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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
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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