- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 873670, 10 pages
Chaotic Hopfield Neural Network Swarm Optimization and Its Application
1Department of Electrical Engineering, Tshwane University of Technology, Pretoria 0001, South Africa
2School of Engineering, University of South Africa, Florida 1710, South Africa
Received 7 February 2013; Accepted 20 March 2013
Academic Editor: Xiaojing Yang
Copyright © 2013 Yanxia Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. C. Sprott, Chaos and Time-Series Analysis, Oxford University Press, New York, NY, USA, 2004.
- K. Aihara and G. Matsumoto, Chaos in Biological Systems, Plenum Press, New York, NY, USA, 1987.
- C. A. Skarda and W. J. Freeman, “How brains make chaos in order to make sense of the world,” Behavioral and Brain Sciences, vol. 10, pp. 161–165, 1987.
- L. Wang, D. Z. Zheng, and Q. S. Lin, “Survey on chaotic optimization methods,” Computation Technology Automation, vol. 20, pp. 1–5, 2001.
- B. Li and W. S. Jiang, “Optimizing complex functions by chaos search,” Cybernetics and Systems, vol. 29, no. 4, pp. 409–419, 1998.
- J. J. Hopfield and D. W. Tank, “‘Neural’ computation of decisons in optimization problems,” Biological Cybernetics, vol. 52, no. 3, pp. 141–152, 1985.
- Z. Wang, Y. Liu, K. Fraser, and X. Liu, “Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays,” Physics Letters A, vol. 354, no. 4, pp. 288–297, 2006.
- T. Tanaka and E. Hiura, “Computational abilities of a chaotic neural network,” Physics Letters A, vol. 315, no. 3-4, pp. 225–230, 2003.
- K. Aihara, T. Takabe, and M. Toyoda, “Chaotic neural networks,” Physics Letters A, vol. 144, no. 6-7, pp. 333–340, 1990.
- S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science, vol. 220, no. 4598, pp. 671–680, 1983.
- L. Chen and K. Aihara, “Chaotic simulated annealing by a neural network model with transient chaos,” Neural Networks, vol. 8, no. 6, pp. 915–930, 1995.
- L. Chen and K. Aihara, “Chaos and asymptotical stability in discrete-time neural networks,” Physica D, vol. 104, no. 3-4, pp. 286–325, 1997.
- L. Wang, “On competitive learning,” IEEE Transactions on Neural Networks, vol. 8, no. 5, pp. 1214–1217, 1997.
- L. Wang and K. Smith, “On chaotic simulated annealing,” IEEE Transactions on Neural Networks, vol. 9, no. 4, pp. 716–718, 1998.
- M. Clerc and J. Kennedy, “The particle swarm-explosion, stability, and convergence in a multidimensional complex space,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 1, pp. 58–73, 2002.
- J. Ke, J. X. Qian, and Y. Z. Qiao, “A modified particle swarm optimization algorithm,,” Journal of Circuits and Systems, vol. 10, pp. 87–91, 2003.
- B. Liu, L. Wang, Y. H. Jin, F. Tang, and D. X. Huang, “Improved particle swarm optimization combined with chaos,” Chaos, Solitons and Fractals, vol. 25, no. 5, pp. 1261–1271, 2005.
- T. Xiang, X. Liao, and K. W. Wong, “An improved particle swarm optimization algorithm combined with piecewise linear chaotic map,” Applied Mathematics and Computation, vol. 190, no. 2, pp. 1637–1645, 2007.
- C. Fan and G. Jiang, “A simple particle swarm optimization combined with chaotic search,” in Proceedings of the 7th World Congress on Intelligent Control and Automation (WCICA '08), pp. 593–598, Chongqing, China, June 2008.
- J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks, pp. 1942–1948, Perth, Australia, December 1995.
- S. H. Chen, A. J. Jakeman, and J. P. Norton, “Artificial Intelligence techniques: an introduction to their use for modelling environmental systems,” Mathematics and Computers in Simulation, vol. 78, no. 2-3, pp. 379–400, 2008.
- J. J. Hopfield, “Hopfield network,” Scholarpedia, vol. 2, article 1977, 2007.
- J. J. Hopfield, “Neurons with graded response have collective computational properties like those of two-state neurons,” Proceedings of the National Academy of Sciences of the United States of America, vol. 81, no. 10, pp. 2554–2558, 1984.
- Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J. C. Hernandez, and R. G. Harley, “Particle swarm optimization: basic concepts, variants and applications in power systems,” IEEE Transactions on Evolutionary Computation, vol. 12, no. 2, pp. 171–195, 2008.
- J. D. Schaffer, R. A. Caruana, L. J. Eshelman, and R. Das, “A study of control parameters affectiong online performance of genetic algorithms for function optimization,” in Proceedings of the 3rd International Conference on Genetic Algorithms, pp. 51–60, 1989.
- A. I. de Freitas Vaz and E. M. da Graça Pinto Fernandes, “Optimization of nonlinear constrained particle swarm,” Technological and Economic Development of Economy, vol. 12, no. 1, pp. 30–36, 2006.
- X. Hu, R. C. Eberhart, and Y. Shi, “Engineering optimization with particle swarm,” in Proceedings of the IEEE Swarm Intelligence Symposium, pp. 53–57, 2003.
- C. A. C. Coello, “Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art,” Computer Methods in Applied Mechanics and Engineering, vol. 191, no. 11-12, pp. 1245–1287, 2002.
- J. Kennedy, “Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance,” Neural Networks, vol. 18, pp. 205–217, 1997.