TREGO.nsteps {DiceOptim}

Trust-region based EGO algorithm.

Description

Executes nsteps iterations of the TREGO method to an object of class km. At each step, a kriging model is re-estimated (including covariance parameters re-estimation) based on the initial design points plus the points visited during all previous iterations; then a new point is obtained by maximizing the Expected Improvement criterion (EI) over either the entire search space or restricted to a trust region. The trust region is updated at each iteration based on a sufficient decrease condition.

Usage

TREGO.nsteps(
  model,
  fun,
  nsteps,
  lower,
  upper,
  control = NULL,
  kmcontrol = NULL,
  trcontrol = NULL,
  trace = 0,
  n.cores = 1,
  ...
)

Arguments

model

an object of class km,

fun

the objective function to be minimized,

nsteps

an integer representing the desired number of iterations,

lower, upper

vector of lower and upper bounds for the variables to be optimized over,

control

an optional list of control parameters for optimization. For now only the number of restarts can be set.

kmcontrol

an optional list representing the control variables for the re-estimation of the kriging model.

trcontrol

an optional list of control parameters for the trust-region scheme: sigma the initial size of the trust region, x0 its initial center, beta the contraction factor, alpha its dilatation factor, kappa the forcing factor, crit the criterion used inside the TR (either "EI" or "gpmean"), GLratio number of consecutive global and local steps, algo either "TREGO" or "TRIKE", minsigma minimal sigma value, maxsigma maximal sigma value, minEI stopping criterion for TRIKE, local.model Boolean; if TRUE, a local model is used within the trust region, local.trend, local.covtype trend and covariance for the local model, n.local.min minimal number of points used to build the local model,

trace

between -1 (no trace) and 3 (full messages)

n.cores

number of cores used for EI maximisation

...

additional parameters to be given to fun

Value

A list with components:

par

a data frame representing the additional points visited during the algorithm,

value

a data frame representing the response values at the points given in par,

npoints

an integer representing the number of parallel computations (=1 here),

nsteps

an integer representing the desired number of iterations (given in argument),

lastmodel

an object of class km corresponding to the last kriging model fitted. If warping is true, y values are normalized (warped) and will not match value.

all.success

a vector of Boolean indicating the successful steps according to the sufficient decrease condtion

all.steps

a vector of Boolean indicating which steps were global

all.sigma

history of trust region size

all.x0

history of trust region centers

local.model

if trcontrol$local.model=TRUE, the latest local model

Author(s)

Victor Picheny

References

Diouane, Picheny, Le Riche, Scotto Di Perrotolo (2021), TREGO: a Trust-Region Framework for Efficient Global Optimization, ArXiv

See Also

EI, max_crit, EI.grad

Examples

set.seed(123)
###############################################################
### 	10 ITERATIONS OF TREGO ON THE BRANIN FUNCTION, 	 ####
###	 STARTING FROM A 9-POINTS FACTORIAL DESIGN         ####
###############################################################

# a 9-points factorial design, and the corresponding response
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) 
names(response.branin) <- "y" 

# model identification
fitted.model1 <- km(~1, design=design.fact, response=response.branin, 
covtype="gauss", control=list(pop.size=50,trace=FALSE), parinit=c(0.5, 0.5))

# TREGO n steps
nsteps <- 5
lower <- rep(0, d) 
upper <- rep(1, d)     
oEGO <- TREGO.nsteps(model=fitted.model1, fun=branin, nsteps=nsteps, 
lower=lower, upper=upper)
print(oEGO$par)
print(oEGO$value)

# graphics
n.grid <- 15 # Was 20, reduced to 15 for speeding up compilation
x.grid <- y.grid <- seq(0,1,length=n.grid)
design.grid <- expand.grid(x.grid, y.grid)
response.grid <- apply(design.grid, 1, branin)
z.grid <- matrix(response.grid, n.grid, n.grid)
contour(x.grid, y.grid, z.grid, 40)
title("Branin function")
points(design.fact[,1], design.fact[,2], pch=17, col="blue")
points(oEGO$par, pch=19, col="red")
text(oEGO$par[,1], oEGO$par[,2], labels=1:nsteps, pos=3)