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On the convergence of “Threshold Accepting”

Abstract

Simulated Annealing (SA) has become a very popular tool in combinatorial optimization since its introduction in 1982. Recently Dueck and Scheuer proposed another simple modification of local search which they called “Threshold Accepting” (TA). In this paper some convergence results for TA are presented. The proofs are not constructive and make use of the fact that in a certain sense “SA belongs to the convex hull of TA”.

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References

  1. G. Dueck and T. Scheuer, Threshold accepting: A general purpose optimization algorithm appearing superior to simulated annealing, Journal of Computational Physics 90 (1990), 161–175.

    Google Scholar 

  2. P. Erdös and J. Spencer, Probabilistic Methods in Combinatorics, Academic Press, New York, 1974.

    Google Scholar 

  3. S. B. Gelfand and S. K. Mitter, Analysis of simulated annealing for optimization, Technical Report LIDS-P-1495, August 1985.

  4. S. B. Gelfand and S. K. Mitter, Analysis of simulated annealing for optimization, Proc. 24th Conf. on Decision and Control, Ft Lauderdale, December 1985, pp. 779–786.

  5. M. Grötschel, Polyedrische Kombinatorik und Schnittebenenverfahren, Preprint No. 38, Universität Augsburg, 1984.

  6. B. Hajek and G. Sasaki, Simulated annealing—to cool or not, Systems & Control Letters 12 (1989), 443–447.

    Google Scholar 

  7. S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi, Optimization by simulated annealing, IBM Research Report RC 9355, 1982.

  8. S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi, Optimization by simulated annealing, Science 220 (1983), 671–680.

    Google Scholar 

  9. P. J. M. van Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Applications, Reidel, Dordrecht, 1987.

    Google Scholar 

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Althöfer, I., Koschnick, KU. On the convergence of “Threshold Accepting”. Appl Math Optim 24, 183–195 (1991). https://doi.org/10.1007/BF01447741

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  • DOI: https://doi.org/10.1007/BF01447741

Keywords

  • Local Search
  • System Theory
  • Simulated Annealing
  • Mathematical Method
  • Convex Hull