max_AEI {DiceOptim}

Maximizer of the Augmented Expected Improvement criterion function

Description

Maximization, based on the package rgenoud of the Augmented Expected Improvement (AEI) criterion.

Usage

max_AEI(
  model,
  new.noise.var = 0,
  y.min = NULL,
  type = "UK",
  lower,
  upper,
  parinit = NULL,
  control = NULL
)

Arguments

model

a Kriging model of "km" class

new.noise.var

the (scalar) noise variance of the new observation.

y.min

The kriging mean prediction at the current best point (point with smallest kriging quantile). If not provided, this quantity is evaluated inside the AEI function (may increase computational time).

type

Kriging type: "SK" or "UK"

lower

vector containing the lower bounds of the variables to be optimized over

upper

optional vector containing the upper bounds of the variables to be optimized over

parinit

optional vector containing the initial values for the variables to be optimized over

control

optional list of control parameters for optimization. One can control "pop.size" (default : [N=3*2^dim for dim<6 and N=32*dim otherwise]), "max.generations" (12), "wait.generations" (2) and "BFGSburnin" (2) of function "genoud" (see genoud). Numbers into brackets are the default values

Value

A list with components:

par

the best set of parameters found.

value

the value AEI at par.

Author(s)

Victor Picheny

David Ginsbourger

Examples

library(DiceDesign)
set.seed(100)

# Set test problem parameters
doe.size <- 10
dim <- 2
test.function <- get("branin2")
lower <- rep(0,1,dim)
upper <- rep(1,1,dim)
noise.var <- 0.2

# Generate DOE and response
doe <- as.data.frame(lhsDesign(doe.size, dim)$design)
y.tilde <- rep(0, 1, doe.size)
for (i in 1:doe.size)  {y.tilde[i] <- test.function(doe[i,]) 
+ sqrt(noise.var)*rnorm(n=1)}
y.tilde <- as.numeric(y.tilde)

# Create kriging model
model <- km(y~1, design=doe, response=data.frame(y=y.tilde),
     covtype="gauss", noise.var=rep(noise.var,1,doe.size), 
     lower=rep(.1,dim), upper=rep(1,dim), control=list(trace=FALSE))

# Optimisation using max_AEI
res <- max_AEI(model, new.noise.var=noise.var, type = "UK", 
lower=c(0,0), upper=c(1,1)) 
X.genoud <- res$par

# Compute actual function and criterion on a grid
n.grid <- 12 # Change to 21 for a nicer picture
x.grid <- y.grid <- seq(0,1,length=n.grid)
design.grid <- expand.grid(x.grid, y.grid)
names(design.grid) <- c("V1","V2")
nt <- nrow(design.grid)
crit.grid <- apply(design.grid, 1, AEI, model=model, new.noise.var=noise.var)

## Not run: 
# # 2D plots
z.grid <- matrix(crit.grid, n.grid, n.grid)
tit <- "Green: best point found by optimizer"
filled.contour(x.grid,y.grid, z.grid, nlevels=50, color = rainbow,
plot.axes = {title(tit);points(model@X[,1],model@X[,2],pch=17,col="blue"); 
points(X.genoud[1],X.genoud[2],pch=17,col="green");
axis(1); axis(2)})

## End(Not run)