The objective is to produce maximin LHS. SA is an efficient algorithm to produce space-filling designs.
maximinSA_LHS(design, T0=10, c=0.95, it=2000, p=50, profile="GEOM", Imax=100)A list containing:
the starting design
the initial temperature of the SA algorithm
the constant parameter regulating how the temperature goes down
the number of iterations
power required in phiP criterion
the temperature down-profile
The parameter given in the Morris down-profile
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 SA algorithm
A constant parameter regulating how the temperature goes down
The number of iterations
power required in phiP criterion
The temperature down-profile, purely geometric called "GEOM", geometrical according to the Morris algorithm called "GEOM_MORRIS" or purely linear called "LINEAR"
A parameter given only if you choose the Morris down-profile. It adjusts the number of iterations without improvement before a new elementary perturbation
G. Damblin & B. Iooss
This function implements a classical routine to produce optimized LHS. It is based on the work of Morris and Mitchell (1995). They have proposed a SA version for LHS optimization according to mindist criterion. Here, it has been adapted to the phiP criterion. It has been shown (Pronzato and Muller, 2012, Damblin et al., 2013) that optimizing phiP is more efficient to produce maximin designs than optimizing mindist. When \(p\) tends to infinity, optimizing a design with phi_p is equivalent to optimizing a design with mindist.
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 (discrepSA_LHS, maximinESE_LHS, discrepESE_LHS)
dimension <- 2
n <- 10
X <- lhsDesign(n ,dimension)$design
Xopt <- maximinSA_LHS(X, T0=10, c=0.99, it=2000)
plot(Xopt$design)
plot(Xopt$critValues, type="l")
plot(Xopt$tempValues, type="l")
if (FALSE) {
Xopt <- maximinSA_LHS(X, T0=10, c=0.99, it=1000, profile="GEOM_MORRIS")
}
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