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Convergence and finite-time behavior of simulated annealing

Published online by Cambridge University Press:  01 July 2016

Debasis Mitra ,
Fabio Romeo  and
Alberto Sangiovanni-Vincentelli
Debasis Mitra*
Affiliation:
AT&T Bell Laboratories
Fabio Romeo*
Affiliation:
University of California, Berkeley
Alberto Sangiovanni-Vincentelli*
Affiliation:
University of California, Berkeley
*
∗Postal address: AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ 07974, USA.
∗∗Postal address: Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720, USA.
∗∗Postal address: Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720, USA.
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Abstract

Simulated annealing is a randomized algorithm which has been proposed for finding globally optimum least-cost configurations in large NP-complete problems with cost functions which may have many local minima. A theoretical analysis of simulated annealing based on its precise model, a time-inhomogeneous Markov chain, is presented. An annealing schedule is given for which the Markov chain is strongly ergodic and the algorithm converges to a global optimum. The finite-time behavior of simulated annealing is also analyzed and a bound obtained on the departure of the probability distribution of the state at finite time from the optimum. This bound gives an estimate of the rate of convergence and insights into the conditions on the annealing schedule which gives optimum performance.

Keywords

GLOBAL OPTIMIZATIONRANDOMIZED ALGORITHMSTIME-INHOMOGENEOUS MARKOV CHAINS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 3 , September 1986 , pp. 747 - 771
Copyright
Copyright © Applied Probability Trust 1986 

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References

1. Binder, K. (1978) Monte Carlo Methods in Statistical Physics. Springer-Verlag, Berlin.Google Scholar
2. Dobrushin, R. L. (1956) Central limit theorem for nonstationary Markov chains, I, II. Theory Prob. Appl. 1, 65–80; 329-383.CrossRefGoogle Scholar
3. Garey, M. R. and Johnson, D. S. (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco.Google Scholar
4. Geman, S. and Geman, D. (1948) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Analysis and Machine Intelligence 6, 721–741.Google Scholar
5. Gidas, B. (1985) Non-stationary Markov chains and convergence of the annealing algorithm. J. Statist. Phys. 39, 73–131.CrossRefGoogle Scholar
6. Hajek, B. (1985) Cooling schedules for optimal annealing. Preprint.Google Scholar
7. Isaacson, D. L. and Madsen, R. W. (1976) Markov Chains: Theory and Applications. Wiley, New York.Google Scholar
8. Iosifescu, M. (1980) Finite Markov Processes and their Applications. Wiley, New York.Google Scholar
9. Johnson, D. S. (1984) Simulated annealing performance studies. Presented at the Simulated Annealing Workshop, Yorktown Heights.Google Scholar
10. Kelly, F. P. (1980) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
11. Kirkpatrick, S., Gelatt, C. D. and Vecchi, M. P. (1983) Optimization by simulated annealing. Science 220, 671–680.CrossRefGoogle ScholarPubMed
12. Lundy, M. and Mees, A. (1984) Convergence of the annealing algorithm. Presented at Simulated Annealing Workshop, Yorktown Heights.Google Scholar
13. Madsen, R. W. and Isaacson, D. L. (1973) Strongly ergodic behavior for non-stationary Markov processes. Ann. Prob. 1, 329–335.CrossRefGoogle Scholar
14. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N. and Teller, A. H. (1953) Equations of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1091.CrossRefGoogle Scholar
15. Romeo, F. and Sangiovanni-Vincentelli, A. (1984) Probabilistic hill climbing algorithms: properties and applications. ERL Memo, University of California, Berkeley.Google Scholar
16. Sechen, C. and Sangiovanni-Vincentelli, A. (1984) The timber wolf placement and routing package. Proc. 1984 Custom Integrated Circuit Conference , Rochester.Google Scholar
17. Schwartz, J. (1980) Fast probabilistic algorithms for verification of polynomial identities. J. Assoc. Comput, Mach. 27, 701–717.CrossRefGoogle Scholar
18. Seneta, E. (1980) Non-negative Matrices and Markov Chains , 2nd edn. Springer-Verlag, New York.Google Scholar
19. Vecchi, M. P. and Kirkpatrick, S. (1983) Global wiring by simulated annealing. IEEE Trans. Computer-Aided Design 2, 215–222.CrossRefGoogle Scholar