max_timse_parallel {KrigInv}

Minimizer of the parallel timse criterion

Description

Minimization, based on the package rgenoud (or on exhaustive search on a discrete set), of the timse criterion for a batch of candidate sampling points.

Usage

max_timse_parallel(lower, upper, optimcontrol = NULL, 
batchsize, integration.param, T,
model, new.noise.var = 0,
epsilon=0,imse=FALSE)

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 optimisation using the genoud algorithm, or "discrete" for an optimisation 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. Finally, one can control the field optim.option in order to decide how to optimize the sampling criterion. If optim.option is set to 2 (default), batchsize sequential optimizations in dimension d are performed to find the optimum. If optim.option is set to 1, only one optimization in dimension batchsize*d is performed. This option is only available with "genoud". This option might provide more global and accurate solutions, but is a lot more expensive.

batchsize

Number of points to sample simultaneously. The sampling criterion will return batchsize points at a time for sampling.

integration.param

Optional list of control parameter for the computation of integrals, containing the fields integration.points: a p*d matrix corresponding to p integrations points and integration.weights: a vector of size p corresponding to the weights of these integration points. If nothing is specified, default values are used (see: function integration_design for more details).

T

Array containing one or several thresholds.

model

A Kriging model of km class.

new.noise.var

Optional scalar value of the noise variance of the new observations.

epsilon

Optional tolerance value (a real positive number). Default value is 0.

imse

Optional boolean to decide if the "imse" criterion should be used instead of "timse". default: FALSE.

Value

A list with components:

par

the best set of parameters found.

value

the value of the sur 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)

Clement Chevalier (University of Neuchatel, Switzerland)

References

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)

Picheny V. (2009) Improving accuracy and compensating for uncertainty in surrogate modeling, Ph.D. thesis, University of Florida and Ecole Nationale Superieure des Mines de Saint-Etienne

Chevalier C., Bect J., Ginsbourger D., Vazquez E., Picheny V., Richet Y. (2014), Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set, Technometrics, vol. 56(4), pp 455-465

See Also

EGIparallel,max_sur_parallel

Examples

#max_timse_parallel


set.seed(9)
N <- 20 #number of observations
T <- c(40,80) #thresholds
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=200,optim.option=2)
integcontrol <- list(distrib="timse",n.points=400,init.distrib="MC")
integration.param <- integration_design(integcontrol=integcontrol,d=2,
                                            lower=lower,upper=upper,model=model,
                                            T=T)
batchsize <- 5 #number of new points

## Not run: 
obj <- max_timse_parallel(lower=lower,upper=upper,optimcontrol=optimcontrol,
                        batchsize=batchsize,T=T,model=model,
                        integration.param=integration.param,epsilon=0,imse=FALSE)
                        #5 optims in dimension 2 !

obj$par;obj$value #optimum in 5 new points
new.model <- update(object=model,newX=obj$par,newy=apply(obj$par,1,testfun),
                       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=batchsize,col.points.end="red",cex.points=2.5,
main="updated probability of excursion")


## End(Not run)