R: Enhanced Stochastic Evolutionnary (ESE) algorithm for Latin...
discrepESE_LHS
R Documentation
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.
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.
http://www.gdr-mascotnum.fr/doku.php?id=iooss1
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)