Abstract
We propose a multi-dimensional fast simulated annealing method based on a multivariate Cauchy probability distribution and an initial temperature estimated from the configuration’s variation. While conventional multi-dimensional fast simulated annealing adopts the product of onedimensional random variables generated by a univariate Cauchy distribution, the proposed method generates a random vector from a multivariate Cauchy distribution. In this way, fast simulated annealing for a multi-dimensional problem maintains the same annealing schedule as that for the one-dimensional case. The proposed method also utilizes the initial temperature estimated from the configuration’s variation to generate a candidate state in addition to the conventional initial temperature derived from the variation of the objective function for the acceptance probability. The proposed method is shown not only to guarantee a fast annealing schedule but also to enhance the search capability. The proposed method was tested against the optimization of real-valued functions. We empirically found that the configuration’s initial temperature, together with multivariate Cauchy distribution, is more suitable than the conventional scheme for a fast annealing schedule. Moreover, the proposed method outperforms the conventional one in optimization problems having many variables.
Similar content being viewed by others
References
S. Kirkpatrick, C. Gelatt and M. Vecchi, Science 220, 671 (1983).
V. Černý and J. Optimiz. Theory App. 45, 41 (1985).
S. Geman and D. Geman, IEEE Trans. Patt. Anan. Mach. Int. 6, 721 (1984).
V. Nascimento, V. Carvalho, C. de Castilho, B. Costa and E. Soares, Surf. Sci. 487, 15 (2001).
S. Sharma and A. Biswas, Geophysics 78, WB3 (2013).
Y. Dong, C. Zhao, G. Yang, L. Chen, J. Wang and H. Feng, Math. Comput. Model. 58, 877 (2013).
H. Szu and R. Hartley, Phys. Lett. A 122, 157 (1987).
C. Tsallis and D. Stariolo, Physica A 233, 395 (1996).
L. Ingber, Math. Comput. Model. 12, 967 (1989).
N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller and E. Teller, J. Chem. Phys. 21, 1087 (1953).
For a review, see B. Suman and P. Kumar, J. Oper. Res. Soc. 57, 1143 (2006).
C-Y. Lee and D. Lee, Comput. Optim. Appl. 58, 503 (2014).
M. Johnson, Multivariate statistical simulation (Wiley, New York, 1987), Chap. 3.
G. Molenberghs and E. Lesaffre, Stat. Sinica 7, 713 (1997).
G. Fishman, Commun. ACM 19, 407 (1976).
C-Y. Lee and X. Yao, IEEE Trans. Evol. Comput. 8, 1 (2004).
A. Hedar and M. Fukushima, Eur. J. Oper. Res. 170, 329 (2006).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lee, CY. Fast simulated annealing with a multivariate Cauchy distribution and the configuration’s initial temperature. Journal of the Korean Physical Society 66, 1457–1466 (2015). https://doi.org/10.3938/jkps.66.1457
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3938/jkps.66.1457