Journal of Global Optimization

, Volume 8, Issue 1, pp 1–13 | Cite as

Simulated Annealing for noisy cost functions

  • Walter J. Gutjahr
  • Georg Ch. Pflug


We generalize a classical convergence result for the Simulated Annealing algorithm to a stochastic optimization context, i.e., to the case where cost function observations are disturbed by random noise. It is shown that for a certain class of noise distributions, the convergence assertion remains valid, provided that the standard deviation of the noise is reduced in the successive steps of cost function evaluation (e.g., by repeated observation) with a speed O(k ), where γ is an arbitrary constant larger than one.

Key words

Simulated Annealing stochastic optimization noisy cost functions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aarts, E. and Korst, J. (1990), Simulated Annealing and the Boltzmann Machine, Wiley.Google Scholar
  2. 2.
    Bertsimas, D. and Tsitsiklis, J. Simulated Annealing, Statistical Science 8, pp. 10–15.Google Scholar
  3. 3.
    BirnbaumZ. W. (1948), On Random Variables with Comparable Peakedness, Ann. Math. Statist. 19, 76–81.Google Scholar
  4. 4.
    CatoniO. (1992), Rough Large Deviation Estimates for Simulated Annealing: Application to Exponential Schedules, Annals of Probability 20, 1109–1146.Google Scholar
  5. 5.
    Gelfand, S. B. and Mitter, S. K. (1985), Analysis of Simulated Annealing for Optimization, Proc. 24th IEEE Conf. on Decision and Control, Ft. Lauderdale, pp. 779–786.Google Scholar
  6. 6.
    HajekB. (1988), Cooling Schedules for Optimal Annealing, Math. of Operations Research 13, 311–329Google Scholar
  7. 7.
    HorstH. and PardalosP.M. (Eds), (1995), Handbook of Global Optimization, Kluwer Academic Publishers, Dordrecht.Google Scholar
  8. 8.
    KirkpatrickS., GelattJr., and VecchiM.P. (1983), Optimization by Simulated Annealing, Science 220, 671–680.MathSciNetGoogle Scholar
  9. 9.
    LaarhovenP.J.M.van and AartsE.H.L. (1987), Simulated Annealing: Theory and Applications, Reidel, Dordrecht.Google Scholar
  10. 10.
    Roenko, N. (1990), Simulated Annealing under Uncertainty, Technical Report, Inst. f. Operations Research, Univ. Zürich.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Walter J. Gutjahr
    • 1
  • Georg Ch. Pflug
    • 1
  1. 1.Department of Statistics, OR and Computer ScienceUniversity of ViennaViennaAustria

Personalised recommendations