Simulated Stochastic Approximation Annealing for Global Optimization With a Square-Root Cooling Schedule

Faming Liang, Yichen Cheng, Guang Lin

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Simulated annealing has been widely used in the solution of optimization problems. As known by many researchers, the global optima cannot be guaranteed to be located by simulated annealing unless a logarithmic cooling schedule is used. However, the logarithmic cooling schedule is so slow that no one can afford to use this much CPU time. This article proposes a new stochastic optimization algorithm, the so-called simulated stochastic approximation annealing algorithm, which is a combination of simulated annealing and the stochastic approximation Monte Carlo algorithm. Under the framework of stochastic approximation, it is shown that the new algorithm can work with a cooling schedule in which the temperature can decrease much faster than in the logarithmic cooling schedule, for example, a square-root cooling schedule, while guaranteeing the global optima to be reached when the temperature tends to zero. The new algorithm has been tested on a few benchmark optimization problems, including feed-forward neural network training and protein-folding. The numerical results indicate that the new algorithm can significantly outperform simulated annealing and other competitors. Supplementary materials for this article are available online.
Original languageEnglish (US)
Pages (from-to)847-863
Number of pages17
JournalJournal of the American Statistical Association
Issue number506
StatePublished - Jun 13 2014
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: Faming Liang is Professor (E-mail:, and Yichen Cheng is Graduate Student (E-mail:, Department of Statistics, Texas A&M University, College Station, TX 77843. Guang Lin is Research Scientist, Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, MSIN K7-90, Richland, WA 99352 (E-mail: Liang's research was partially supported by grants from the National Science Foundation (DMS-1106494 and DMS-1317131) and the award (KUS-C1-016-04) made by King Abdullah University of Science and Technology (KAUST). The authors thank the editor, associate editor, and three referees for their constructive comments, which have led to significant improvement of this article.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


Dive into the research topics of 'Simulated Stochastic Approximation Annealing for Global Optimization With a Square-Root Cooling Schedule'. Together they form a unique fingerprint.

Cite this