Simulated Annealing for noisy cost functions
Received: 15 November 1994 Accepted: 08 May 1995 DOI:
Cite this article as: Gutjahr, W.J. & Pflug, G.C. J Glob Optim (1996) 8: 1. doi:10.1007/BF00229298 Abstract
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. -γ Key words Simulated Annealing stochastic optimization noisy cost functions References
Aarts, E. and Korst, J. (1990),
Simulated Annealing and the Boltzmann Machine, Wiley.
Bertsimas, D. and Tsitsiklis, J. Simulated Annealing,
8, pp. 10–15.
BirnbaumZ. W. (1948), On Random Variables with Comparable Peakedness,
Ann. Math. Statist.
CatoniO. (1992), Rough Large Deviation Estimates for Simulated Annealing: Application to Exponential Schedules,
Annals of Probability
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.
HajekB. (1988), Cooling Schedules for Optimal Annealing,
Math. of Operations Research
HorstH. and PardalosP.M. (Eds), (1995),
Handbook of Global Optimization
, Kluwer Academic Publishers, Dordrecht.
KirkpatrickS., GelattJr., and VecchiM.P. (1983), Optimization by Simulated Annealing,
MathSciNet Google Scholar
LaarhovenP.J.M.van and AartsE.H.L. (1987),
Simulated Annealing: Theory and Applications
, Reidel, Dordrecht.
Roenko, N. (1990), Simulated Annealing under Uncertainty, Technical Report, Inst. f. Operations Research, Univ. Zürich.
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