max_infill_criterion {KrigInv}

Optimizer for the infill criteria

Description

Optimization, of the chosen infill criterion (maximization or minimization, depending on the case)

Usage

max_infill_criterion(lower, upper, optimcontrol = NULL, 
method, T, model, method.param = NULL)

Arguments

lower

Vector containing the lower bounds of the design space.

upper

Vector containing the upper bounds of the design space.

optimcontrol

Optional list of control parameters for the optimization of the sampling criterion. The field method defines which optimization method is used. It can be either "genoud" (default) for an optimization using the genoud algorithm, or "discrete" for an optimization over a specified discrete set. If the field method is set to "genoud", one can set some parameters of this algorithm: pop.size (default : 50*d), max.generations (10*d), wait.generations (2), BFGSburnin (2) and the mutations P1, P2, up to P9 (see genoud). Numbers into brackets are the default values. If the field method is set to "discrete", one can set the field optim.points: p * d matrix corresponding to the p points where the criterion will be evaluated. If nothing is specified, 100*d points are chosen randomly.

method

Criterion used for choosing observations: "ranjan" (default) , "bichon", "tsee", or "tmse".

T

Array containing one or several thresholds. The "tmse" criterion can be used with multiple thresholds. The "ranjan", "bichon", "tsee" criteria can be used with only one threshold.

model

A Kriging model of km class.

method.param

Optional tolerance value (scalar). Default value is 1 for "ranjan" and "bichon", and 0 for "tmse".

Value

A list with components:

par

The best set of parameters found.

value

The value of the chosen criterion at par.

allvalues

If an optimization on a discrete set of points is chosen, the value of the criterion at all these points.

Author(s)

Victor Picheny (INRA, Toulouse, France)

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

Clement Chevalier (University of Neuchatel, Switzerland)

References

Bect J., Ginsbourger D., Li L., Picheny V., Vazquez E. (2012), Sequential design of computer experiments for the estimation of a probability of failure, Statistics and Computing vol. 22(3), pp 773-793

Picheny V., Ginsbourger D., Roustant O., Haftka R.T., (2010) Adaptive designs of experiments for accurate approximation of a target region, J. Mech. Des. vol. 132(7)

Bichon B.J., Eldred M.S., Swiler L.P., Mahadevan S., McFarland J.M. (2008) Efficient global reliability analysis for nonlinear implicit performance functions, AIAA Journal 46(10), pp 2459-2468

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

See Also

EGI,ranjan_optim,tmse_optim,bichon_optim,tsee_optim

Examples

#max_infill_criterion

set.seed(9)
N <- 20 #number of observations
T <- 80 #threshold
testfun <- branin
lower <- c(0,0)
upper <- c(1,1)

#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")

optimcontrol <- list(method="genoud",pop.size=50)

## Not run: 
obj <- max_infill_criterion(lower=lower,upper=upper,optimcontrol=optimcontrol,
                             method="bichon",T=T,model=model)

obj$par;obj$value
new.model <- update(object=model,newX=obj$par,newy=testfun(obj$par),cov.reestim=TRUE)

par(mfrow=c(1,2))
print_uncertainty(model=model,T=T,type="pn",lower=lower,upper=upper,
cex.points=2.5,main="probability of excursion")

print_uncertainty(model=new.model,T=T,type="pn",lower=lower,upper=upper,
new.points=1,col.points.end="red",cex.points=2.5,main="updated probability of excursion")

## End(Not run)