Skip to main content
Log in

Convergence of a Simulated Annealing Algorithm for Continuous Global Optimization

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

In this paper a simulated annealing algorithm for continuous global optimization will be considered. The algorithm, in which a cooling schedule based on the distance between the function value in the current point and an estimate of the global optimum value is employed, has been first introduced in Bohachevsky, Johnson and Stein (1986) [2], but without any proof of convergence. Here it will be proved that, under suitable assumptions, the algorithm is convergent

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.

Similar content being viewed by others

References

  1. Belisle, C.J.P. (1992), Convergence theorems for a class of simulated annealing algorithms on Rd, Journal of Applied Probability 29: 885-892.

    Google Scholar 

  2. Bohachevsky, I.O., Johnson, M.E. and Stein, M.L. (1986), Generalized simulated annealing for function optimization, Technometrics 28: 209-217.

    Google Scholar 

  3. Brooks, D.G. and Verdini, W.A. (1988), Computational experience with generalized simulated annealing over continuous variables, Amer. J. of Mathematical and Management Sciences 8: 425-449.

    Google Scholar 

  4. Černy, V. (1985), Thermodynamical approach to the travelling salesman problem: An efficient simulation algorithm, J. Optim. Theory Appl. 45: 41-51.

    Google Scholar 

  5. Coleman, T., Shalloway, D. and Zhijun Wu (1994), A parallel build-up algorithm for global energy minimizations of molecular clusters using effective energy simulated annealing, J. of Global Optimization 4: 171-185.

    Google Scholar 

  6. Corana, A., Marchesi, M., Martini, C. and Ridella, S. (1987), Minimizing multimodal functions of continuous variables with the 'simulated Annealing' algorithm, ACM Trans. Math. Software 13: 262-280.

    Google Scholar 

  7. Gelfand, S.B. and Mitter, S.K. (1993), Metropolis-type annealing algorithms for global optimization in Rd, SIAM J. of Control and Optimization 31(1): 111-131.

    Google Scholar 

  8. Jones, A.E.W. and Forbes, G.W. (1995), An adaptive simulated annealing algorithm for global optimization over continuous variables, J. of Global Optimization 6: 1-37.

    Google Scholar 

  9. Kirkpatrick, S., Gelatt, C.D. and Vecchi, M.P. (1983), Optimization by simulated annealing, Science 220(4598): 671-680.

    Google Scholar 

  10. Locatelli, M. (1996), Convergence properties of simulated annealing for continuous global optimization, J. of Applied Probability 33: 1127-1140.

    Google Scholar 

  11. Locatelli, M. (2000), Simulated annealing algorithms for continuous global optimization: convergence conditions, J. of Optimization Theory and Applications 104: 121-133.

    Google Scholar 

  12. Locatelli, M. (1999), On convergence of simulated annealing algorithms for continuous ´ global optimization, Technical Report 01-99, Dip. di Sistemi e Informatica, Universita di Firenze, also available at the web site www.dsi.unifi.it / users / locatell / dist4.ps

  13. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N. and Teller, A.H. (1953), Equation of state calculations by fast computer machines, J. Chem. Phys. 21: 1087.

    Google Scholar 

  14. Romeijn, H.E. and Smith, R.L. (1994), Simulated annealing and adaptive search in global optimization, Probability in the Engineering and Informational Sciences 8: 571-590.

    Google Scholar 

  15. Romeijn, H.E. and Smith, R.L. (1994), Simulated annealing for constrained global optimization, J. of Global Optimization 5: 101-126.

    Google Scholar 

  16. Vanderbilt, D. and Louie, S.G. (1984), A Monte Carlo simulated annealing approach to optimization over continuous variables, J. of Computational Physics 56: 259-271.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Locatelli, M. Convergence of a Simulated Annealing Algorithm for Continuous Global Optimization. Journal of Global Optimization 18, 219–233 (2000). https://doi.org/10.1023/A:1008339019740

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008339019740

Navigation