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.
The number of partitions (simulations or design points)
The number of replications (variables)
The number of designs in the initial population
The number of generations over which the algorithm is applied
The probability with which a mutation occurs in a column of the progeny
The optimality criterium of the algorithm. Default is
Print informational messages. Default is
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
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
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.
pop random latin hypercube designs of size
Calculate the S optimality measure of each design
Keep the best design in the first position and throw away half of the rest of the population
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
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
k Latin Hypercube Sample matrix with values uniformly distributed on [0,1]
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.
geneticLHS(4, 3, 50, 5, .25)