Advertisement

Generating Random Deviates Consistent with the Long Term Behavior of Stochastic Search Processes in Global Optimization

  • Arturo Berrones
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4507)

Abstract

A new stochastic search algorithm is proposed, which in first instance is capable to give a probability density from which populations of points that are consistent with the global properties of the associated optimization problem can be drawn. The procedure is based on the Fokker – Planck equation, which is a linear differential equation for the density. The algorithm is constructed in such a way that only involves linear operations and a relatively small number of evaluations of the given cost function.

Keywords

global optimization stochastic search statistical physics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Haykin, S.: Neural Networks: a Comprehensive Foundation. Prentice Hall, Englewood Cliffs (1999)zbMATHGoogle Scholar
  2. 2.
    Pardalos, P.M., Schoen, F.: Recent Advances and Trends in Global Optimization: Deterministic and Stochastic Methods. In: Proceedings of the Sixth International Conference on Foundations of Computer–Aided Process Design, DSI 1–2004, pp. 119–131 (2004)Google Scholar
  3. 3.
    Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., Teller, E.: Equations of State Calculations by Fast Computing Machines. Journal of Chemical Physics 21, 1087–1092 (1953)CrossRefGoogle Scholar
  4. 4.
    Kirkpatrick, S.: Optimization by Simulated Annealing. Science 220, 671–680 (1983)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Suykens, J.A.K., Verrelst, H., Vandewalle, J.: On–Line Learning Fokker–Planck Machine. Neural Processing Letters 7(2), 81–89 (1998)CrossRefGoogle Scholar
  6. 6.
    Gidas, B.: Metropolis–type Monte Carlo Simulation Algorithms and Simulated Annealing. In: Topics in Contemporary Probability and its Applications. Prob. Stochastic Ser., pp. 159–232. CRC Press, Boca Raton (1995)Google Scholar
  7. 7.
    Parpas, P., Rustem, B., Pistikopoulos, E.N.: Linearly Constrained Global Optimization and Stochastic Differential Equations. Journal of Global Optimization 36(2), 191–217 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Geman, S., Hwang, C.R.: Diffusions for Global Optimization. SIAM J. Control Optim. 24(5), 1031–1043 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Risken, H.: The Fokker–Planck Equation. Springer, Berlin (1984)zbMATHGoogle Scholar
  10. 10.
    Van Kampen, N.G.: Stochastic Processes in Physics and Chemistry. North-Holland, Amsterdam (1992)Google Scholar
  11. 11.
    Grasman, J., van Herwaarden, O.A.: Asymptotic Methods for the Fokker–Planck Equation and the Exit Problem in Applications. Springer, Berlin (1999)zbMATHGoogle Scholar
  12. 12.
    Movellan, J.R., McClelland, J.L.: Learning Continuous Probability Distributions with Symmetric Diffusion Networks. Cognitive Science 17, 463–496 (1993)CrossRefGoogle Scholar
  13. 13.
    Kosmatopoulos, E.B., Christodoulou, M.A.: The Boltzmann g–RHONN: a Learning Machine for Estimating Unknown Probability Distributions. Neural Networks 7(2), 271–278 (1994)CrossRefGoogle Scholar
  14. 14.
    Chelouah, R., Siarry, P.: Tabu Search Applied to Global Optimization. European Journal of Operational Research 123, 256–270 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes in C++, the Art of Scientific Computing. Cambridge University Press, Cambridge (2005)Google Scholar
  16. 16.
    Berrones, A.: work in progressGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Arturo Berrones
    • 1
  1. 1.Posgrado en Ingeniería de Sistemas, Facultad de Ingeniería Mecánica y Eléctrica Universidad Autónoma de Nuevo León AP 126, Cd. Universitaria, San Nicolás de los Garza, NL 66450México

Personalised recommendations