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Partially parallel simulated annealing: Low and high temperature approach of the invariante measure

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Book cover Applied Stochastic Analysis

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 177))

Abstract

In this paper, we consider parallelization of simulated annealing for a product configuration space L S. At every step of the algorithm, each site is activated with probability τ and all the activated sites update synchronously their value. Concerning reversibility conditions and behaviour in the low temperature region, we show that the fully parallel algorithm (τ=1) is a quite singular case and we prove that for the 2-D Ising Model the invariant probability measure at constant temperature T converges to the uniform probability measure on the two global minima when T→0 iff τ<1.

The high temperature region is studied for S=ℤ and translation invariant potential. We construct a sequence of approximations converging towards the invariant probability measure which can be derived from an implementable algorithm and we show that this sequence may be useful to compute valuable approximations of such statistical quantities as the mean energy

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Authors and Affiliations

  1. Lmens-Diam, Ecole Normale Supérieure, 45,rue d'Ulm, 75230, Paris Cedex 05

    A. Trouvé

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  1. A. Trouvé
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Ioannis Karatzas Daniel Ocone

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© 1992 Springer-Verlag

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Trouvé, A. (1992). Partially parallel simulated annealing: Low and high temperature approach of the invariante measure. In: Karatzas, I., Ocone, D. (eds) Applied Stochastic Analysis. Lecture Notes in Control and Information Sciences, vol 177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007063

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  • DOI: https://doi.org/10.1007/BFb0007063

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55296-3

  • Online ISBN: 978-3-540-47017-5

  • eBook Packages: Springer Book Archive

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