Abstract
The weight normalisation process used for constraint satisfaction in a self-organising neural network (SONN) for combinatorial optimisation is investigated in this paper. The process relies on the mutual interaction of neuronal weights for computation, and we present a theoretical model to capture its longterm equilibrium dynamics. By solving the equilibrium states numerically, we reveal some nonlinear system phenomena hidden in the normalisation process: fixed point, symmetry-breaking bifurcation and cascades of period-doubling bifurcations to chaos. This leads to a new perspective of the weight normalisation within the SONN as a computational process based on nonlinear dynamics.
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References
Kohonen, T.: Self-organized Formation of Topologically Correct Feature Maps. Biol. Cybern., Vol. 43. (1982) 59–69
Durbin, R., Willshaw, D.: An Analogue Approach to the Travelling Salesman Problem Using an Elastic Net Method. Nature, Vol. 326. (1987) 689–691
Fort, J. C.: Solving a Combinatorial Problem via Self-organizing Process: An Application of the Kohonen Algorithm to the Travelling Salesman Problem. Biol. Cybern., Vol. 59. (1988) 33–40
Favata, F., Walker, R.: A Study of the Application of Kohonen-type Neural Networks to the Travelling Salesman Problem. Biol. Cybern., Vol. 64. (1991) 463–468
Smith, K. A., Palaniswami, M., Krishnamoorthy, M.: A Hybrid Neural Approach to Combinatorial Optimization. Computers Ops. Res., Vol. 23. (1996) 597–610
Smith, K. A.: Neural Techniques for Combinatorial Optimization with Applications. IEEE Trans. Neural Networks, Vol. 9, No. 6. (1998) 1301–1318
Guerrero, F., Smith, K. A., Lozano, S.: Self-organizing Neural Approach for Solving the Quadratic Assignment Problem. Proc. Int. Workshop on Soft Computing in Industry (1999) 13–18
Van den Bout, D. E., Miller, T. K.: Improving the Performance of the Hopfield-Tank Neural Network Through Normalization and Annealing. Biol. Cybern., Vol. 62. (1989) 129–139
Kirkpatrick, S., Gelatt, C. D., Vecchi, M. P.: Optimisation by Simulated Annealing. Science, Vol. 220. (1983) 671–680
Kwok, T., Smith, K. A.: Improving the Optimisation Performance of a Self-organizing Neural Network with Weight Normalisation. Proc. Int. ICSC Congress on Intelligent Systems & Applications (ISA’2000), Paper no. 1513–285. (2000)
Guerrero, F., Lozano, S., Smith, K. A., Kwok, T.: Manufacturing Cell Formation Using a New Self-organizing Neural Network. Proc. 26th Int. Conf. Computers & Industrial Engineering, Vol. 1. (1999) 668–672
Peitgen, H.-O., Jürgens, H., Saupe, D.: Chaos and Fractals: New Frontiers of Science. Springer-Verlag, Berlin Heidelberg New York (1992)
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Kwok, T., Smith, K.A. (2001). Nonlinear System Dynamics in the Normalisation Process of a Self-Organising Neural Network for Combinatorial Optimisation. In: Mira, J., Prieto, A. (eds) Connectionist Models of Neurons, Learning Processes, and Artificial Intelligence. IWANN 2001. Lecture Notes in Computer Science, vol 2084. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45720-8_88
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DOI: https://doi.org/10.1007/3-540-45720-8_88
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