R: Enhanced Stochastic Evolutionnary (ESE) algorithm for Latin...

maximinESE_LHS {DiceDesign} | R Documentation

## Enhanced Stochastic Evolutionnary (ESE) algorithm for Latin Hypercube Sample (LHS) optimization via phiP criteria

### Description

The objective is to produce maximin LHS. ESE is a powerful genetic algorithm allowing to produce space-filling designs.

### Usage

    maximinESE_LHS(design, T0=0.005*phiP(design,p=50), inner_it=100, J=50, it=1, p=50)

### Arguments

`design` | a matrix (or a data.frame) corresponding to the design of experiments.
`T0` | The initial temperature of the ESE algorithm
`inner_it` | The number of iterations for inner loop
`J` | The number of new proposed LHS inside the inner loop
`it` | The number of iterations for outer loop
`p` | power required in phiP criterion

### Details

This function implements a stochastic algorithm (ESE) to produce optimized LHS. It is based on Jin et al works (2005).

### Value

A list containing:

`InitialDesign` | the starting design
`T0` | the initial temperature of the ESE algorithm
`inner_it` | the number of iterations for inner loop
`J` | the number of new proposed LHS inside the inner loop
`it` | the number of iterations for outer loop
`p` | power required in phiP criterion
`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 (`maximinSA_LHS`, `discrepESE_LHS`, `discrepSA_LHS`)

### Examples

    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")

[Package DiceDesign version 1.9 Index]