| discrepSA_LHS {DiceDesign} | R Documentation |
Simulated annealing (SA) routine for Latin Hypercube Sample (LHS) optimization via L2-discrepancy criteria
Description
The objective is to produce low-discrepancy LHS. SA is an efficient algorithm to produce space-filling designs. It has been adapted here to main discrepancy criteria.
Usage
discrepSA_LHS(design, T0=10, c=0.95, it=2000, criterion="C2", profile="GEOM", Imax=100)
Arguments
design |
a matrix (or a data.frame) corresponding to the design of experiments |
T0 |
The initial temperature |
c |
A constant parameter regulating how the temperature goes down |
it |
The number of iterations |
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") |
profile |
The temperature down-profile, purely geometric called "GEOM", geometrical according to the Morris algorithm called "GEOM_MORRIS" or purely linear called "LINEAR" |
Imax |
A parameter given only if you choose the Morris down-profile. It adjusts the number of iterations without improvement before a new elementary perturbation |
Details
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 some discrepancy criteria taking in account new ideas about the reevaluations of a 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 SA algorithm |
c |
the constant parameter regulating how the temperature goes down |
it |
the number of iterations |
criterion |
the criterion to be optimized |
profile |
the temperature down-profile |
Imax |
The parameter given in the Morris down-profile |
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.
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.
See Also
Latin Hypercube Sample(lhsDesign),discrepancy criteria(discrepancyCriteria), geometric criterion (mindistphiP), optimization (maximinSA_LHS,maximinESE_LHS ,discrepESE_LHS)
Examples
dimension <- 2
n <- 10
X <- lhsDesign(n, dimension)$design
## Optimize the LHS with C2 criterion
Xopt <- discrepSA_LHS(X, T0=10, c=0.99, it=2000, criterion="C2")
plot(Xopt$design)
plot(Xopt$critValues, type="l")
## Optimize the LHS with C2 criterion and GEOM_MORRIS profile
## Not run:
Xopt2 <- discrepSA_LHS(X, T0=10, c=0.99, it=1000, criterion="C2", profile="GEOM_MORRIS")
plot(Xopt2$design)
## End(Not run)