Skip to main content

Simulated Annealing

  • Chapter
  • First Online:
Search and Optimization by Metaheuristics

Abstract

This chapter is dedicated to simulated annealing (SA) metaheuristic for optimization. SA is a probabilistic single-solution-based search method inspired by the annealing process in metallurgy. Annealing is a physical process where a solid is slowly cooled until its structure is eventually frozen at a minimum energy configuration. Various SA variants are also introduced.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Also known as the Boltzmann–Gibbs distribution.

References

  1. Aarts E, Korst J. Simulated annealing and Boltzmann machines. Chichester: Wiley; 1989.

    MATH  Google Scholar 

  2. Andrieu A, de Freitas JFG, Doucet A. Robust full Bayesian learning for radial basis networks. Neural Comput. 2001;13:2359–407.

    Article  MATH  Google Scholar 

  3. Azencott R. Simulated annealing: parallelization techniques. New York: Wiley; 1992.

    MATH  Google Scholar 

  4. Cerny V. Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J Optim Theory Appl. 1985;45:41–51.

    Article  MathSciNet  MATH  Google Scholar 

  5. Czech ZJ. Three parallel algorithms for simulated annealing. In: Proceedings of the 4th international conference on parallel processing and applied mathematics, Naczow, Poland. London: Springer; 2001. p. 210–217.

    Google Scholar 

  6. Geman S, Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell. 1984;6:721–41.

    Article  MATH  Google Scholar 

  7. Green PJ. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika. 1995;82:711–32.

    Article  MathSciNet  MATH  Google Scholar 

  8. Hajek B. Cooling schedules for optimal annealing. Math Oper Res. 1988;13(2):311–29.

    Article  MathSciNet  MATH  Google Scholar 

  9. Ingber L. Very fast simulated re-annealing. Math Comput Model. 1989;12(8):967–73.

    Article  MathSciNet  MATH  Google Scholar 

  10. Kirkpatrick S, Gelatt CD Jr, Vecchi MP. Optimization by simulated annealing. Science. 1983;220:671–80.

    Article  MathSciNet  MATH  Google Scholar 

  11. Liang F. Annealing stochastic approximation Monte Carlo algorithm for neural network training. Mach Learn. 2007;68:201–33.

    Article  Google Scholar 

  12. Liang F, Liu C, Carroll RJ. Stochastic approximation in Monte Carlo computation. J Am Stat Assoc. 2007;102:305–20.

    Article  MathSciNet  MATH  Google Scholar 

  13. Locatelli M. Convergence and first hitting time of simulated annealing algorithms for continuous global optimization. Math Methods Oper Res. 2001;54:171–99.

    Article  MathSciNet  MATH  Google Scholar 

  14. Metropolis N, Rosenbluth A, Rosenbluth M, Teller A, Teller E. Equations of state calculations by fast computing machines. J Chem Phys. 1953;21(6):1087–92.

    Article  Google Scholar 

  15. Richardt J, Karl F, Muller C. Connections between fuzzy theory, simulated annealing, and convex duality. Fuzzy Sets Syst. 1998;96:307–34.

    Article  MathSciNet  Google Scholar 

  16. Rose K, Gurewitz E, Fox GC. A deterministic annealing approach to clustering. Pattern Recognit Lett. 1990;11(9):589–94.

    Article  MATH  Google Scholar 

  17. Rose K. Deterministic annealing for clustering, compression, classification, regression, and related optimization problems. Proc IEEE. 1998;86(11):2210–39.

    Article  Google Scholar 

  18. Szu HH, Hartley RL. Nonconvex optimization by fast simulated annealing. Proc IEEE. 1987;75:1538–40.

    Article  Google Scholar 

  19. Tsallis C, Stariolo DA. Generalized simulated annealing. Phys A. 1996;233:395–406.

    Article  Google Scholar 

  20. Ventresca M, Tizhoosh HR. Simulated annealing with opposite neighbors. In: Proceedings of the IEEE symposium on foundations of computational intelligence (SIS 2007), Honolulu, Hawaii, 2007. p. 186–192.

    Google Scholar 

  21. Xavier-de-Souza S, Suykens JAK, Vandewalle J, Bolle D. Coupled simulated annealing. IEEE Trans Syst Man Cybern Part B. 2010;40(2):320–35.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ke-Lin Du .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Du, KL., Swamy, M.N.S. (2016). Simulated Annealing. In: Search and Optimization by Metaheuristics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-41192-7_2

Download citation

Publish with us

Policies and ethics