a matrix (or a data.frame) corresponding to the design of experiments
T0
The initial temperature of the SA algorithm
c
A constant parameter regulating how the temperature goes down
it
The number of iterations
p
power required in phiP criterion
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 the phiP criterion. It has been shown (Pronzato and Muller, 2012, Damblin et al., 2013) that optimizing phiP is more efficient to produce maximin designs than optimizing mindist. When p tends to infinity, optimizing a design with phi_p is equivalent to optimizing a design with mindist.
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
p
power required in phiP criterion
profile
the temperature down-profile
Imax
The parameter given in the Morris down-profile
design
the matrix of the final design (maximin 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.
Pronzato, L. and Muller, W. (2012). Design of computer experiments: space filling and beyond, Statistics and Computing, 22:681-701.
See Also
Latin Hypercube Sample(lhsDesign),discrepancy criteria(discrepancyCriteria), geometric criterion (mindistphiP), optimization (discrepSA_LHS,maximinESE_LHS ,discrepESE_LHS)
Examples
dimension <- 2
n <- 10
X <- lhsDesign(n,dimension)$design
Xopt <- maximinSA_LHS(X,T0=10,c=0.99,it=2000)
plot(Xopt$design)
plot(Xopt$critValues,type="l")
plot(Xopt$tempValues,type="l")
## Not run:
Xopt <- maximinSA_LHS(X,T0=10,c=0.99,it=1000,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/maximinSA_LHS.Rd_%03d_medium.png", width=480, height=480)
> ### Name: maximinSA_LHS
> ### Title: Simulated annealing (SA) routine for Latin Hypercube Sample
> ### (LHS) optimization via phiP criteria
> ### Aliases: maximinSA_LHS
> ### Keywords: design
>
> ### ** Examples
>
> dimension <- 2
> n <- 10
> X <- lhsDesign(n,dimension)$design
> Xopt <- maximinSA_LHS(X,T0=10,c=0.99,it=2000)
> plot(Xopt$design)
> plot(Xopt$critValues,type="l")
> plot(Xopt$tempValues,type="l")
> ## Not run:
> ##D Xopt <- maximinSA_LHS(X,T0=10,c=0.99,it=1000,profile="GEOM_MORRIS")
> ## End(Not run)
>
>
>
>
>
> dev.off()
null device
1
>