bichon_optim | R Documentation |
Evaluation of Bichon's Expected Feasibility criterion. To be used in optimization routines, like in max_infill_criterion
.
bichon_optim(x, model, T, method.param = 1)
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 |
T |
Target value (scalar). |
method.param |
Scalar tolerance around the target T. Default value is 1. |
Bichon EF 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.
Victor Picheny (INRA, Toulouse, France)
David Ginsbourger (IDIAP Martigny and University of Bern, Switzerland)
Clement Chevalier (University of Neuchatel, Switzerland)
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
EGI
, max_infill_criterion
#bichon_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 bichon criterion bichon_optim(x=x,T=T,model=model) n.grid <- 20 # resolution. You may use a larger value. x.grid <- y.grid <- seq(0,1,length=n.grid) x <- expand.grid(x.grid, y.grid) bichon.grid <- bichon_optim(x=x,T=T,model=model) z.grid <- matrix(bichon.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(bichon.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 Bichon criterion (black) and of f(x)=T (blue)")
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