Chaotic simulated annealing by a neural network with a variable delay: Design and application

IEEE Transactions on Neural Networks

Volumn 22, Issue 10, 2011, Pages 1557-1565

  Chen, Shyan Shiou ^a  

^a NATIONAL TAIWAN NORMAL UNIVERSITY   (Taiwan)

Author keywords

Constant delay; Lyapunov function; neural network; optimization; variable delay

Indexed keywords

BIFURCATION DIAGRAM; CHAOTIC WANDERING; CONNECTION WEIGHTS; CONSTANT DELAYS; DELAYED MODELS; DELAYED NEURAL NETWORKS; DELAYED SYSTEMS; DESIGN AND APPLICATION; LINEAR MATRIX INEQUALITY APPROACH; LMI APPROACH; LYAPUNOV; OBJECTIVE FUNCTIONS; QUADRATIC COST FUNCTIONS; SEARCHING ABILITY; SECOND ORDERS; SELF-FEEDBACK CONNECTION WEIGHTS; SINGLE NEURON; STOCHASTIC PROPERTIES; TRANSIENTLY CHAOTIC NEURAL NETWORKS; VARIABLE DELAYS;

COST FUNCTIONS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; OPTIMIZATION; ROBUSTNESS (CONTROL SYSTEMS); SIMULATED ANNEALING; STOCHASTIC MODELS; TRAVELING SALESMAN PROBLEM;

NEURAL NETWORKS;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; COMPUTER PROGRAM; COMPUTER SIMULATION; HUMAN; NONLINEAR SYSTEM; STATISTICS; TIME;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTER SIMULATION; HUMANS; MODELS, NEUROLOGICAL; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS; SOFTWARE DESIGN; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 80053619905     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2011.2163080     Document Type: Article

References (26)

1. T. Kwok and S. K. Smith, "A unified framework for chaotic neural network approaches to combinatorial optimization," IEEE Trans. Neural Netw., vol. 10, no. 4, pp. 978-981, Jul. 1999.
2. M. J. Seow and V. K. Asari, "Recurrent neural network as a linear attractor for pattern association," IEEE Trans. Neural Netw., vol. 17, no. 1, pp. 246-250, Jan. 2006. (Pubitemid 43263956)
3. P. B. Watta, K. Wang, and M. H. Hassoun, "Recurrent neural nets as dynamical Boolean systems with application to associative memory," IEEE Trans. Neural Netw., vol. 8, no. 6, pp. 1268-1280, Nov. 1997. (Pubitemid 127765156)
4. K. S. Narendra and K. Parthasarathy, "Identification and control of dynamical systems using neural networks," IEEE Trans. Neural Netw., vol. 1, no. 1, pp. 4-27, Mar. 1990. (Pubitemid 20689507)
5. S. Mohamad and K. Gopalsamy, "Exponential stability of continuoustime and discrete-time cellular neural networks with delays," Appl. Math. Comput., vol. 135, no. 1, pp. 17-38, Feb. 2003.
6. H. Huang, J. Cao, and J. Wang, "Global exponential stability and periodic solutions of recurrent neural networks with delays," Phys. Lett. A, vol. 298, nos. 5-6, pp. 393-404, Jun. 2002.
7. J. Liang and J. Cao, "Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays," Phys. Lett. A, vol. 314, nos. 5-6, pp. 434-442, Aug. 2003.
8. X. Liao, G. Chen, and E. N. Sanchez, "Delay-dependent exponential stability analysis of delayed neural networks: An LMI approach," Neural Netw., vol. 15, no. 7, pp. 855-866, Sep. 2002. (Pubitemid 35299581)
9. X. Liao, G. Chen, and E. N. Sanchez, "Delay-dependent exponential stability analysis of delayed neural networks: An LMI approach," Neural Netw., vol. 16, no. 10, pp. 1401-1402, 2003. (Pubitemid 37386359)
10. J. Liang, J. Cao, and J. Lam, "Convergence of discrete-time recurrent neural networks with variable delay," Int. J. Bifur. Chaos Appl. Sci. Eng., vol. 15, no. 2, pp. 581-595, 2005. (Pubitemid 40661911)
11. S. S. Chen, L. F. Chen, Y. T. Wu, Y. Z. Wu, P. L. Lee, T. C. Yeh, and J. C. Hsieh, "Detection of synchronization between chaotic signals: An adaptive similarity-based approach," Phys. Rev. E, vol. 76, no. 6, pp. 066208-1-066208-11, Dec. 2007.
12. S. S. Chen, P. C. Tu, T. P. Su, J. C. Hsieh, Y. C. Lin, and L. F. Chen, "Impaired frontal synchronization of spontaneous magnetoencephalographic activity in patients with bipolar disorder," Neurosci. Lett., vol. 445, no. 2, pp. 174-178, Nov. 2008.
13. K. Kaneko and I. Tsuda, "Chaotic itinerancy," Chaos, vol. 13, no. 3, pp. 926-936, 2003. (Pubitemid 37180744)
14. K. Aihara, T. Takabe, and M. Toyoda, "Chaotic neural networks," Phys. Lett. A, vol. 144, nos. 6-7, pp. 333-340, Mar. 1990.
15. 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.
16. L. Chen and K. Aihara, "Chaotic simulated annealing by a neural network model with transient chaos," Neural Netw., vol. 8, no. 6, pp. 915-930, 1995.
17. L. Chen and K. Aihara, "Chaos and asymptotical stability in discretetime neural networks," Phys. D: Nonlin. Phenom., vol. 104, nos. 3-4, pp. 286-325, Jun. 1997. (Pubitemid 127701453)
18. L. Chen and K. Aihara, "Global searching ability of chaotic neural networks," IEEE Trans. Circuits Syst. I: Fundam. Theory Appl., vol. 46, no. 8, pp. 974-993, Aug. 1999.
19. F. R. Marotto, "Snap-back repellers imply chaos in Rn," J. Math. Anal. Appl., vol. 63, no. 1, pp. 199-223, Mar. 1978.
20. L. Wang and K. Smith, "On chaotic simulated annealing," IEEE Trans. Neural Netw., vol. 9, no. 4, pp. 716-718, Jul. 1998. (Pubitemid 128750033)
21. L. Wang, S. Li, F. Tian, and X. Fu, "A noisy chaotic neural network for solving combinatorial optimization problems: Stochastic chaotic simulated annealing," IEEE Trans. Syst., Man, Cybern., Part B: Cybern., vol. 34, no. 5, pp. 2119-2125, Oct. 2004.
22. L. Wang and H. Shi, "A gradual noisy chaotic neural network for solving the broadcast scheduling problem in packet radio networks," IEEE Trans. Neural Netw., vol. 17, no. 4, pp. 989-1000, Jul. 2006. (Pubitemid 44194157)
23. L. Zhao, M. Sun, J. H. Cheng, and Y. Q. Xu, "A novel chaotic neural network with the ability to characterize local features and its application," IEEE Trans. Neural Netw., vol. 20, no. 4, pp. 735-742, Mar. 2009.
24. S.-S. Chen, "Delayed transiently chaotic neural networks and their application," Chaos, vol. 19, no. 3, pp. 033125-1-033125-10, Aug. 2009.
25. R. Bowen and D. Ruelle, "The ergodic theory of axiom a flows," Invent. Math., vol. 29, no. 3, pp. 181-202, 1975.
26. M. L. Lyra and C. Tsallis, "Nonextensivity and multifractality in lowdimensional dissipative systems," Phys. Rev. Lett., vol. 80, no. 1, pp. 53-56, 1998. (Pubitemid 128622803)