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.

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]