Skip to main content
Log in

On the convergence of “Threshold Accepting”

  • Published:
Applied Mathematics and Optimization Submit manuscript

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”.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

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 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Accepted:

  • Issue Date:

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

Keywords

Navigation