On parameter settings of Hopfield networks applied to traveling salesman problems

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 52, Issue 5, 2005, Pages 994-1002

  Tan, K C ^a   Tang, Huajin ^a   Ge, S S ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Hopfield neural networks; Parameter setting; Stability; Traveling salesman problem (TSP)

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PARAMETER ESTIMATION; QUADRATIC PROGRAMMING; THEOREM PROVING; TRAVELING SALESMAN PROBLEM;

CONTINUOUS TIME HOPFIELD NETWORK; HOPFIELD NEURAL NETWORKS; LYAPUNOV FUNCTION; PARAMETER SETTING; STABILITY ANALYSIS;

NEURAL NETWORKS;

EID: 20144376397     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2005.846666     Document Type: Article

References (21)

1. J. J. Hopfiled and D. W. Tank, "Neural computation of decision in optimization problem," Biol. Cybern., vol. 52, pp. 141-152, 1985.
2. S. V. B. Aiyer, M. Niranjan, and F. Fallside, "A theoretical investigation into the performance of the Hopfield model," IEEE Trans. Neural Netw., vol. 1, no. 2, pp. 204-215, Feb. 1990.
3. S. Abe, "Global convergence and suppression of spurious states of the Hopfield neural networks," IEEE Trans. Circuits Syst. I, vol. 40, no. 4, pp. 246-257, Apr. 1993.
4. M. Peng, K. Narendra, and A. Gupta, "An investigation into the improvement of local minimum of the Hopfield network," Neural Netw., vol. 9, pp. 1241-1253, 1996.
5. B. Cooper, "Stability analysis of higher-order neural networks for combinatorial optimization," Int. J. Neural Syst., vol. 12, no. 3, pp. 177-186, 2002.
6. L. Chen and K. Aihara, "Chaotic simulated annealing by a neural network model with transient chaos," Neural Netw., vol. 8, pp. 915-930, 1995.
7. M. Hasegawa, T. Ikeguchi, and K. Aihara, "Solving large scale traveling salesman problems by chaotic neurodynamics," Neural Netw., vol. 15, pp. 271-283, 2002.
8. H. Nozawa, "A neural network model as a globally coupled map and applications based on chaos," Chaos, vol. 2, no. 3, pp. 377-386, 1992.
9. L. Wang and K. Smith, "On chaotic simulated annealing," IEEE Trans. Neural Netw., vol. 9, no. 4, pp. 716-718, Jun. 1998.
10. L. Wang and F. Tian, "Noisy chaotic neural networks for solving combinatorial optimization problems," in Proc. Int. Joint Conference on Neural Networks (IJCNN), Combo, Italy, July 24-27, 2000.
11. V. Wilson and G. S. Pawley, "On the stability of the TSP problem algorithm of Hopfield and tank," Bio. Cybern., vol. 58, pp. 63-70, 1988.
12. B. Kamgar-Parsi and B. Kamgar-Parsi, "Dynamical stability and parameter selection in neural optimization," in Proc. Int. Joint Conf. Neural Networks, vol. 4, 1992, pp. 566-571.
13. R. D. Brandt, Y. Wang, A. J. Laub, and S. K. Mitra, "Alternative networks for solving the traveling salesman problem and the list-matching problem," in Proc. Int. Joint Conf. Neural Networks, vol. 2, 1988, pp. 333-340.
14. K. A. Smith, "Neural networks for combinatorial optimization: A review of more than a decade of research," INFORMS J. Comput., vol. 11, no. 1, 15-34, 1999.
15. P. M. Talaván and J. Yáñez, "Parameter setting of the Hopfield network applied to TSP," Neural Netw., vol. 15, pp. 363-373, 2002.
16. X. S. Zhang, Neural Networks in Optimization. Norwell, MA: Kluwer Academic, 2000.
17. Y. Tachibana, G. H. Lee, H. Ichihashi, and T. Miyoshi, "A simple steepest descent method for minimizing Hopfield energy to obtain optimal solution of the TSP with reasonable certainty," in Proc. Int. Conf. Neural Netw., 1995, pp. 1871-1875.
18. S. Matsuda, ""Optimal" Hopfield network for combinatorial optimization with linear cost function," IEEE Trans. Neural Netw., vol. 9, no. 6, pp. 1319-1330, Dec. 1998.
19. S. Park, "Signal space interpretations for Hopfield neural network for optimization," in Proc. IEEE Int. Symp. Circuits Systems, May 1989, pp. 2181-2184.
20. L. Wang, "On the dynamics of discrete-time, continuous-state Hopfield neural networks," IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 45, no. 6, pp. 747-749, Jun. 1998.
21. L. Wang, "Discrete-time convergence theory and updating roles for neural networks with energy functions," IEEE Trans. Neural Netw., vol. 8, no. 2, pp. 445-447, Apr. 1997.