lhs (version 0.16)

geneticLHS: Latin Hypercube Sampling with a Genetic Algorithm

Description

Draws a Latin Hypercube Sample from a set of uniform distributions for use in creating a Latin Hypercube Design. This function attempts to optimize the sample with respect to the S optimality criterion through a genetic type algorithm.

Usage

geneticLHS(n=10, k=2, pop=100, gen=4, pMut=.1, criterium="S", verbose=FALSE)

Arguments

n

The number of partitions (simulations or design points)

k

The number of replications (variables)

pop

The number of designs in the initial population

gen

The number of generations over which the algorithm is applied

pMut

The probability with which a mutation occurs in a column of the progeny

criterium

The optimality criterium of the algorithm. Default is S. Maximin is also supported

verbose

Print informational messages. Default is FALSE

Value

An n by k Latin Hypercube Sample matrix with values uniformly distributed on [0,1]

Details

Latin hypercube sampling (LHS) was developed to generate a distribution of collections of parameter values from a multidimensional distribution. A square grid containing possible sample points is a Latin square iff there is only one sample in each row and each column. A Latin hypercube is the generalisation of this concept to an arbitrary number of dimensions. When sampling a function of k variables, the range of each variable is divided into n equally probable intervals. n sample points are then drawn such that a Latin Hypercube is created. Latin Hypercube sampling generates more efficient estimates of desired parameters than simple Monte Carlo sampling.

This program generates a Latin Hypercube Sample by creating random permutations of the first n integers in each of k columns and then transforming those integers into n sections of a standard uniform distribution. Random values are then sampled from within each of the n sections. Once the sample is generated, the uniform sample from a column can be transformed to any distribution by using the quantile functions, e.g. qnorm(). Different columns can have different distributions.

S-optimality seeks to maximize the mean distance from each design point to all the other points in the design, so the points are as spread out as possible.

Genetic Algorithm:

1. Generate pop random latin hypercube designs of size n by k

2. Calculate the S optimality measure of each design

3. Keep the best design in the first position and throw away half of the rest of the population

4. Take a random column out of the best matrix and place it in a random column of each of the other matricies, and take a random column out of each of the other matricies and put it in copies of the best matrix thereby causing the progeny

5. For each of the progeny, cause a genetic mutation pMut percent of the time. The mutation is accomplished by swtching two elements in a column

References

Stocki, R. (2005) A method to improve design reliability using optimal Latin hypercube sampling Computer Assisted Mechanics and Engineering Sciences 12, 87--105.

Stein, M. (1987) Large Sample Properties of Simulations Using Latin Hypercube Sampling. Technometrics. 29, 143--151.

See Also

randomLHS, improvedLHS, maximinLHS, and optimumLHS to generate Latin Hypercube Samples. optAugmentLHS, optSeededLHS, and augmentLHS to modify and augment existing designs.

Examples

# NOT RUN {
  geneticLHS(4, 3, 50, 5, .25)
# }