package ‘ga4stratiﬁcation’ fileauthor sebnem er, timur keskinturk, charlie daly maintainer...

Package ‘GA4Stratification’February 15, 2013

Type Package

Title A genetic algorithm approach to determine stratum boundaries andsample sizes of each stratum in stratified sampling

Version 1.0

Date 2010-12-03

Author Sebnem Er, Timur Keskinturk, Charlie Daly

Maintainer Sebnem Er <[email protected]>

Description This is a Genetic Algorithm package for the determinationof the stratum boundaries and sample sizes of each stratum in stratified sampling

License GPL-2

LazyLoad yes

LazyData yes

Repository CRAN

Date/Publication 2012-10-29 08:57:06

NeedsCompilation no

R topics documented:GA4Stratification-package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2beta10_3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4chi1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4chi10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5chi15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5chi5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6GA4Stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6GA4StratificationP1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8GA4StratificationP1fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1

2 GA4Stratification-package

GA4StratificationP1fitt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13GA4StratificationP1m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15GA4StratificationP1x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17GA4StratificationP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19GA4StratificationP2fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22GA4StratificationP2fitt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25GA4StratificationP2m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27GA4StratificationP2x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29GA4StratificationP3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32GA4StratificationP3fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34GA4StratificationP3fitt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37GA4StratificationP3m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39GA4StratificationP3x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41GA4StratificationP4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44GA4StratificationP4fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46GA4StratificationP4fitt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49GA4StratificationP4m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51GA4StratificationP4x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54GA4StratificationSelection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57iso2004 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58normal100_10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59P75 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60randomnumGenerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Index 62

GA4Stratification-package

A genetic algorithm approach to determine stratum boundaries andsample sizes of each stratum in stratified sampling

Description

This is a package for Genetic Algorithm approach for the determination of the stratum boundariesand sample sizes in each stratum in stratified sampling developed by Keskinturk and Er in 2007.

Details

Package: GA4StratificationType: PackageVersion: 1.0Date: 2010-12-03License: GPL-2LazyLoad: yes

GA4Stratification-package 3

Note

This study is part of a project supported by the Scientific and Technological Research Council ofTurkey (TUBITAK).

Author(s)

Sebnem Er, Timur Keskinturk, Charlie Daly

Maintainer: Sebnem Er <[email protected]>

References

http://ideas.repec.org/a/eee/csdana/v52y2007i1p53-67.html

See Also

iso2004 P75 chi1 chi5 chi10 chi15 normal100_10 beta10_3

GA4StratificationP1 GA4StratificationP1fit GA4StratificationP1fitt GA4StratificationP1mGA4StratificationP1x




GA4StratificationSelection randomnumGenerator

Examples

data(chi1)data(chi10)data(chi15)data(chi5)data(iso2004)data(normal100_10)data(beta10_3)data(P75)GA4Stratification(chi1,2,80,10,35,0.15,"Equal")GA4Stratification(chi10,3,81,10,35,0.15,"Proportional")GA4Stratification(chi15,4,80,10,35,0.15,"Neyman")GA4Stratification(chi5,5,80,10,35,0.15,"GA")GA4Stratification(iso2004,6,84,10,35,0.15,"Equal")GA4Stratification(normal100_10,2,80,10,35,0.15,"Proportional")GA4Stratification(beta10_3,3,81,10,35,0.15,"Neyman")GA4Stratification(P75,4,80,10,35,0.15,"GA")

4 chi1

beta10_3 A randomly generated data

Description

beta10_3 is a randomly generated data from beta distribution with parameters of 10 and 3.

Usage

data(beta10_3)

Format

A data frame with 1000 observations on the following variable.

V1 a numeric vector

References

http://www.sciencedirect.com/science/article/B6V8V-4NHM520-1/2/a21e0295aa1616ff56da1ddf2c0ba1ac

Examples

data(beta10_3)

chi1 A randomly generated data

Description

Chi1 is a randomly generated data from Chisquare distribution with 1 degrees of freedom.

Usage

data(chi1)

Format


V1 a numeric vector

References


Examples

data(chi1)

chi10 5


Description


Usage

data(chi10)

Format


V1 a numeric vector

References


Examples

data(chi10)


Description


Usage

data(chi15)

Format


V1 a numeric vector

References


Examples

data(chi15)

6 GA4Stratification


Description


Usage

data(chi5)

Format


V1 a numeric vector

References


Examples

data(chi5)

GA4Stratification A genetic algorithm approach to determine stratum boundaries andsample sizes of each stratum in stratified sampling

Description

This is a package for Genetic Algorithm approach for the determination of the stratum boundariesand sample sizes in each stratum in stratified sampling.

Usage

GA4Stratification(dataName, numberOfStrata, sampleSize, iteration, GAgenerationSize, mutationRate, sampleAllocation)

GA4Stratification 7

Arguments

dataName A string: The name of any type of numeric data containing the values of aunivariate stratification variable.

numberOfStrata An integer: The number of strata.

sampleSize An integer: The total sample size.

iteration An integer: The number of iterations in the Genetic Algorithm process.GAgenerationSize

An integer: The number of generations in the Genetic Algorithm process.

mutationRate A numeric: The mutation rate in the Genetic Algorithm process. Mutation ratemust be in between 0 and 1, inclusive. Small levels of mutation rate is preferablein Genetic Algorithm approach.

sampleAllocation

A string: sampleAllocation defines the type of the sample allocation method,which could be either "Equal", "Proportional", "Neyman" or "GA".

