DiceDesign (version 1.8)

discrepSA_LHS: 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

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

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).

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.

See Also

Latin Hypercube Sample(lhsDesign),discrepancy criteria(discrepancyCriteria), geometric criterion (mindistphiP), optimization (maximinSA_LHS,maximinESE_LHS ,discrepESE_LHS)

Examples

# NOT RUN {
dimension <- 2
n <- 10
X <- lhsDesign(n, dimension)$design

## Optimize the LHS with C2 criterion
Xopt <- discrepSA_LHS(X, T0=10, c=0.99, it=2000, criterion="C2")
plot(Xopt$design)
plot(Xopt$critValues, type="l")

## Optimize the LHS with C2 criterion and GEOM_MORRIS profile
# }
# NOT RUN {
Xopt2 <- discrepSA_LHS(X, T0=10, c=0.99, it=1000, criterion="C2", profile="GEOM_MORRIS")
plot(Xopt2$design)
# }