LHD (version 1.4.1)

LaPSO: Particle Swarm Optimization for LHD

Description

LaPSO returns a n by k LHD matrix generated by particle swarm optimization algorithm (PSO)

Usage

LaPSO(
  n,
  k,
  m = 10,
  N = 10,
  SameNumP = 0,
  SameNumG = n/4,
  p0 = 1/(k - 1),
  OC = "phi_p",
  p = 15,
  q = 1,
  maxtime = 5
)

Value

If all inputs are logical, then the output will be a n by k LHD. Here are some general suggestions about the parameters:

• SameNumP is approximately n/2 when SameNumG is 0.

• SameNumG is approximately n/4 when SameNumP is 0.

• p0 * (k - 1) = 1 to 2 is often sufficient. So p0 = 1/(k - 1) to 2/(k - 1).

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 integer, which stands for the number of particles. 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.

SameNumP

A non-negative integer, which stands for how many elements in current column of current particle LHD should be the same as corresponding Personal Best. SameNumP=0, 1, 2, ..., n, and 0 means to skip the "exchange". The default is set to be 0.

SameNumG

A non-negative integer, which stands for how many elements in current column of current particle LHD should be the same as corresponding Global Best. SameNumP=0, 1, 2, ..., n, and 0 means to skip the "exchange". The default is set to be n/4. SameNumP and SameNumG cannot be 0 at the same time.

p0

A probability of exchanging two randomly selected elements in current column of current particle LHD. 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.

References

Chen, R.-B., Hsieh, D.-N., Hung, Y., and Wang, W. (2013) Optimizing Latin hypercube designs by particle swarm. Stat. Comput., 23, 663-676.

Examples

#generate a 5 by 3 maximin distance LHD with the default setting
try=LaPSO(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=LaPSO(n=8,k=4,OC="AvgAbsCor")
try2
AvgAbsCor(try2)  #calculate the average absolute correlation.