discrepESE_LHS {DiceDesign}

Enhanced Stochastic Evolutionnary (ESE) algorithm for Latin Hypercube Sample (LHS) optimization via L2-discrepancy criteria

Description

The objective is to produce low-discrepancy LHS. ESE is a powerful genetic algorithm to produce space-filling designs. It has been adapted here to main discrepancy criteria.

Usage

discrepESE_LHS(design, T0=0.005*discrepancyCriteria(design,type='C2')[[1]], 
inner_it=100, J=50, it=2, criterion="C2")

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

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")

Details

This function implements a stochastic algorithm (ESE) to produce optimized LHS. It is based on Jin et al works (2005). Here, it has been adapted to some discrepancy criteria taking into account new ideas about the revaluations of 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 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

criterion

the criterion to be optimized

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.

M. Morris and J. Mitchell (1995) Exploratory designs for computational 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, discrepSA_LHS)

Examples

## Not run: 
dimension <- 2
n <- 10
X <- lhsDesign(n, dimension)$design
Xopt <- discrepESE_LHS(X, T0=0.005*discrepancyCriteria(X, type='C2')[[1]], 
                       inner_it=100, J=50, it=2)
plot(Xopt$design)
plot(Xopt$critValues, type="l")

## End(Not run)