Skip to main content
SpringerLink
Log in

Simulated Annealing Using Hybrid Monte Carlo

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We propose a variant of the simulated annealing method for optimization in the multivariate analysis of differentiable functions. The method uses global actualizations via the hybrid Monte Carlo algorithm in their generalized version for the proposal of new configurations. We show how this choice can improve upon the performance of simulated annealing methods (mainly when the number of variables is large) by allowing a more effective searching scheme and a faster annealing schedule.

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

Access this article

Log in via an institution

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. P. J. M. van Laarhoven and E. H. L. Aarts,Simulated Annealing: Theory and Applications (Kluwer Academic Publishers, Netherlands, 1988).

    Google Scholar 

  2. M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979).

    MATH  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  4. W. T. Vetterling, W. H. Press, S. A. Teukolsky, and B. P. Flannery,Numerical Recipes in FORTRAN: The Art of Scientific Computing (Cambridge University, New York, 1994).

    Google Scholar 

  5. M. H. Kalos and P. A. Whitlock,Monte Carlo Methods (Wiley, New York, 1986).

    MATH  Google Scholar 

  6. D. Heermann,Computer Simulation Methods (Springer-Verlag, Berlin, Heidelberg, 1986).

    Google Scholar 

  7. K. Binder, ed.,The Monte Carlo Method in Condensed Matter Physics (Springer-Verlag, Berlin, Heidelberg, 1992).

    Google Scholar 

  8. S. Duane, A. D. Kennedy, B. J. Pendelton, and D. Roweth, Hybrid Monte Carlo,Phys. Lett. B 195:216–222(1987).

    Article  ADS  Google Scholar 

  9. R. Toral and A. L. Ferreira, Generalized Hybrid Monte Carlo, inProceedings of the Conference Physics Computing ’94, p. 265 (European Physical Society, Geneva, Switzerland, 1994), R. Gruber and M. Tomasini, eds.

  10. A. L. Ferreira and R. Toral, Hybrid Monte Carlo method for conserved-order-parameter systems,Phys. Rev. E 47:R3848-R3851 (1993).

    Article  ADS  Google Scholar 

  11. S. German and D. German, Stochastic relaxation, Gibbs distribution and the Bayesian restoration in images,IEEE Trans. Patt. Anan. Mach. Int 6:721–741 (1984).

    Article  Google Scholar 

  12. H. Szu and R. Hartley, Fast simulated annealing,Phys. Lett. A 3-14:157–162 (1987).

    Article  ADS  Google Scholar 

  13. L. Ingber and B. Rosen, Genetic algorithms and very fast simulated reannealing: A comparison,Mathl. Comput. Modelling 16:87–100 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  14. A similar procedure is used in [15] in the context of sampling Tsallis statistics. In their method, the configuration energy difference δE(x) is used instead of the total Hamiltonian difference δH(x) as the acceptance criterion. In general, this procedure does not properly sample the Gibbs distribution, Eq. (1), at temperatureT, although it coincides with the one used in this paper asT → 0.

  15. I. Andricioaei and J. E. Straub, Generalized simulated annealing algorithms using tsallis statistics: Application to conformational optimization of a tetrapeptide,Physical Review E 53:R3055-R3058(1996).

    Article  ADS  Google Scholar 

  16. Time reversibility implies that the original coordinates are exactly recovered after numerical integration during a time step if the momenta are reversed. Area preserving implies that the Jacobian of the mapping (10) is equal to one.

  17. R. Toral, Computational field theory and pattern formation, in3rd Granada Lectures in Computational Physics, p. 1 (Springer-Verlag, Heidelberg, 1995), P. L. Garrido and J. Marro, eds.

    Google Scholar 

  18. K. A. De Jong,An Analysis of the Behavior of a Class of Genetic Adaptive System, Ph.D. thesis, University of Michigan, 1981.

  19. A. Corana, M. Martini, and S. Ridella, Minimizing multimodal functions of continuous variables with the simulated annealing algorithm,ACM Trans. Mathematical Software 13:272–280(1987).

    Article  MathSciNet  Google Scholar 

  20. S. G. Dykes and B. E. Rosen, Parallel very fast simulated reannealing by temperature block partitioning, inIEEE International Conference on Systems, Man, and Cybernetics. Humans, Information and Technology (IEEE press, New York, 1994), pp. 1914–1919.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departament de Fisica, Universitat de les Illes Balears, 07071, Palma de Mallorca, Spain

    R. Salazar & R. Toral

  2. Instituto Mediterráneo de Estudios Avanzados (IMEDEA, UIB-CSIC), 07071, Palma de Mallorca, Spain

    R. Toral

Authors
  1. R. Salazar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Toral
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Salazar, R., Toral, R. Simulated Annealing Using Hybrid Monte Carlo. J Stat Phys 89, 1047–1060 (1997). https://doi.org/10.1007/BF02764221

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02764221

Key words

Search

Navigation