| maximinESE_LHS {DiceDesign} | R Documentation |
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 |
Details
This function implements a stochastic algorithm (ESE) to produce optimized LHS. It is based on Jin et al works (2005).
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 |
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 (maximinSA_LHS, discrepESE_LHS, discrepSA_LHS)
Examples
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")