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

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...

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Published in:Journal of the American Statistical Association Vol. 109; no. 506; pp. 847 - 863
Main Authors: Liang, Faming, Cheng, Yichen, Lin, Guang
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 01.06.2014
Taylor & Francis Group, LLC
Taylor & Francis Ltd
Subjects:
Algorithms
Annealing
Approximation
Competitors
Cooling
Energy value
Evolution
Local trap
Markov chain Monte Carlo
Mathematical minima
Monte Carlo simulation
Neural networks
Optimization
protein folding
Sampling distributions
Simulated annealing
Simulation
Statistics
Stochastic approximation Monte Carlo
Stochastic models
Stochastic optimization
temperature
Theory and Methods
Truncation
ISSN:1537-274X, 0162-1459, 1537-274X
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Abstract 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.
AbstractList 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.
Author Cheng, Yichen
Liang, Faming
Lin, Guang
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Cites_doi 10.1090/S0025-5718-1970-0258249-6
10.1198/016214506000001202
10.1080/00207169408804329
10.1007/s11222-010-9176-1
10.1016/0022-1236(89)90023-2
10.1007/s11222-008-9110-y
10.1007/s10898-004-9972-2
10.1080/07350015.1995.10524579
10.1016/0925-2312(91)90003-T
10.1109/TPAMI.1984.4767596
10.1007/s10994-007-5017-7
10.1073/pnas.95.13.7270
10.1073/pnas.94.26.14220
10.1126/science.220.4598.671
10.1016/0167-6377(96)00030-2
10.2307/1427681
10.1007/978-1-4757-4145-2
10.1016/0893-6080(91)90009-T
10.1017/CBO9780511626630
10.1007/BF01594945
10.1021/bi00327a032
10.1198/106186007X238459
10.1103/PhysRevE.48.1469
10.1093/imamat/6.1.76
10.1016/0304-4076(81)90117-2
10.1017/CBO9780511526237
10.1090/S0025-5718-1970-0274029-X
10.1007/BF00341287
10.1214/aoms/1177729586
10.1002/jcc.20995
10.1103/PhysRevE.71.066705
10.1007/BF00933504
10.1007/BF02551274
10.1103/PhysRevE.68.037703
10.1103/PhysRevE.52.2872
10.1016/j.spl.2008.10.007
10.7551/mitpress/5236.001.0001
10.1137/S0363012902417267
10.1080/01621459.1995.10476548
10.1063/1.1665529
10.1214/07-AOS577
10.1023/A:1008202821328
10.1093/comjnl/13.3.317
10.1007/978-1-4684-9352-8
10.1287/opre.32.6.1296
10.1103/PhysRevLett.86.2050
10.1007/s00186-006-0082-4
10.1007/978-3-642-75894-2
10.1117/12.152626
10.1093/biomet/83.1.95
10.2307/3318737
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References cit0033
cit0031
cit0030
Chen H.F. (cit0013) 2002
cit0039
Baum E.B. (cit0009) 1991
cit0037
cit0038
Chen H.F. (cit0014) 1986; 29
cit0035
cit0036
cit0022
cit0023
Berger J.O. (cit0011) 1993
cit0021
cit0062
cit0060
cit0061
Rumelhart D.E. (cit0051) 1986
Lang K.J. (cit0034) 1989
cit0028
cit0029
cit0026
cit0027
cit0024
cit0025
cit0055
cit0012
cit0056
cit0053
cit0010
cit0054
cit0052
cit0050
cit0019
cit0017
Tan C.M. (cit0057) 2008
cit0018
Fahlman S.E. (cit0020) 1990
cit0015
cit0059
cit0016
cit0058
cit0044
cit0001
cit0045
cit0042
cit0043
cit0040
Atchadé Y.F. (cit0008) 2010; 20
cit0041
cit0007
cit0048
cit0005
cit0049
cit0002
cit0046
cit0003
cit0047
References_xml – ident: cit0023
  doi: 10.1090/S0025-5718-1970-0258249-6
– ident: cit0042
  doi: 10.1198/016214506000001202
– ident: cit0002
  doi: 10.1080/00207169408804329
– ident: cit0041
  doi: 10.1007/s11222-010-9176-1
– ident: cit0028
  doi: 10.1016/0022-1236(89)90023-2
– ident: cit0007
  doi: 10.1007/s11222-008-9110-y
– ident: cit0001
  doi: 10.1007/s10898-004-9972-2
– ident: cit0019
  doi: 10.1080/07350015.1995.10524579
– ident: cit0003
  doi: 10.1016/0925-2312(91)90003-T
– ident: cit0022
  doi: 10.1109/TPAMI.1984.4767596
