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

maximinSA_LHS {DiceDesign} | R Documentation

## Simulated annealing (SA) routine for Latin Hypercube Sample (LHS) optimization via phiP criteria

### Description

The objective is to produce maximin LHS. SA is an efficient algorithm to produce space-filling designs.

### Usage

    maximinSA_LHS(design, T0=10, c=0.95, it=2000, p=50, profile="GEOM", Imax=100)

### Arguments

`design` | a matrix (or a data.frame) corresponding to the design of experiments
`T0` | The initial temperature of the SA algorithm
`c` | A constant parameter regulating how the temperature goes down
`it` | The number of iterations
`p` | power required in phiP criterion
`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 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`.

### 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
`p` | power required in phiP criterion
`profile` | the temperature down-profile
`Imax` | The parameter given in the Morris down-profile
`design` | the matrix of the final design (maximin 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.

Pronzato, L. and Muller, W. (2012). Design of computer experiments: space filling and beyond, Statistics and Computing, 22:681-701.

### See Also

Latin Hypercube Sample (`lhsDesign`), discrepancy criteria (`discrepancyCriteria`), geometric criterion (`mindist`, `phiP`), optimization (`discrepSA_LHS`, `maximinESE_LHS`, `discrepESE_LHS`)

### Examples

    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")

    ## Not run:
      Xopt <- maximinSA_LHS(X, T0=10, c=0.99, it=1000, profile="GEOM_MORRIS")

    ## End(Not run)

[Package DiceDesign version 1.9 Index]