Monte Carlo dynamics in global optimization.
Several very different optimization problems are studied by using the fixed-temperature Monte Carlo dynamics and found to share many common features. The most surprising result is that the cost function of these optimization problems itself is a very good stochastic variable to describe the complicated Monte Carlo processes. A multidimensional problem can therefore be mapped into a one-dimensional diffusion problem. This problem is either solved by direct numerical simulation or by using the Fokker-Planck equations. Above certain temperatures, the first passage time distribution functions of the original Monte Carlo processes are reproduced. At low temperatures, the first passage time has a path dependence and the single-stochastic-variable description is no longer valid. This analysis also provides a simple method to characterize the energy landscapes.
Chen
C N
CN
Institute of Physics, Academia Sinica, Taipei, Taiwan.
Chou
C I
CI
Hwang
C R
CR
Kang
J
J
Lee
T K
TK
Li
S P
SP
D018360:Crystallography, X-Ray; D009010:Monte Carlo Method; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D017510:Protein Folding; D013816:Thermodynamics