sampleFromEI {DiceOptim}

Sampling points according to the expected improvement criterion

Description

Samples n points from a distribution proportional to the expected improvement (EI) computed from a km object.

Usage

sampleFromEI(
  model,
  minimization = TRUE,
  n = 1,
  initdistrib = NULL,
  lower = rep(0, model@d),
  upper = rep(1, model@d),
  T = NULL
)

Arguments

model

an object of class km,

minimization

logical specifying if EI is used in minimiziation or in maximization,

n

number of points to be sampled,

initdistrib

matrix of candidate points.

lower

vector of lower bounds,

upper

vector of upper bounds,

T

optional scalar : if provided, it replaces the current minimum (or maximum) of observations.

Value

A n*d matrix containing the sampled points. If NULL, 1000*d points are obtained by latin hypercube sampling,

Author(s)

Sebastien Marmin

Clement Chevalier

David Ginsbourger

References

D.R. Jones, M. Schonlau, and W.J. Welch (1998), Efficient global optimization of expensive black-box functions, Journal of Global Optimization, 13, 455-492.

See Also

EI, km, qEI

Examples

set.seed(004)

# a 9-points factorial design, and the corresponding responses
d <- 2
n <- 9
design.fact <- expand.grid(seq(0,1,length=3), seq(0,1,length=3)) 
names(design.fact)<-c("x1", "x2")
design.fact <- data.frame(design.fact) 
names(design.fact)<-c("x1", "x2")
response.branin <- apply(design.fact, 1, branin)
response.branin <- data.frame(response.branin) 
lower <- c(0,0)
upper <- c(1,1)
names(response.branin) <- "y" 


# model identification
fitted.model <- km(~1, design=design.fact, response=response.branin, 
                   covtype="gauss", control=list(pop.size=50,trace=FALSE), parinit=c(0.5, 0.5))

# sample a 30 point batch
batchSize <- 30
x <- sampleFromEI(model = fitted.model, n = batchSize, lower = lower, upper = upper)

# graphics 
# displays the EI criterion, the design points in black and the EI-sampled points in red.
nGrid <- 15
gridAxe1 <- seq(lower[1],upper[1],length=nGrid)
gridAxe2 <- seq(lower[2],upper[2],length=nGrid)
grid <- expand.grid(gridAxe1,gridAxe2)
aa <- apply(grid,1,EI,model=fitted.model)
myMat <- matrix(aa,nrow=nGrid)
image(x = gridAxe1, y = gridAxe2, z = myMat, 
      col = colorRampPalette(c("darkgray","white"))(5*10), 
      ylab = names(design.fact)[1], xlab=names(design.fact)[2], 
      main = "Sampling from the expected improvement criterion", 
      axes = TRUE, zlim = c(min(myMat), max(myMat)))
contour(x = gridAxe1, y = gridAxe2, z = myMat, 
        add = TRUE, nlevels = 10)
points(x[,1],x[,2],pch=19,col='red')
points(fitted.model@X[,1],fitted.model@X[,2],pch=19)