GA {LHD}

Genetic Algorithm for LHD

Description

GA returns a n by k LHD matrix generated by genetic algorithm (GA)

Usage

GA(
  n,
  k,
  m = 10,
  N = 10,
  pmut = 1/(k - 1),
  OC = "phi_p",
  p = 15,
  q = 1,
  maxtime = 5
)

Arguments

n

A positive integer, which stands for the number of rows (or run size).

k

A positive integer, which stands for the number of columns (or factor size).

m

A positive even integer, which stands for the population size and it must be an even number. The default is set to be 10. A large value of m will result a high CPU time, and it is recommended to be no greater than 100.

N

A positive integer, which stands for the number of iterations. The default is set to be 10. A large value of N will result a high CPU time, and it is recommended to be no greater than 500.

pmut

A probability, which stands for the probability of mutation. The default is set to be 1/(k - 1).

OC

An optimality criterion. The default setting is "phi_p", and it could be one of the following: "phi_p", "AvgAbsCor", "MaxAbsCor", "MaxProCriterion".

p

A positive integer, which is the parameter in the phi_p formula, and p is prefered to be large. The default is set to be 15.

q

The default is set to be 1, and it could be either 1 or 2. If q is 1, dij is the Manhattan (rectangular) distance. If q is 2, dij is the Euclidean distance.

maxtime

A positive number, which indicates the expected maximum CPU time given by user, and it is measured by minutes. For example, maxtime=3.5 indicates the CPU time will be no greater than three and half minutes. The default is set to be 5.

Value

If all inputs are logical, then the output will be a n by k LHD.

References

Liefvendahl, M., and Stocki, R. (2006) A study on algorithms for optimization of Latin hypercubes. Journal of Statistical Planning and Inference, 136, 3231-3247.

Examples

#generate a 5 by 3 maximin distance LHD with the default setting
try=GA(n=5,k=3)
try
phi_p(try)   #calculate the phi_p of "try".

#Another example
#generate a 8 by 4 nearly orthogonal LHD
try2=GA(n=8,k=4,OC="AvgAbsCor")
try2
AvgAbsCor(try2)  #calculate the average absolute correlation.