DiceDesign (version 1.8)

maximinESE_LHS: Enhanced Stochastic Evolutionnary (ESE) algorithm for Latin Hypercube Sample (LHS) optimization via phiP criteria

Description

The objective is to produce maximin LHS. ESE is a powerful genetic algorithm allowing to produce space-filling designs.

Usage

maximinESE_LHS(design, T0=0.005*phiP(design,p=50), inner_it=100, J=50, it=1, p=50)

Arguments

design

a matrix (or a data.frame) corresponding to the design of experiments.

T0

The initial temperature of the ESE algorithm

inner_it

The number of iterations for inner loop

J

The number of new proposed LHS inside the inner loop

it

The number of iterations for outer loop

p

power required in phiP criterion

Value

A list containing:

InitialDesign

the starting design

T0

the initial temperature of the ESE algorithm

inner_it

the number of iterations for inner loop

J

the number of new proposed LHS inside the inner loop

it

the number of iterations for outer loop

p

power required in phiP criterion

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

Details

This function implements a stochastic algorithm (ESE) to produce optimized LHS. It is based on Jin et al works (2005).

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 (mindist, phiP), optimization (maximinSA_LHS, discrepESE_LHS, discrepSA_LHS)

Examples

# NOT RUN {
dimension <- 2
n <- 10
X <- lhsDesign(n, dimension)$design
Xopt <- maximinESE_LHS(X, T0=0.005*phiP(X), inner_it=100, J=50, it=2)
plot(Xopt$design)
plot(Xopt$critValues, type="l")

# }