R: Generic function to build integration points (for the SUR...

integration_design_cst {DiceOptim}

R Documentation

Generic function to build integration points (for the SUR criterion)

Description

Modification of the function integration_design from the package KrigInv to be usable for SUR-based optimization with constraints.

Usage

integration_design_cst(
  integcontrol = NULL,
  lower,
  upper,
  model.fun = NULL,
  model.constraint = NULL,
  equality = FALSE,
  critcontrol = NULL,
  min.prob = 0.001
)

Arguments

`integcontrol`	Optional list specifying the procedure to build the integration points and weights. Many options are possible. A) If nothing is specified, 100d 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 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 `n.points` (default: 100d) and a specific distribution `distrib`. 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 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 set of `n.candidates` points (default: `n.points`10) which are distributed according to a distribution `init.distrib` (default: "`sobol`"). Possible values for `init.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 field `init.distrib.spec` to specify himself a n.candidates * d matrix of points in dimension d.
`lower`	Vector containing the lower bounds of the design space.
`upper`	Vector containing the upper bounds of the design space.
`model.fun`	object of class `km` corresponding to the objective functions, or, if the objective function is fast-to-evaluate, a `fastfun` object,
`model.constraint`	either one or a list of objects of class `km`, one for each constraint function,
`equality`	either `FALSE` if all constraints are for inequalities, else a vector of boolean indicating which are equalities
`critcontrol`	optional list of parameters (see `crit_SUR_cst`); here only the component `tolConstraints` is used.
`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 M points, the maximum weight becomes `1/min.prob * 1/M`.

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 size p corresponding to the weight of each point. If all the points are equally weighted, integration.weights is set to NULL

Author(s)

Victor Picheny

Mickael Binois

References

Chevalier C., Picheny V., Ginsbourger D. (2012), The KrigInv package: An efficient and user-friendly R implementation of Kriging-based inversion algorithms, Computational Statistics and Data Analysis, 71, 1021-1034.

Chevalier C., Bect J., Ginsbourger D., Vazquez E., Picheny V., Richet Y. (2011), Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set, Technometrics, 56(4), 455-465.

V. Picheny (2014), A stepwise uncertainty reduction approach to constrained global optimization, Proceedings of the 17th International Conference on Artificial Intelligence and Statistics, JMLR W&CP 33, 787-795.