– ident: cit0037
  doi: 10.1007/s10994-007-5017-7
– ident: cit0024
  doi: 10.1073/pnas.95.13.7270
– ident: cit0061
  doi: 10.1073/pnas.94.26.14220
– ident: cit0031
  doi: 10.1126/science.220.4598.671
– ident: cit0015
  doi: 10.1016/0167-6377(96)00030-2
– ident: cit0025
  doi: 10.2307/1427681
– volume-title: Stochastic Approximation and Its Applications
  year: 2002
  ident: cit0013
– ident: cit0048
  doi: 10.1007/978-1-4757-4145-2
– ident: cit0029
  doi: 10.1016/0893-6080(91)90009-T
– ident: cit0043
  doi: 10.1017/CBO9780511626630
– start-page: 25
  volume-title: Multivariate Analysis: Future Directions
  year: 1993
  ident: cit0011
– volume: 29
  start-page: 914
  year: 1986
  ident: cit0014
  publication-title: Scientia Sinica, Series A
– ident: cit0017
  doi: 10.1007/BF01594945
– ident: cit0018
  doi: 10.1021/bi00327a032
– start-page: 524
  volume-title: Advances in Neural Information Processing Systems 2
  year: 1990
  ident: cit0020
– ident: cit0038
  doi: 10.1198/106186007X238459
– ident: cit0055
  doi: 10.1103/PhysRevE.48.1469
– ident: cit0012
  doi: 10.1093/imamat/6.1.76
– ident: cit0027
  doi: 10.1016/0304-4076(81)90117-2
– ident: cit0044
  doi: 10.1017/CBO9780511526237
– ident: cit0052
  doi: 10.1090/S0025-5718-1970-0274029-X
– ident: cit0062
  doi: 10.1007/BF00341287
– ident: cit0047
  doi: 10.1214/aoms/1177729586
– ident: cit0035
  doi: 10.1002/jcc.20995
– ident: cit0058
  doi: 10.1103/PhysRevE.71.066705
– volume-title: Simulated Annealing
  year: 2008
  ident: cit0057
– start-page: 52
  volume-title: Proceedings of the 1988 Connectionist Models
  year: 1989
  ident: cit0034
– ident: cit0046
  doi: 10.1007/BF00933504
– ident: cit0016
  doi: 10.1007/BF02551274
– ident: cit0030
  doi: 10.1103/PhysRevE.68.037703
– ident: cit0054
  doi: 10.1103/PhysRevE.52.2872
– ident: cit0039
  doi: 10.1016/j.spl.2008.10.007
– start-page: 318
  volume-title: Parallel Distributed Processing: Explorations in the Microstructure of Cognition (Vol. 1)
  year: 1986
  ident: cit0051
  doi: 10.7551/mitpress/5236.001.0001
– ident: cit0005
  doi: 10.1137/S0363012902417267
– ident: cit0050
  doi: 10.1080/01621459.1995.10476548
– ident: cit0036
  doi: 10.1063/1.1665529
– ident: cit0040
  doi: 10.1214/07-AOS577
– ident: cit0056
  doi: 10.1023/A:1008202821328
– ident: cit0021
  doi: 10.1093/comjnl/13.3.317
– start-page: 904
  volume-title: Advances in Neural Information Processing Systems
  year: 1991
  ident: cit0009
– ident: cit0033
  doi: 10.1007/978-1-4684-9352-8
– ident: cit0053
  doi: 10.1287/opre.32.6.1296
– ident: cit0060
  doi: 10.1103/PhysRevLett.86.2050
– ident: cit0059
  doi: 10.1007/s00186-006-0082-4
– ident: cit0010
  doi: 10.1007/978-3-642-75894-2
– ident: cit0045
  doi: 10.1117/12.152626
– ident: cit0049
  doi: 10.1093/biomet/83.1.95
– volume: 20
  start-page: 209
  year: 2010
  ident: cit0008
  publication-title: Statistica Sinica
– ident: cit0026
  doi: 10.2307/3318737
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Snippet 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...
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SubjectTerms Algorithms
Annealing
Approximation
Competitors
Cooling
Energy value
Evolution
Local trap
Markov chain Monte Carlo
Mathematical minima
Monte Carlo simulation
Neural networks
Optimization
protein folding
Sampling distributions
Simulated annealing
Simulation
Statistics
Stochastic approximation Monte Carlo
Stochastic models
Stochastic optimization
temperature
Theory and Methods
Truncation
Title Simulated Stochastic Approximation Annealing for Global Optimization With a Square-Root Cooling Schedule
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