The objective is to produce maximin LHS. ESE is a powerful genetic algorithm allowing to produce space-filling designs.
maximinESE_LHS(design, T0=0.005*phiP(design,p=50), inner_it=100, J=50, it=1, p=50)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
power required in phiP criterion
the matrix of the final design (maximin 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
power required in phiP criterion
G. Damblin & B. Iooss
This function implements a stochastic algorithm (ESE) to produce optimized LHS. It is based on Jin et al works (2005).
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.
Latin Hypercube Sample (lhsDesign),
discrepancy criteria (discrepancyCriteria),
geometric criterion (mindist, phiP),
optimization (maximinSA_LHS, discrepESE_LHS, discrepSA_LHS)
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")
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