mxComputeSimAnnealing: Optimization using generalized simulated annealing

In OpenMx/OpenMx: Extended Structural Equation Modelling

Optimization using generalized simulated annealing

Description

Performs simulated annealing to minimize the fit function. If the original starting values are outside of the feasible set, a few attempts are made to find viable starting values.

Usage

mxComputeSimAnnealing(freeSet=NA_character_, ..., fitfunction='fitfunction',
 plan=mxComputeOnce('fitfunction','fit'),
 verbose=0L, method=c("tsallis1996", "ingber2012"), control=list(),
 defaultGradientStepSize=imxAutoOptionValue("Gradient step size"),
 defaultFunctionPrecision=imxAutoOptionValue("Function precision"))

Arguments

freeSet	names of matrices containing free variables
...	Not used. Forces remaining arguments to be specified by name.
fitfunction	name of the fitfunction (defaults to 'fitfunction')
plan	compute plan to optimize the model
verbose	level of debugging output
method	which algorithm to use
control	control parameters specific to the chosen method
defaultGradientStepSize	the default gradient step size
defaultFunctionPrecision	the default function precision

Details

For method ‘tsallis1996’, the number of function evaluations are determined by the tempStart and tempEnd parameters. There is no provision to stop early because there is no way to determine whether the algorithm has converged. The Markov step is implemented by cycling through each parameters in turn and considering a univariate jump (like a Gibbs sampler).

Control parameters include qv to control the shape of the visiting distribution, qaInit to control the shape of the initial acceptance distribution, lambda to reduce the probability of acceptance in time, tempStart to specify starting temperature, tempEnd to specify ending temperature, and stepsPerTemp to set the number of Markov steps per temperature step.

Non-linear constraints are accommodated by a penalty function. Inequality constraints work reasonably well, but equality constraints do not work very well. Constrained optimization will likely require increasing stepsPerTemp.

Classical simulated annealing (CSA) can be obtained with qv=qa=1 and lambda=0. Fast simulated annealing (FSA) can be obtained with qv=2, qa=1, and lambda=0. FSA is faster than CSA, but GSA is faster than FSA. GenSA default parameters are set to those identified in Xiang, Sun, Fan & Gong (1997).

Method ‘ingber2012’ has spawned a cultural tradition over more than 30 years that is documented in Aguiar e Oliveira et al (2012). Options are specified using the traditional option names in the control list. However, there are a few option changes to make ASA fit better with OpenMx. Instead of option Curvature_0, use mxComputeNumericDeriv. ASA_PRINT output is directed to /dev/null by default. To direct ASA_PRINT output to console use control=list('Asa_Out_File'= '/dev/fd/1'). ASA's option to control the finite differences gradient step size, Delta_X, defaults to mxOption's ‘Gradient step size’ instead of ASA's traditional 0.001. Similarly, Cost_Precision defaults to mxOption's ‘Function Precision’ instead of ASA's traditional 1e-18.

References

Aguiar e Oliveira, H., Ingber, L., Petraglia, A., Petraglia, M. R., & Machado, M. A. S. (2012). Stochastic global optimization and its applications with fuzzy adaptive simulated annealing. Springer Publishing Company, Incorporated.

Tsallis, C., & Stariolo, D. A. (1996). Generalized simulated annealing. Physica A: Statistical Mechanics and its Applications, 233(1-2), 395-406.

Xiang, Y., Sun, D. Y., Fan, W., & Gong, X. G. (1997). Generalized simulated annealing algorithm and its application to the Thomson model. Physics Letters A, 233(3), 216-220.

See Also

mxComputeTryHard

Examples

library(OpenMx)
m1 <- mxModel(
	"poly22", # Eqn 22 from Tsallis & Stariolo (1996)
	mxMatrix(type='Full', values=runif(4, min=-1e6, max=1e6),
		ncol=1, nrow=4, free=TRUE, name='x'),
	mxAlgebra(sum((x*x-8)^2) + 5*sum(x) + 57.3276, name="fit"),
	mxFitFunctionAlgebra('fit'),
	mxComputeSimAnnealing())

m1 <- mxRun(m1)
summary(m1)

OpenMx/OpenMx documentation built on April 17, 2024, 3:32 p.m.