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Minimization, based on the package rgenoud (or on exhaustive search on a discrete set), of the sur criterion for a batch of candidate sampling points.
max_sur_parallel(lower, upper, optimcontrol = NULL,
batchsize, integration.param, T,
model, new.noise.var = 0)Vector containing the lower bounds of the design space.
Vector containing the upper bounds of the design space.
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.
Number of points to sample simultaneously. The sampling criterion will return batchsize points at a time for sampling.
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).
Target value (scalar).
A Kriging model of km class.
Optional scalar value of the noise variance of the new observations.
A list with components:
the best set of points found.
the value of the sur criterion at par.
If an optimization on a discrete set of points is chosen, the value of the criterion at all these points.
Chevalier C., Bect J., Ginsbourger D., Vazquez E., Picheny V., Richet Y. (2011), Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set ,http://hal.archives-ouvertes.fr/hal-00641108/
Chevalier C., Ginsbourger D. (2012), Corrected Kriging update formulae for batch-sequential data assimilation ,http://arxiv.org/pdf/1203.6452.pdf
# NOT RUN {
#max_sur_parallel
set.seed(8)
N <- 9 #number of observations
T <- 80 #threshold
testfun <- branin
lower <- c(0,0)
upper <- c(1,1)
#a 9 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,optim.option=1)
integcontrol <- list(distrib="sur",n.points=50,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_sur_parallel(lower=lower,upper=upper,optimcontrol=optimcontrol,
batchsize=batchsize,T=T,model=model,
integration.param=integration.param)
#one optim in dimension 5*2 !
obj$par;obj$value #optimum in 5 new points
new.model <- update_km(model=model,NewX=obj$par,NewY=apply(obj$par,1,testfun),
CovReEstimate=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")
# }
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