integration_design_optim {GPareto} | R Documentation |
Function to build integration points (for the SUR criterion)
Description
Modification of the function integration_design
from the package KrigInv-package
to
be usable for SUR-based optimization. Handles two or three objectives.
Available important sampling schemes: none so far.
Usage
integration_design_optim(
SURcontrol = NULL,
d = NULL,
lower,
upper,
model = NULL,
min.prob = 0.001
)
Arguments
SURcontrol |
Optional list specifying the procedure to build the integration points and weights. Many options are possible; see 'Details'. |
d |
The dimension of the input set. If not provided |
lower |
Vector containing the lower bounds of the design space. |
upper |
Vector containing the upper bounds of the design space. |
model |
A list of kriging models of |
min.prob |
This argument applies only when importance sampling distributions are chosen.
For numerical reasons we give a minimum probability for a point to
belong to the importance sample. This avoids probabilities equal to zero and importance sampling
weights equal to infinity. In an importance sample of |
Details
The SURcontrol
argument is a list with possible entries integration.points
, integration.weights
, n.points
,
n.candidates
, distrib
, init.distrib
and init.distrib.spec
. It can be used
in one of the three following ways:
A) If nothing is specified,
100 * d
points are chosen using the Sobol sequence;B) One can directly set the field
integration.points
(p * d
matrix) for prespecified integration points. In this case these integration points and the corresponding vectorintegration.weights
will be used for all the iterations of the algorithm;C) If the field
integration.points
is not set then the integration points are renewed at each iteration. In that case one can control the number of integration pointsn.points
(default:100*d
) and a specific distributiondistrib
. Possible values for distrib are: "sobol
", "MC
" and "SUR
" (default: "sobol
"):C.1) The choice "
sobol
" corresponds to integration points chosen with the Sobol sequence in dimensiond
(uniform weight);C.2) The choice "
MC
" corresponds to points chosen randomly, uniformly on the domain;C.3) The choice "
SUR
" corresponds to importance sampling distributions (unequal weights).
When important sampling procedures are chosen,n.points
points are chosen using importance sampling among a discrete set ofn.candidates
points (default:n.points*10
) which are distributed according to a distributioninit.distrib
(default: "sobol
"). Possible values forinit.distrib
are the space filling distributions "sobol
" and "MC
" or an user defined distribution "spec
". The "sobol
" and "MC
" choices correspond to quasi random and random points in the domain. If the "spec
" value is chosen the user must fill in manually the fieldinit.distrib.spec
to specify himself an.candidates * d
matrix of points in dimensiond
.
Value
A list with components:
-
integration.points
,p x d
matrix of p points used for the numerical calculation of integrals, -
integration.weights
, a vector of sizep
corresponding to the weight of each point. If all the points are equally weighted,integration.weights
is set toNULL
.
References
V. Picheny (2014), Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction, Statistics and Computing.
See Also
GParetoptim
crit_SUR
integration_design