R: Simulated annealing (SA) routine for Latin Hypercube Sample...

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 (`mindist` `phiP`), 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)

[Package DiceDesign version 1.9 Index]