KrigInv (version 1.4.2)

ranjan_optim: Ranjan et al.'s Expected Improvement criterion

Description

Evaluation of Ranjan's Expected Feasibility criterion. To be used in optimization routines, like in max_infill_criterion.

Usage

ranjan_optim(x, model, T, method.param = 1)

Value

Ranjan EI criterion. When the argument x is a vector the function returns a scalar. When the argument x is a p*d matrix the function returns a vector of size p.

Arguments

x

Input vector at which one wants to evaluate the criterion. This argument can be either a vector of size d (for an evaluation at a single point) or a p*d matrix (for p simultaneous evaluations of the criterion at p different points).

model

An object of class km (Kriging model).

T

Target value (scalar).

method.param

Scalar tolerance around the target T. Default value is 1.

Author

Victor Picheny (INRA, Toulouse, France)

David Ginsbourger (IDIAP Martigny and University of Bern, Switzerland)

Clement Chevalier (University of Neuchatel, Switzerland)

References

Ranjan, P., Bingham, D., Michailidis, G. (2008) Sequential experiment design for contour estimation from complex computer codes Technometrics 50(4), pp 527-541

Bect J., Ginsbourger D., Li L., Picheny V., Vazquez E. (2010), Sequential design of computer experiments for the estimation of a probability of failure, Statistics and Computing, pp.1-21, 2011, https://arxiv.org/abs/1009.5177

See Also

EGI, max_infill_criterion

Examples

########################################################################
#ranjan_optim

set.seed(9)
N <- 20 #number of observations
T <- 80 #threshold
testfun <- branin

#a 20 points initial design
design <- data.frame( matrix(runif(2*N),ncol=2) )
response <- testfun(design)

#km object with matern3_2 covariance
#params estimated by ML from the observations
model <- km(formula=~., design = design, 
	response = response,covtype="matern3_2")

x <- c(0.5,0.4)#one evaluation of the ranjan criterion
ranjan_optim(x=x,T=T,model=model)

n.grid <- 20 #you can run it with 100
x.grid <- y.grid <- seq(0,1,length=n.grid)
x <- expand.grid(x.grid, y.grid)
ranjan.grid <- ranjan_optim(x=x,T=T,model=model)
z.grid <- matrix(ranjan.grid, n.grid, n.grid)

#plots: contour of the criterion, DOE points and new point
image(x=x.grid,y=y.grid,z=z.grid,col=grey.colors(10))
contour(x=x.grid,y=y.grid,z=z.grid,25,add=TRUE)
points(design, col="black", pch=17, lwd=4,cex=2)

i.best <- which.max(ranjan.grid)
points(x[i.best,], col="blue", pch=17, lwd=4,cex=3)

#plots the real (unknown in practice) curve f(x)=T
testfun.grid <- apply(x,1,testfun)
z.grid.2 <- matrix(testfun.grid, n.grid, n.grid)
contour(x.grid,y.grid,z.grid.2,levels=T,col="blue",add=TRUE,lwd=5)
title("Contour lines of Ranjan criterion (black) and of f(x)=T (blue)")