SA2008

From LHD v0.1.0
0th

Percentile

Simulated Annealing for LHD with Multi-objective Optimization Approach

SA2008 returns a maximin distance LHD constructed by simulated annealing algorithm with multi-objective optimization approach.

Usage
SA2008(n, k, N, T0, rate, Tmin, Imax, p = 50, q = 1)
Arguments
n

A positive integer.

k

A positive integer.

N

A positive integer.

T0

A positive number.

rate

A positive percentage.

Tmin

A positive number.

Imax

A positive integer.

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).

• N stands for the number of iterations.

• T0 stands for the user-defined initial temperature.

• 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.

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

• 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.

• 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

This modified simulated annealing algorithm reduces columnwise correlations, but with a cost of more computational time.

References

Joseph, V.R., and Hung, Y. (2008) Orthogonal-maximin Latin hypercube designs. Statistica Sinica, 18, 171-186.

• SA2008
Examples
# NOT RUN {
#create a 5 by 3 maximin distance LHD, with # of iterations =10, initial
#temperature is set to be 10, decrease rate is 10%, minimium temperature is 1,
#maximum perturbations the algorithm will try without improvements is 5, and p=50
try=SA2008(n=5,k=3,N=10,T0=10,rate=0.1,Tmin=1,Imax=5,p=50,q=1)
try
phi_p(try,p=50)   #calculate the phi_p of "try".

#Another example with different input
try2=SA2008(n=9,k=2,N=5,T0=8,rate=0.1,Tmin=1,Imax=3,p=50,q=1)
try2
# }
Documentation reproduced from package LHD, version 0.1.0, License: MIT + file LICENSE

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