rate to control the relaxation process. Analysis suggests that the relaxation process has an important impact on the quality of a solution. A relaxation rate is then introduced to control the relaxation process in order to achieve solutions with better quality. Two types of relaxation rate (constant and dynamic) are proposed and evaluated through simulations based on 200 randomly generated city distributions of the 10-city traveling salesman problem. The result shows that using a relaxation rate can decrease the error rate by 9.87% and increase the percentage of valid tours by 14.0% as compared to those without using a relaxation rate. Using a dynamic relaxation rate can further decrease the error 3rate by 4.2% and increase the percentage of valid tours by 0.4% as compared to those using a constant relaxation rate.
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References
Hopfield, J. J. and Tank, D. W.: Neural Computations of Decisions in Optimization Problems. Biological Cybernetics, vol. 52, pp. 141–152, 1985.
Wilson, G. V. and Pawley, G. S.: On the Stability of the Traveling Salesman Problem Algorithm of Hopfield and Tank. Biological Cybernetics, vol. 58, pp. 63–70, 1988.
Brandt, R. D., Wang, Y., Laub, A. J. and Mitra, S. K.: Alternative Networks for Solving the Traveling Salesman Problem and the List-Matching Problem. Proceedings of IEEE International Conference on Neural Networks, San Diego, CA. II: 333–340, 1988.
Aiyer, S. V. B., Niranjan, M. and Fallside, F.: A Theoretical Investigation into the Performance of the Hopfield Model. IEEE Transactions on Neural Networks, vol. 1, no. 2, pp. 204–215, 1990.
Li, S. Z.: Improving Convergence and Solution Quality of Hopfield-Type Neural Networks with Augmented Lagrange Multipliers. IEEE Transactions On Neural Networks, vol. 7, no. 6, pp. 1507–1516, 1996.
Catania, V., Cavalieri, S. and Russo, M.: Tuning Hopfield Neural Network by a Fuzzy Approach. Proceedings of IEEE International Conference on Neural Networks, pp. 1067–1072, 1996.
Liang, Y.:Combinatorial Optimization by Hopfield Networks Using Adjusting Neurons. Information Sciences, vol. 94, pp. 261–276, 1996.
Cooper, B. S.: Higher Order Neural Networks-Can they help us Optimise?. Proceedings of the Sixth Australian Conference on Neural Networks (ACNN′95), pp. 29–32, 1995.
Van den Bout, D. E. and Miller, T. K.: Improving the Performance of the Hopfield-Tank Neural Network Through Normalization and Annealing. Biological Cybernetics, vol. 62, pp. 129–139, 1989.
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© 1999 Springer-Verlag Wien
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Zeng, X., Martinez, T.R. (1999). Improving the Performance of the Hopfield Network By Using A Relaxation Rate. In: Artificial Neural Nets and Genetic Algorithms. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6384-9_12
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DOI: https://doi.org/10.1007/978-3-7091-6384-9_12
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83364-3
Online ISBN: 978-3-7091-6384-9
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