LaPSO

0th

Percentile

Particle Swarm Optimization for LHD

LaPSO returns a maximin distance LHD constructed by particle swarm optimization algorithm (PSO)

Usage
LaPSO(n, k, m, N, SameNumP, SameNumG, p0, p = 50, q = 1)
Arguments
n

A positive integer.

k

A positive integer.

m

A positive integer.

N

A positive integer.

SameNumP

A non-negative integer.

SameNumG

A non-negative integer.

p0

A probability.

p

A positive integer.

q

The default is set to be 1, and it could be either 1 or 2.

Details

  • n stands for the number of rows (or run size).

  • k stands for the number of columns (or the number of factors).

  • m stands for the number of particles.

  • N stands for the number of iterations.

  • SameNumP 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".

  • SameNumG 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".

  • SameNumP and SameNumG cannot be 0 at the same time.

  • p0 stands the probability of exchange two randomly selected elements in current column of current particle LHD.

  • p is the parameter in the phi_p formula, and p is prefered to be large.

  • If q is 1 (the default setting), dij is the rectangular distance. If q is 2, dij is the Euclidean distance.

Value

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

Note

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 or 2 is often sufficient. So p0 = 1/(k - 1) or 2/(k - 1).

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.

Aliases
  • LaPSO
Examples
# NOT RUN {
#create a 8 by 3 maximin distance LHD, with # of particles and iterations = 10, when SameNumG is 0
tryLaPSO1=LaPSO(n=8,k=3,m=10,N=10,SameNumP=8/2,SameNumG=0,p0=1/(3-1),p=50,q=1)
tryLaPSO1
phi_p(tryLaPSO1,p=50)   #calculate the phi_p of "tryLaPSO1".

#create a 8 by 3 maximin distance LHD, with # of particles and iterations = 10, when SameNumP is 0
tryLaPSO2=LaPSO(n=8,k=3,m=10,N=10,SameNumP=0,SameNumG=8/4,p0=1/(3-1),p=50,q=1)
tryLaPSO2
phi_p(tryLaPSO2,p=50)   #calculate the phi_p of "tryLaPSO2".
# }
Documentation reproduced from package LHD, version 0.1.0, License: MIT + file LICENSE

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