Abstract
A global optimal algorithm based on novel interval analysis was proposed for Feedforward neural networks (FNN). When FNN are trained with BP algorithm, there exists some local minimal points in error function, which make FNN training failed. In that case, interval analysis was took into FNN to work out the global minimal point. For interval FNN algorithm, an interval extension model was presented, which creates a narrower interval domain. And more, in the FNN training, hybrid strategy was employed in discard methods to accelerate the algorithm’s convergence. In the proposed algorithm, the objective function gradient was utilized sufficiently to reduce the training time in both interval extension and discard methods procedure. At last, simulation experiments show the new interval FNN algorithm’s availability.
This work is supported by national natural science foundation of P. R. China Grant # 60674063, by national postdoctoral science foundation of P. R. China Grant # 2005037755, by natural science foundation of Liaoning Province Grant # 20062024.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Xue, J., Li, Y., Chen, D.: A Neural Network’s Learning Algorithm Based on Interval Optimization[J]. Computer Engineering 32, 192–194 (2006)
Liu, B.: A Neural Network Global Optimization Algorithm Based on Interval Optimization[J]. Computer Engineering and Application 23, 90–92 (2005)
Shen, Z.H., Huang, Z.Y., Wolfe, M.A.: An interval maximum entropy method for a discrete minimax problem[J]. Applied Math And Compute. 87, 49–68 (1997)
Cao, D.X., Huang, Z.Y.: An interval algorithm for a discrete minimax problem[J]. Journal of Nanjing University Mathematical Biquarterly 14, 74–82 (1997)
Moore, R., Yang, C.: Interval Analysis [J]. Technical Document Lockheed Missiles and Space Division 12, 87–95 (1959)
Moore, R.: Methods and Applications of Interval Analysis [M]. Society for Industrial and Applied Mathematics, pp. 100–133 (1979)
Asaithambi, N.S., Shen, M.R.E.: On computing the range of values[J]. Computing 28, 225–237 (1982)
Corliss, G., Kearfott, B.: Rogorous global search industrial applications [J]. Reliable Computing 2, 7–16 (1999)
Shen, P.P., Zhang, K.C.: An interval method for non-smooth global optimization problem[J]. OR Transactions 6, 9–18 (2000)
Casado, L.G., Garcia, I., Martinez, J.A.: Experiments with a new selection criterion in a fast interval optimization algorithm[J]. Journal of Global Optimization 19, 1247–1264 (2001)
Ming, G., Liu, X., Sheng, L.: A New Global Optimization BP Neural Networks[J]. Jouenal of Binzhou Teachers College 20, 37–41 (2004)
Lihuan-qin, Wanbai-wu: A New Global Optimization Algorithm for Training Feed-forward Neural Networks and Its Application[J]. System Engineering Theory and Practice 8, 42–47 (2003)
Casado, L.G., Garcia, I., Csendes, T.: A new multi-section technique in interval methods for global optimization[J]. Computing 65, 263–269 (2000)
Wolfe, M.A.: An interval algorithm for constrained globle optimization[J]. Journal of Computational and Applied Mathematics 50, 605–612 (1994)
Kearfott, R.B.: Interval extensions of non-smooth function for global optimization and nonlinear systems solvers[J]. Computing 57, 149–162 (1996)
Ratschek, H., Voller, R.L.: Global Optimization Over Unbounded Donmains. SIAM [J]. Control and Optimization 28, 528–539 (1990)
David, J.J., Frenzel, J.F.: Training Product Unit Neural Networks with Genetic Algorithms[J]. IEEE Expert 8, 26–33 (1993)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing[J]. Science 220, 371–380 (1993)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, H., Li, H., Du, Y. (2007). A Global Optimization Algorithm Based on Novel Interval Analysis for Training Neural Networks. In: Kang, L., Liu, Y., Zeng, S. (eds) Advances in Computation and Intelligence. ISICA 2007. Lecture Notes in Computer Science, vol 4683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74581-5_31
Download citation
DOI: https://doi.org/10.1007/978-3-540-74581-5_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74580-8
Online ISBN: 978-3-540-74581-5
eBook Packages: Computer ScienceComputer Science (R0)