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.
discrepESE_LHS(design, T0=0.005*discrepancyCriteria(design,type='C2')[[1]],
inner_it=100, J=50, it=2, criterion="C2")A list containing:
the starting design
the initial temperature of the ESE algorithm
the number of iterations for inner loop
the number of new proposed LHS inside the inner loop
the number of iterations for outer loop
the criterion to be optimized
the matrix of the final design (low-discrepancy LHS)
vector of criterion values along the iterations
vector of temperature values along the iterations
vector of acceptation probability values along the iterations
a matrix (or a data.frame) corresponding to the design of experiments.
The initial temperature of the ESE algorithm
The number of iterations for inner loop
The number of new proposed LHS inside the inner loop
The number of iterations for outer loop
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")
G.Damblin & B. Iooss
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).
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.
Latin Hypercube Sample(lhsDesign),
discrepancy criteria(discrepancyCriteria),
geometric criterion (mindistphiP),
optimization (maximinSA_LHS, maximinESE_LHS, discrepSA_LHS)
if (FALSE) {
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")
}
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