R: Designs of Computer Experiments

DiceDesign-package {DiceDesign} | R Documentation

## Designs of Computer Experiments

### Description

Space-Filling Designs (SFD) and space-filling criteria (distance-based and uniformity-based).

### Details

This package provides tools to create some specific Space-Filling Design (SFD) and to test their quality:

- Latin Hypercube designs (randomized or centered)

- Strauss SFD and Maximum entropy SFD, WSP designs

- Optimal (low-discrepancy and maximin) Latin Hypercube desigsn by simulated annealing and genetic algorithms,

- Orthogonal and Nearly Orthogonal Latin Hypercube designs,

- Discrepancies criteria, distance measures,

- Minimal spanning tree criteria,

- Radial scanning statistic

### Note

Part of this work was conducted on 2006-2009 within the frame of the DICE (Deep Inside Computer Experiments) Consortium between ARMINES, Renault, EDF, IRSN, ONERA and TOTAL S.A. (http://dice.emse.fr/).

In this package, only Faure's sequence is implemented. Note that the randtoolbox package provides the following quasi random sequences: the Sobol sequence, the Halton (hence Van Der Corput) sequence and the Torus sequence (also known as Kronecker sequence). Note also that the lhs package provides other types of algorithms to compute optimized LHS.

### Author(s)

J. Franco, D. Dupuy, O. Roustant, P. Kiener, G. Damblin and B. Iooss. Thanks to A. Jourdan for discussions about OA131.

Maintainer: Celine Helbert Celine.Helbert@ec-lyon.fr

### References

Cioppa T.M., Lucas T.W. (2007). Efficient nearly orthogonal and space-filling Latin hypercubes. Technometrics 49, 45-55.

Damblin G., Couplet M., and Iooss B. (2013). Numerical studies of space filling designs: optimization of Latin Hypercube Samples and subprojection properties, Journal of Simulation, 7:276-289, 2013.

De Rainville F.-M., Gagne C., Teytaud O., Laurendeau D. (2012). Evolutionary optimization of low-discrepancy sequences. ACM Transactions on Modeling and Computer Simulation (TOMACS), 22(2), 9.

Dupuy D., Helbert C., Franco J. (2015), DiceDesign and DiceEval: Two R-Packages for Design and Analysis of Computer Experiments, Journal of Statistical Software, 65(11), 1–38.

Fang K.-T., Li R. and Sudjianto A. (2006) Design and Modeling for Computer Experiments, Chapman & Hall.

Fang K-T., Liu M-Q., Qin H. and Zhou Y-D. (2018) Theory and application of uniform experimental designs. Springer.

Nguyen N.K. (2008) A new class of orthogonal Latinhypercubes, Statistics and Applications, Volume 6, issues 1 and 2, pp.119-123.

Owen A.B. (2020), On dropping the first Sobol point, https://arxiv.org/abs/2008.08051.

Roustant O., Franco J., Carraro L., Jourdan A. (2010), A radial scanning statistic for selecting space-filling designs in computer experiments, MODA-9 proceedings.

Santner T.J., Williams B.J. and Notz W.I. (2003) The Design and Analysis of Computer Experiments, Springer, 121-161.

### Examples

    # **********************
    # Designs of experiments
    # **********************

    # A maximum entropy design with 20 points in [0,1]^2
    p <- dmaxDesign(20,2,0.9,200)
    plot(p$design,xlim=c(0,1),ylim=c(0,1))

    # Change the dimnames, adjust to range (-10, 10) and round to 2 digits
    xDRDN(p, letter = "T", dgts = 2, range = c(-10, 10))

    # ************************
    # Criteria: L2-discrepancy
    # ************************
    dp <- discrepancyCriteria(p$design,type=c('L2','C2'))
    # Coverage measure
    covp <- coverage(p$design)

    # *******************************
    # Criteria: Minimal Spanning Tree
    # *******************************
    mstCriteria(p$design,plot2d=TRUE)

    # ****************************************************************
    # Radial scanning statistic: Detection of defects of Sobol designs
    # ****************************************************************

    # requires randtoolbox package
    library(randtoolbox)

    # in 2D
    rss <- rss2d(design=sobol(n=20, dim=2), lower=c(0,0), upper=c(1,1),
    	type="l", col="red")

    # in 8D. All pairs of dimensions are tried to detect the worst defect
    # (according to the specified goodness-of-fit statistic).
    d <- 8
    n <- 10*d
    rss <- rss2d(design=sobol(n=n, dim=d), lower=rep(0,d), upper=rep(1,d),
    	type="l", col="red")

    # avoid this defect with scrambling ?
    #    1. Faure-Tezuka scrambling (type "?sobol" for more details and options)
    rss <- rss2d(design=sobol(n=n, dim=d, scrambling=2), lower=rep(0,d),
    	upper=rep(1,d), type="l", col="red")
    #    2. Owen scrambling
    rss <- rss2d(design=sobol(n=n, dim=d, scrambling=1), lower=rep(0,d),
    	upper=rep(1,d), type="l", col="red")

[Package DiceDesign version 1.9 Index]