Modification of the function
integration_design from the package
be usable for SUR-based optimization. Handles two or three objectives.
Available important sampling schemes: none so far.
1 2 3 4 5 6 7 8
Optional list specifying the procedure to build the integration points and weights. Many options are possible; see 'Details'.
The dimension of the input set. If not provided
Vector containing the lower bounds of the design space.
Vector containing the upper bounds of the design space.
A list of kriging models of
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
SURcontrol argument is a list with possible entries
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
p * d matrix) for prespecified integration points.
In this case these integration points and the corresponding vector
integration.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 points
100*d) and a specific
distrib. Possible values for distrib are: "
MC" and "
C.1) The choice "
sobol" corresponds to integration points chosen with the Sobol sequence in dimension
d (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
n.candidates points (default:
n.points*10) which are distributed according to a distribution
sobol"). Possible values for
init.distrib are the space filling distributions "
sobol" and "
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 field
init.distrib.spec to specify
n.candidates * d matrix of points in dimension
A list with components:
p x d matrix of p points used for the numerical calculation of integrals
integration.weights a vector of size
p corresponding to the weight of each point. If all the points are equally
integration.weights is set to
V. Picheny (2014), Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction, Statistics and Computing.
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