KrigInv (version 1.1)

max_infill_criterion: Optimizer for the infill criteria

Description

Global optimization, based on the package rgenoud (or on exhaustive search on a discrete set), of the chosen infill criterion (maximization or minimization, depending on the case)

Usage

max_infill_criterion(lower, upper, parinit=NULL, sampling.method, 
method.param=0, control=NULL, discrete.X=NULL, T, model, type="UK")

Arguments

lower

vector containing the lower bounds of the variables to be optimized over

upper

vector containing the upper bounds of the variables to be optimized over

parinit

optional vector containing the initial values for the variables to be optimized over

control

optional list of control parameters for optimization. One can control "pop.size" (default : [4+3*log(nb of variables)]), "max.generations" (5), "wait.generations" (2) and "BFGSburnin" (0) of fun

T

target value (a real number)

method.param

optional tolerance value (a real number)

model

An object of class km (Kriging model)

type

Kriging type (string): "SK" or "UK" (default)

sampling.method

criterion used for choosing observations: "ranjan" (default) , "bichon", or "tmse"

discrete.X

optional matrix of candidate points. If provided, the search for new observations is made on this discrete set instead of running the continuous optimisation

Value

• A list with components:
• par
  the best set of parameters found.
• value
  the value of the chosen criterion at par.

References

Bect J., Ginsbourger D., Li L., Picheny V., Vazquez E. (2010), Sequential design of computer experiments for the estimation of a probability of failure, accepted with minor revisions to the Journal of Statistics and Computing, http://arxiv.org/abs/1009.5177 Picheny, V., Ginsbourger, D., Roustant, O., Haftka, R.T., Adaptive designs of experiments for accurate approximation of a target region, J. Mech. Des. - July 2010 - Volume 132, Issue 7, http://dx.doi.org/10.1115/1.4001873 Bichon, B.J., Eldred, M.S., Swiler, L.P., Mahadevan, S., McFarland, J.M.: Efficient global reliability analysis for nonlinear implicit performance functions. AIAA Journal 46 (10), 2459-2468 (2008) Ranjan, P., Bingham, D., Michailidis, G.: Sequential experiment design for contour estimation from complex computer codes. Technometrics 50(4), 527-541 (2008)

See Also

EGI,ranjan_optim,tmse_optim,bichon_optim

Examples

##################################################################
#a 9-point full factorial initial design
design.fact <- expand.grid(seq(0,1,length=3), seq(0,1,length=3))

design.fact <- data.frame(design.fact)
names(design.fact) <- c ( "x1","x2")
testfun <- camelback2			#our test function

#the response
response <- testfun(design.fact)

#the initial km model
model <- km(formula=~., design = design.fact, response = response, 
covtype="matern5_2")

#the integration points
n.grid <- 30
x.grid <- y.grid <- seq(0,1,length=n.grid)
design.grid <- expand.grid(x.grid, y.grid)

#evaluate Bichon's criterion on the grid
T <- 0
bichon.EI.grid <- apply(design.grid, 1, bichon_optim, T=T, 
method.param=0.1, model=model)
z.grid <- matrix(bichon.EI.grid, n.grid, n.grid)

#plots: contour of the criterion, doe points and new point
contour(x.grid,y.grid,z.grid,25)
points(design.fact, col="black", pch=20, lwd=4)

#plots: contour of the actual function at threshold
testfun.grid <- testfun(design.grid)
z.grid.2 <- matrix(testfun.grid, n.grid, n.grid)
contour(x.grid,y.grid,z.grid.2,levels=T,col="blue",add=TRUE)
title("Contour lines of Bichon criterion (black) and of f(x)=T (blue)")

#search best point with Genoud
opt <- max_infill_criterion(lower=c(0,0), upper=c(1,1), 
sampling.method="bichon", method.param=0.1, T=T, model=model)
points(opt$par, col="blue", pch=20, lwd=4)

##################################################################