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R: Simulated annealing (SA) routine for Latin Hypercube Sample...

discrepSA_LHS

R Documentation

Simulated annealing (SA) routine for Latin Hypercube Sample (LHS) optimization via L2-discrepancy criteria

Description

The objective is to produce low-discrepancy LHS. SA is an efficient algorithm to produce space-filling designs. It has been adapted here to main discrepancy criteria.

Usage

discrepSA_LHS(design,T0=10,c=0.95,it=2000,criterion="C2",
profile="GEOM",Imax=100)

Arguments

`design`	a matrix (or a data.frame) corresponding to the design of experiments
`T0`	The initial temperature
`c`	A constant parameter regulating how the temperature goes down
`it`	The number of iterations
`criterion`	The criterion to be optimized. One can choose three different L2-discrepancies: the C2 (centered) discrepancy ("C2"), the L2-star discrepancy ("L2star") and the W2 (wrap-around) discrepancy ("W2")
`profile`	The temperature down-profile, purely geometric called "GEOM", geometrical according to the Morris algorithm called "GEOM_MORRIS" or purely linear called "LINEAR"
`Imax`	A parameter given only if you choose the Morris down-profile. It adjusts the number of iterations without improvement before a new elementary perturbation

Details

This function implements a classical routine to produce optimized LHS. It is based on the work of Morris and Mitchell (1995). They have proposed a SA version for LHS optimization according to mindist criterion. Here, it has been adapted to some discrepancy criteria taking in account new ideas about the reevaluations of a discrepancy value after a LHS elementary perturbation (in order to avoid computing all terms in the discrepancy formulas).

Value

A list containing:

`InitialDesign`	the starting design
`T0`	the initial temperature of the SA algorithm
`c`	the constant parameter regulating how the temperature goes down
`it`	the number of iterations
`criterion`	the criterion to be optimized
`profile`	the temperature down-profile
`Imax`	The parameter given in the Morris down-profile
`design`	the matrix of the final design (low-discrepancy LHS)
`critValues`	vector of criterion values along the iterations
`tempValues`	vector of temperature values along the iterations
`probaValues`	vector of acceptation probability values along the iterations

Author(s)

G.Damblin & B. Iooss

References

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. http://www.gdr-mascotnum.fr/doku.php?id=iooss1

M. Morris and J. Mitchell (1995) Exploratory designs for computationnal experiments. Journal of Statistical Planning and Inference, 43:381-402.

R. Jin, W. Chen and A. Sudjianto (2005) An efficient algorithm for constructing optimal design of computer experiments. Journal of Statistical Planning and Inference, 134:268-287.

Examples

dimension <- 2
n <- 10
X <- lhsDesign(n,dimension)$design
Xopt <- discrepSA_LHS(X,T0=10,c=0.99,it=2000,criterion="C2")
plot(Xopt$design)
plot(Xopt$critValues,type="l")
## Not run: 
  Xopt <- discrepSA_LHS(X,T0=10,c=0.99,it=1000,criterion="C2",profile="GEOM_MORRIS")

## End(Not run)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(DiceDesign)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/DiceDesign/discrepSA_LHS.Rd_%03d_medium.png", width=480, height=480)
> ### Name: discrepSA_LHS
> ### Title: Simulated annealing (SA) routine for Latin Hypercube Sample
> ###   (LHS) optimization via L2-discrepancy criteria
> ### Aliases: discrepSA_LHS
> ### Keywords: design
> 
> ### ** Examples
> 
> dimension <- 2
> n <- 10
> X <- lhsDesign(n,dimension)$design
> Xopt <- discrepSA_LHS(X,T0=10,c=0.99,it=2000,criterion="C2")
> plot(Xopt$design)
> plot(Xopt$critValues,type="l")
> ## Not run: 
> ##D   Xopt <- discrepSA_LHS(X,T0=10,c=0.99,it=1000,criterion="C2",profile="GEOM_MORRIS")
> ## End(Not run)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>