| max_qEI {DiceOptim} | R Documentation |
Maximization of multipoint expected improvement criterion (qEI)
Description
Maximization of the qEI criterion. Two options are available
: Constant Liar (CL), and brute force qEI maximization with
Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, or GENetic Optimization
Using Derivative (genoud) algorithm.
Usage
max_qEI(
model,
npoints,
lower,
upper,
crit = "exact",
minimization = TRUE,
optimcontrol = NULL
)
Arguments
model |
an object of class |
npoints |
an integer representing the desired number of iterations, |
lower |
vector of lower bounds, |
upper |
vector of upper bounds, |
crit |
"exact", "CL" : a string specifying the criterion used. "exact"
triggers the maximization of the multipoint expected improvement at each
iteration (see |
minimization |
logical specifying if the qEI to be maximized is used in minimiziation or in maximization, |
optimcontrol |
an optional list of control parameters for optimization. See details. |
Details
- CL is a heuristic method. First, the regular Expected Improvement EI is
maximized (max_EI). Then, for the next points, the Expected
Improvement is maximized again, but with an artificially updated Kriging
model. Since the response values corresponding to the last best point
obtained are not available, the idea of CL is to replace them by an
arbitrary constant value L (a "lie") set by the user (default is the
minimum of all currently available observations).
- The BFGS algorithm is implemented in the standard function
optim. Analytical formulae of qEI and its
gradient qEI.grad are used. The nStarts starting
points are by default sampled with respect to the regular EI
(sampleFromEI) criterion.
- The "genoud" method calls the function genoud using
analytical formulae of qEI and its gradient
qEI.grad.
The parameters of list optimcontrol are :
- optimcontrol$method : "BFGS" (default), "genoud" ; a string
specifying the method used to maximize the criterion (irrelevant when
crit is "CL" because this method always uses genoud),
- when crit="CL" :
+ optimcontrol$parinit : optional matrix of initial values (must
have model@d columns, the number of rows is not constrained),
+ optimcontrol$L : "max", "min", "mean" or a scalar value specifying
the liar ; "min" takes model@min, "max" takes model@max,
"mean" takes the prediction of the model ; When L is NULL, "min" is
taken if minimization==TRUE, else it is "max".
+ The parameters of function genoud. Main parameters are :
"pop.size" (default : [N=3*2^model@d for dim<6 and N=32*model@d
otherwise]), "max.generations" (default : 12),
"wait.generations" (default : 2) and "BFGSburnin" (default :
2).
- when optimcontrol$method = "BFGS" :
+ optimcontrol$nStarts (default : 4),
+ optimcontrol$fastCompute : if TRUE (default), a fast approximation
method based on a semi-analytic formula is used, see [Marmin 2014] for
details,
+ optimcontrol$samplingFun : a function which sample a batch of
starting point (default : sampleFromEI),
+ optimcontrol$parinit : optional 3d-array of initial (or candidate)
batches (for all k, parinit[,,k] is a matrix of size
npoints*model@d representing one batch). The number of initial
batches (length(parinit[1,1,])) is not contrained and does not have to be
equal to nStarts. If there is too few initial batches for
nStarts, missing batches are drawn with samplingFun (default
: NULL),
- when optimcontrol$method = "genoud" :
+ optimcontrol$fastCompute : if TRUE (default), a fast approximation
method based on a semi-analytic formula is used, see [Marmin 2014] for
details,
+ optimcontrol$parinit : optional matrix of candidate starting
points (one row corresponds to one point),
+ The parameters of the genoud function. Main parameters are
"pop.size" (default : [50*(model@d)*(npoints)]),
"max.generations" (default : 5), "wait.generations" (default
: 2), "BFGSburnin" (default : 2).
Value
A list with components:
par |
A matrix containing the |
value |
A value giving the qEI computed in |
Author(s)
Sebastien Marmin
Clement Chevalier
David Ginsbourger
References
C. Chevalier and D. Ginsbourger (2014) Learning and Intelligent Optimization - 7th International Conference, Lion 7, Catania, Italy, January 7-11, 2013, Revised Selected Papers, chapter Fast computation of the multipoint Expected Improvement with applications in batch selection, pages 59-69, Springer.
D. Ginsbourger, R. Le Riche, L. Carraro (2007), A Multipoint Criterion for Deterministic Parallel Global Optimization based on Kriging. The International Conference on Non Convex Programming, 2007.
D. Ginsbourger, R. Le Riche, and L. Carraro. Kriging is well-suited to parallelize optimization (2010), In Lim Meng Hiot, Yew Soon Ong, Yoel Tenne, and Chi-Keong Goh, editors, Computational Intelligence in Expensive Optimization Problems, Adaptation Learning and Optimization, pages 131-162. Springer Berlin Heidelberg.
J. Mockus (1988), Bayesian Approach to Global Optimization. Kluwer academic publishers.
M. Schonlau (1997), Computer experiments and global optimization, Ph.D. thesis, University of Waterloo.
See Also
Examples
set.seed(000)
# 3-points EI maximization.
# 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"
lower <- c(0,0)
upper <- c(1,1)
# number of point in the bacth
batchSize <- 3
# 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))
# maximization of qEI
# With a multistarted BFGS algorithm
maxBFGS <- max_qEI(model = fitted.model, npoints = batchSize, lower = lower, upper = upper,
crit = "exact",optimcontrol=list(nStarts=3,method = "BFGS"))
# comparison
print(maxBFGS$value)
## Not run:
# With a genetic algorithme using derivatives
maxGen <- max_qEI(model = fitted.model, npoints = batchSize, lower = lower, upper = upper,
crit = "exact", optimcontrol=list(nStarts=3,method = "genoud",pop.size=100,max.generations = 15))
# With the constant liar heuristic
maxCL <- max_qEI(model = fitted.model, npoints = batchSize, lower = lower, upper = upper,
crit = "CL",optimcontrol=list(pop.size=20))
print(maxGen$value)
print(maxCL$value)
## End(Not run)