Abstract
In this paper, a novel technique called Fourier smoothing technique, which can be used to improve any global optimization algorithm, is presented. This technique uses a properly truncated Fourier series as the smoothing function to approximate the objective function. This smoothing function can maintain the overall shape or basic shape of the objective function but eliminate its finer details. Thus it can eliminate many local minima but preserve the global minima, and make the search of optimal solution more easier and faster. To demonstrate efficiency of this technique, we integrate this technique into a simple optimization algorithm: Powell direct method. The simulation results indicate this smoothing technique can improve the Powell direct method greatly.
This work was supported by the National Natural Science Foundation of China (60374063), and SRF for ROCS, SEM.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Lee, C.Y., Yao, X.: Evolutionary Programming Using Mutations Based on the Levy Probability Distribution. IEEE Trans. Evol. Comput. 8, 1–13 (2004)
Leung, Y.W., Wang, Y.P.: An Orthogonal Genetic Algorithm with Quantization for Global Numerical Optimization. IEEE Trans. Evol. Comput. 5, 41–53 (2001)
Yao, X., Liu, Y., Lin, G.: Evolutionary Programming Made Faster. IEEE Trans. Evol. Comput. 3, 82–102 (1999)
Fogel, D.B.: Evolutionary Computation: toward a New Philosophy of Machine Intelligence. IEEE Press, New York (1995)
Lucidi, S., Piccialli, V.: New Classes of Globally Convexized Filled Functions for Global Optimization. J. of Global Optimization 24, 219–236 (2002)
Ge, R.P., Qin, Y.F.: Globally Convexized Filled Functions for Global Optimization. Applied Mathematics and Computation 35, 131–158 (1999)
Oblow, E.M.: Stochastic Tunneling Algorithm for Global Optimization. J. of Global Optimization 20, 195–212 (2001)
Cartwright, M.: Fourier Methods for Mathematicians, Scientists and Engineers. Ellis Horwood Limited, Chichester (1990)
Fang, F.T., Wang, Y.: Number-theoretic Methods in Atatistics. Chapman & Hall, London (1994)
Fletcher, R.: Practical Methods of Optimization. Wiley, Chichester (1987)
Leung, Y.W., Wang, Y.P.: Multiobjective Programming Using Uniform Design and Genetic Algorithm. IEEE Trans. Systems, Man, and Cybernetics, Part C: Applications and Review 30, 293–304 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, Y. (2006). Global Optimization Algorithms Using Fourier Smoothing. In: Huang, DS., Li, K., Irwin, G.W. (eds) Intelligent Computing. ICIC 2006. Lecture Notes in Computer Science, vol 4113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11816157_108
Download citation
DOI: https://doi.org/10.1007/11816157_108
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37271-4
Online ISBN: 978-3-540-37273-8
eBook Packages: Computer ScienceComputer Science (R0)