LHD (version 1.1.0)

OASA: Orthogonal-Array-Based Simulated Annealing

Description

OASA returns an LHD matrix generated by orthogonal-array-based simulated annealing algorithm (OASA)

Usage

OASA(
  OA,
  N = 10,
  T0 = 10,
  rate = 0.1,
  Tmin = 1,
  Imax = 5,
  OC = "phi_p",
  p = 15,
  q = 1
)

Arguments

OA

A Matrix.

N

A positive integer.

T0

A positive number.

rate

A positive percentage.

Tmin

A positive number.

Imax

A positive integer.

OC

An optimality criterion.

p

A positive integer.

q

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

Value

If all inputs are logical, then the output will be an LHD whose sizes are the same as input OA.

Details

• OA stands for the input orthogonal array matrix.

• N stands for the number of iterations. The default is set to be 10.

• T0 stands for the user-defined initial temperature. The default is set to be 10.

• rate stands for temperature decrease rate, and it should be in (0,1). For example, rate=0.25 means the temperature decreases by 25% each time. The default is set to be 10%.

• Tmin stands for the minimium temperature allowed. When current temperature becomes smaller or equal to Tmin, the stopping criterion for current loop is met. The default is set to be 1.

• Imax stands for the maximum perturbations the algorithm will try without improvements before temperature is reduced. For the computation complexity consideration, Imax is recommended to be smaller or equal to 5, which is the default setting.

• OC stands for the optimality criterion, the default setting is "phi_p", and it could be one of the following: "phi_p", "AvgAbsCor", "MaxAbsCor", "MaxProCriterion".

• p is the parameter in the phi_p formula, and p is prefered to be large. The default is set to be 15.

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

References

Leary, S., Bhaskar, A., and Keane, A. (2003) Optimal orthogonal-array-based latin hypercubes. Journal of Applied Statistics, 30, 585-598.

Examples

# NOT RUN {
#create an OA(9,2,3,2)
OA=matrix(c(rep(1:3,each=3),rep(1:3,times=3)),ncol=2,nrow=9,byrow = FALSE);OA

#Use above "OA" as the input OA to generate a 9 by 2 maximin distance LHD
#with the default setting
tryOASA=OASA(OA=OA)
tryOASA
phi_p(tryOASA)   #calculate the phi_p of "tryOASA".

#Another example
#generate a 9 by 2 nearly orthogonal LHD
tryOASA2=OASA(OA=OA,OC="MaxAbsCor")
tryOASA2
MaxAbsCor(tryOASA2)  #calculate the maximum absolute correlation.
# }