On the performance of Hopfield network for graph search problem

Neurocomputing

Volumn 14, Issue 4, 1997, Pages 365-381

  Serpen, Gursel ^a   Parvin, Azadeh ^a  

^a The University of Toledo   (United States)

Author keywords

constraint satisfaction; dynamic system; Hopfield networks; neural networks; optimization; stability analysis; weight parameters

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; CONSTRAINT THEORY; OPTIMIZATION; STATE SPACE METHODS; SYSTEM STABILITY; SYSTEMS ANALYSIS;

GRAPH PATH SEARCH PROBLEM; HOPFIELD NEURAL NETWORKS;

NEURAL NETWORKS;

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; COMPUTER SIMULATION; PRIORITY JOURNAL;

EID: 0031579671     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-2312(96)00037-9     Document Type: Article

References (24)

1. [1] S. Abe, J. Kawakama and K. Hirasawa, Solving inequality constrained combinatorial optimization problems by the Hopfield neural networks, Neural Networks 5 (1992) 663-670.
2. [2] S.V.B. Aiyer, M. Niranjan and F. Fallside, A theoretical investigation into the performance of the Hopfield model, IEEE Transactions on Neural Networks 2 (1990) 204-215.
3. [3] M.K.M. Ali and F. Kamoun, Neural networks for shortest path computation and routing in computer networks, IEEE Transactions on Neural Networks 4 (1993) 941-954.
4. [4] A. Bouzerdoum and T. Pattison, Neural network for quadratic optimization with bound constraints, IEEE Transactions on Neural Networks 4 (1993) 293-303.
5. [5] S. Cavalieri et al., Optimal path determination in a graph by Hopfield neural network, Neural Networks 7(2) (1994) 397-404.
6. [6] C. Chiu, Y. Maa and M.A. Shanblatt, Energy Function Analysis of Dynamic Programming Neural Networks, IEEE Transactions on Neural Network, 4 (1991) 418-426.
7. [7] B.J. Hellstrom and L.N. Kanal, Knapsack packing networks, IEEE Transactions on Neural Networks 3 (1992) 302-307.
8. [8] J.J. Hopfield and D.W. Tank, Computing with neural networks: A model, Science 233 (1986) 625-632.
9. [9] J.J. Hopfield and D.W. Tank, Neural computations of decisions in optimization problems, Biological Cybernetics 52 (1985) 141-152.
10. [10] J.J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, Proceedings of the National Academy of Sciences (U.S.A.) 81 (1984) 3088-3092.
11. [11] J.J. Hopfield, Neural networks and physical systems with emergent collective computational properties, Proceedings of the National Academy of Sciences (U.S.A.) 79 (1982) 2554-2558.
12. [12] Y. Kobuchi, State evaluation functions and Lyapunov functions for neural networks, Neural Networks 4 (1991) 505-510.
13. [13] B.W. Lee and B.J. Sheu, Modified hopfield neural networks for retrieving the optimal solution, IEEE Transactions on Neural Networks 1 (1991) 137-142.
14. [14] W.E. Lillo, M.H. Loh, S. Hui and S.H. Zak, On solving constrained optimization problems with neural networks: A penalty method approach, IEEE Transactions on Neural Networks 4 (1993) 931-939.
15. [15] W. Lin, J.G. Delgado-Frias, G.G. Pechanek, and S. Vassiliadis, Impact of energy function on a neural network for optimization problems, IEEE World Congress on Computational Intelligence (1994) 4518-4523.
16. [16] F-L. Luo and Y-D. Li, A theorem concerning the energy function of Hopfield continuous-variable neural networks, International Journal of Electronics 76(3) (1994) 443-446.
17. [17] G. Serpen and D.L. Livingston, Analysis of the relationship between weight parameters and stability of solutions in Hopfield networks from dynamic systems viewpoint, Neural, Parallel and Scientific Computation 2 (1994) 361-372.
18. [18] G. Serpen and D.L. Livingston, Bounds on the weight parameters of hopfield networks for the stability of solutions, Submitted to a Journal.
19. [19] G. Serpen, Bounds on constraint weight parameters of hopfield networks for stability of optimization problem solutions, Ph.D. Dissertation, Old Dominion University, Norfolk, VA, 1992.
20. [20] H. Shirai et al., A solution of combinatorial optimization problem by uniting genetic algorithms with Hopfield's model, IEEE World Congress on Computational Intelligence (1994) 4704-4709.
21. [21] Y. Shrivastava, S. Dasgupta, and S.M. Reddy, Guaranteed convergence in a class of Hopfield networks, IEEE Transactions on Neural Networks 3 (1992) 951-961.
22. [22] M.A. Styblinsky and T.S. Tang, Experiments in nonconvex optimization: Stochastic approximation with function smoothing and simulated annealing, Neural Networks 3 (1990) 467-483.
23. [23] K.T. Sun and H.C. Fu, A hybrid neural network model for solving optimization problems, IEEE Transactions on Computers 42 (1993) 218-227.
24. [24] M. Vidyasagar, Location and stability of the high-gain equilibria of nonlinear neural networks, IEEE Transactions on Neural Networks 4 (1993) 660-671.