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A Bayesian Approach to Simulated Annealing

Published online by Cambridge University Press:  27 July 2009

P.J.M. Van Laarhoven ,
C.G.E. Boender ,
E.H.L. Aarts  and
A. H. G. Rinnooy Kan
P.J.M. Van Laarhoven
Affiliation:
Philips Research Laboratories Eindhoven, the Netherlands
C.G.E. Boender
Affiliation:
Erasmus University, Rotterdam, the Netherlands
E.H.L. Aarts
Affiliation:
Philips Research Laboratories Eindhoven, the Netherlands andEindhoven University of Technology Eindhoven, the Netherlands
A. H. G. Rinnooy Kan
Affiliation:
Erasmus University, Rotterdam, the Netherlands
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Abstract

Simulated annealing is a probabilistic algorithm for approximately solving large combinatorial optimization problems. The algorithm can mathematically be described as the generation of a series of Markov chains, in which each Markov chain can be viewed as the outcome of a random experiment with unknown parameters (the probability of sampling a cost function value). Assuming a probability distribution on the values of the unknown parameters (the prior distribution) and given the sequence of configurations resulting from the generation of a Markov chain, we use Bayes's theorem to derive the posterior distribution on the values of the parameters. Numerical experiments are described which show that the posterior distribution can be used to predict accurately the behavior of the algorithm corresponding to the next Markov chain. This information is also used to derive optimal rules for choosing some of the parameters governing the convergence of the algorithm.

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Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 4 , October 1989 , pp. 453 - 475
Copyright
Copyright © Cambridge University Press 1989

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