Generalized Simulated Annealing Function

Description

This function searches for global minimum of a very complex non-linear objective function with a very large number of optima.

Usage

GenSA(par = NULL, fn, lower, upper, control = list(), ...)

Arguments

Details

The default values of the control components are set for a complex optimization problem. For usual optimization problem with medium complexity, GenSA can find a reasonable solution quickly sot he user is recommended to let GenSA stop earlier by setting threshold.stop. If threshold.stop is the expected function value, or by setting max.time. If the user just want to run GenSA for max.time seconds, or by setting max.call. If the user just want to run GenSA within max.call function calls. Please refer to the examples below. For very complex optimization problems, the user is recommended to increase maxit and temp.

Value

The returned value is a list with the following fields:

value

Numeric. The value of fn corresponding to par.

par

Vector. The best set of parameters found.

trace.mat

A matrix which contains the history of the algorithm. (By columns: Step number, temperature, current objective function value, current minimal objective function value).

counts

Integer. Total number of calls of the objective function.

Author(s)

Yang Xiang, Sylvain Gubian, Brian Suomela, Julia Hoeng, PMP SA. . (Y.Xiang and S.Gubian are equal contributors)

References

Xiang Y, Gubian S, Martin F (2017). "Generalized Simulated Annealing." IntechOpen, Computational Optimization in Engineering, Chapter 2.

Xiang Y, Gubian S, Suomela B, Hoeng (2013). "Generalized Simulated Annealing for Efficient Global Optimization: the GenSA Package for R". The R Journal Volume 5/1, June 2013.

Xiang Y, Sun DY, Gong XG (2000). "Generalized Simulated Annealing Studies on Structures and Properties of Nin (n=2-55) Clusters." Journal of Physical Chemistry A, 104, 2746–2751.

Xiang Y, Gong XG (2000a). "Efficiency of Generalized Simulated Annealing." PHYSICAL REVIEW E, 62, 4473.

Xiang Y, Sun DY, Fan W, Gong XG (1997). "Generalized Simulated Annealing Algorithm and Its Application to the Thomson Model." Physics Letters A, 233, 216–220.

Tsallis C, Stariolo DA (1996). "Generalized Simulated Annealing." Physica A, 233, 395–406.

Tsallis C (1988). "Possible generalization of Boltzmann-Gibbs statistics." Journal of Statistical Physics, 52, 479–487.

Examples

 library(GenSA)
 # Try Rastrgin function (The objective function value for global minimum
 # is 0 with all components of par are 0.)
 Rastrigin <- function(x) {
 sum(x^2 - 10 * cos(2 * pi * x)) + 10 * length(x)
 }
 # Perform the search on a 30 dimensions rastrigin function. Rastrigin
 # function with dimension 30 is known as the most
 # difficult optimization problem according to "Yao X, Liu Y, Lin G (1999).
 # \Evolutionary Programming Made Faster."
 # IEEE Transactions on Evolutionary Computation, 3(2), 82-102.
 # GenSA will stop after finding the targeted function value 0 with
 # absolute tolerance 1e-13
 set.seed(1234) # The user can use any seed.
 dimension <- 30
 global.min <- 0
 tol <- 1e-13
 lower <- rep(-5.12, dimension)
 upper <- rep(5.12, dimension)
 out <- GenSA(lower = lower, upper = upper, fn = Rastrigin,
 control=list(threshold.stop=global.min+tol,verbose=TRUE))
 out[c("value","par","counts")]
 # GenSA will stop after running for about 2 seconds
 # Note: The time for solving this problem by GenSA may vary
 # depending on the computer used.
 set.seed(1234) # The user can use any seed.
 dimension <- 30
 global.min <- 0
 tol <- 1e-13
 lower <- rep(-5.12, dimension)
 upper <- rep(5.12, dimension)
 out <- GenSA(lower = lower, upper = upper, fn = Rastrigin,
 control=list(max.time=2))
 out[c("value","par","counts")]