maximinSA_LHS {DiceDesign}

Simulated annealing (SA) routine for Latin Hypercube Sample (LHS) optimization via phiP criteria

Description

The objective is to produce maximin LHS. SA is an efficient algorithm to produce space-filling designs.

Usage

maximinSA_LHS(design, T0=10, c=0.95, it=2000, p=50, profile="GEOM", Imax=100)

Arguments

design

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.

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 (mindist, phiP), 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)