DEoptim (version 2.2-8)

DEoptim-methods: DEoptim-methods

Description

Methods for DEoptim objects.

Usage

# S3 method for DEoptim
summary(object, ...)
# S3 method for DEoptim
plot(x, plot.type = c("bestmemit", "bestvalit", "storepop"), ...)

Arguments

object

an object of class DEoptim; usually, a result of a call to DEoptim.

x

an object of class DEoptim; usually, a result of a call to DEoptim.

plot.type

should we plot the best member at each iteration, the best value at each iteration or the intermediate populations?

...

further arguments passed to or from other methods.

Author

David Ardia, Katharine Mullen , Brian Peterson and Joshua Ulrich.

Details

Members of the class DEoptim have a plot method that accepts the argument plot.type.
plot.type = "bestmemit" results in a plot of the parameter values that represent the lowest value of the objective function each generation. plot.type = "bestvalit" plots the best value of the objective function each generation. Finally, plot.type = "storepop" results in a plot of stored populations (which are only available if these have been saved by setting the control argument of DEoptim appropriately). Storing intermediate populations allows us to examine the progress of the optimization in detail. A summary method also exists and returns the best parameter vector, the best value of the objective function, the number of generations optimization ran, and the number of times the objective function was evaluated.

References

Ardia, D., Boudt, K., Carl, P., Mullen, K.M., Peterson, B.G. (2011) Differential Evolution with DEoptim. An Application to Non-Convex Portfolio Optimization. R Journal, 3(1), 27-34. tools:::Rd_expr_doi("10.32614/RJ-2011-005")

Ardia, D., Ospina Arango, J.D., Giraldo Gomez, N.D. (2011) Jump-Diffusion Calibration using Differential Evolution. Wilmott Magazine, 55 (September), 76-79. tools:::Rd_expr_doi("10.1002/wilm.10034")

Mullen, K.M, Ardia, D., Gil, D., Windover, D., Cline,J. (2011). DEoptim: An R Package for Global Optimization by Differential Evolution. Journal of Statistical Software, 40(6), 1-26. tools:::Rd_expr_doi("10.18637/jss.v040.i06")

See Also

DEoptim and DEoptim.control.

Examples

  ## Rosenbrock Banana function
  ## The function has a global minimum f(x) = 0 at the point (1,1).  
  ## Note that the vector of parameters to be optimized must be the first 
  ## argument of the objective function passed to DEoptim.
  Rosenbrock <- function(x){
    x1 <- x[1]
    x2 <- x[2]
    100 * (x2 - x1 * x1)^2 + (1 - x1)^2
  }

  lower <- c(-10, -10)
  upper <- -lower
  
  set.seed(1234)
  outDEoptim <- DEoptim(Rosenbrock, lower, upper)
  
  ## print output information
  summary(outDEoptim)

  ## plot the best members
  plot(outDEoptim, type = 'b')

  ## plot the best values
  dev.new()
  plot(outDEoptim, plot.type = "bestvalit", type = 'b', col = 'blue')

  ## rerun the optimization, and store intermediate populations
  outDEoptim <- DEoptim(Rosenbrock, lower, upper,
                        DEoptim.control(itermax = 500,
                        storepopfrom = 1, storepopfreq = 2))
  summary(outDEoptim)
  
  ## plot intermediate populations
  dev.new()
  plot(outDEoptim, plot.type = "storepop")

  ## Wild function
  Wild <- function(x)
    10 * sin(0.3 * x) * sin(1.3 * x^2) +
       0.00001 * x^4 + 0.2 * x + 80

  outDEoptim = DEoptim(Wild, lower = -50, upper = 50,
                       DEoptim.control(trace = FALSE, storepopfrom = 50,
                       storepopfreq = 1))
  
  plot(outDEoptim, type = 'b')

  dev.new()
  plot(outDEoptim, plot.type = "bestvalit", type = 'b')

if (FALSE) {
  ## an example with a normal mixture model: requires package mvtnorm
  library(mvtnorm)

  ## neg value of the density function
  negPdfMix <- function(x) {
     tmp <- 0.5 * dmvnorm(x, c(-3, -3)) + 0.5 * dmvnorm(x, c(3, 3))
     -tmp
  }

  ## wrapper plotting function
  plotNegPdfMix <- function(x1, x2)
     negPdfMix(cbind(x1, x2))

  ## contour plot of the mixture
  x1 <- x2 <- seq(from = -10.0, to = 10.0, by = 0.1)
  thexlim <- theylim <- range(x1)
  z <- outer(x1, x2, FUN = plotNegPdfMix)
  
  contour(x1, x2, z, nlevel = 20, las = 1, col = rainbow(20),
     xlim = thexlim, ylim = theylim)

  set.seed(1234)
  outDEoptim <- DEoptim(negPdfMix, c(-10, -10), c(10, 10),
     DEoptim.control(NP = 100, itermax = 100, storepopfrom = 1,
     storepopfreq = 5))

  ## convergence plot
  dev.new()
  plot(outDEoptim)
  
  ## the intermediate populations indicate the bi-modality of the function
  dev.new()
  plot(outDEoptim, plot.type = "storepop")
}