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Convergence of Simulated Annealing with Feedback Temperature Schedules

Published online by Cambridge University Press:  27 July 2009

M. Kolonko  and
M. T. Tran
M. Kolonko
Affiliation:
Institut für Mathematik, Universität Hildesheim, Marienburger Platz 22, D-31141 Hildesheim, Germany
M. T. Tran
Affiliation:
Institut für Mathematik, Universität Hildesheim, Marienburger Platz 22, D-31141 Hildesheim, Germany
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Abstract

It is well known that the standard simulated annealing optimization method converges in distribution to the minimum of the cost function if the probability a for accepting an increase in costs goes to 0. α is controlled by the “temperature” parameter, which in the standard setup is a fixed sequence of values converging slowly to 0. We study a more general model in which the temperature may depend on the state of the search process. This allows us to adapt the temperature to the landscape of the cost function. The temperature may temporarily rise such that the process can leave a local optimum more easily. We give weak conditions on the temperature schedules such that the process of solutions finally concentrates near the optimal solutions. We also briefly sketch computational results for the job shop scheduling problem.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 3 , July 1997 , pp. 279 - 304
Copyright
Copyright © Cambridge University Press 1997

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