Note


Author(s)



References



Examples

data(iso2004)GA4Stratification(iso2004,2,80,10,35,0.15,"Equal")## The function is currently defined asfunction(dataName,numberOfStrata,sampleSize,iteration,GAgenerationSize,mutationRate,sampleAllocation){

if(sampleAllocation == "Equal"){

GA4StratificationP1(dataName,numberOfStrata,sampleSize,iteration,GAgenerationSize,mutationRate)

} else if(sampleAllocation=="Proportional") {


} else if(sampleAllocation == "Neyman") {


8 GA4StratificationP1

} else if (sampleAllocation == "GA") {


}

}

GA4StratificationP1 The genetic algorithm function to determine the stratum boundariesand sample sizes of each stratum in stratified sampling with EqualSample Allocation Scheme

Description

This is the general function in Genetic Algorithm that initially generates a random generation andthen applies the fitness function, selects, mutates and crossovers in order to obtain the best solution.

Usage

GA4StratificationP1(dataName, numberOfStrata, sampleSize, iteration, GAgenerationSize, mutationRate)

Arguments





An integer: The number of the generations in the Genetic Algorithm process.


Note


Author(s)



GA4StratificationP1 9

References



See Also

GA4StratificationP1fit GA4StratificationP1fitt GA4StratificationP1m GA4StratificationP1x


Examples

## The function is currently defined asfunction(dataName,numberOfStrata,sampleSize,iteration,GAgenerationSize,mutationRate){

dataName=data.frame(dataName)dataName=data.frame(dataName[order(dataName[,1]),])tableData=as.data.frame(table(dataName))randomnumRange=cumsum(tableData[,2])lengthRandomnum=length(randomnumRange)

lengthData=nrow(dataName)randomGeneration=array(0,dim=c(GAgenerationSize,lengthData))

nocrom=nrow(randomGeneration)fitp1=array(0,dim=c(1,nocrom))fit=array(0,dim=c(nocrom,1))N=means=s=n=vars=mas=NN=k=p=t=array(0,dim=c(nocrom,numberOfStrata))dd=array(0,dim=c(nocrom,1))

randomNumbers=array(0,dim=c(GAgenerationSize,numberOfStrata-1))

randomNumbersX=array(0,dim=c(nocrom,2))

aftermut=array(0,dim=c(GAgenerationSize,lengthData+numberOfStrata+1))cumTotal=cumsum(dataName)sumSquares=cumsum(dataName^2)

for (i in 1:GAgenerationSize){

randomNumbers[i,]=randomnumGenerator(randomnumRange,lengthRandomnum,numberOfStrata-1)

}

son=array(lengthData,dim=c(GAgenerationSize,1))indis=array(c(1:GAgenerationSize,randomNumbers,son),dim=c(GAgenerationSize,(numberOfStrata+1)))

for(i in 2:(numberOfStrata+1)){randomGeneration[indis[,c(1,i)]]=1

10 GA4StratificationP1fit

}

bestValue=-99999999999999999999999999999999999999999999999999999999999999for ( i in 1:iteration ){

fitnessValueGeneration=GA4StratificationP1fit(randomGeneration,dataName,numberOfStrata,sampleSize,cumTotal,sumSquares,lengthData,dd,nocrom,fitp1,fit,N,means,s,n,vars,mas,NN,k,p,t)if ( max(fitnessValueGeneration)>bestValue ){

bestValue=max(fitnessValueGeneration)bestGeneration=randomGeneration[max(which(fitnessValueGeneration==bestValue)),]

}

randomGeneration=GA4StratificationSelection(randomGeneration,fitnessValueGeneration)

randomGeneration=GA4StratificationP1x(randomGeneration,bestGeneration,dataName,numberOfStrata,sampleSize,fitnessValueGeneration,cumTotal,sumSquares,lengthData,dd,nocrom,fitp1,fit,N,means,s,n,vars,mas,NN,k,p,t,randomNumbersX,tableData,randomnumRange,lengthRandomnum)

randomGeneration=GA4StratificationP1m(randomGeneration,mutationRate,i)

fitnessValueGeneration=GA4StratificationP1fit(randomGeneration,dataName,numberOfStrata,sampleSize,cumTotal,sumSquares,lengthData,dd,nocrom,fitp1,fit,N,means,s,n,vars,mas,NN,k,p,t)

if ( max(fitnessValueGeneration)>bestValue ){


} else

{randomGeneration[sample(GAgenerationSize,1),]=bestGeneration}

cat(i, " ",-bestValue,’\n’)flush.console()Sys.sleep(1)

}GA4StratificationP1fitt(bestGeneration,dataName,numberOfStrata,sampleSize,-bestValue,cumTotal,sumSquares)}

GA4StratificationP1fit

The genetic algorithm (GA) fitness function that calculates the vari-ance of the estimate of each chromosome in the GA generation withan Equal Sample Allocation Scheme

Description

This is the fitness function in GA that calculates the variance of the estimate according to theboundaries obtained with GA and sample sizes obtained with Equal Allocation.

GA4StratificationP1fit 11

Usage

GA4StratificationP1fit(randomGeneration, dataName, numberOfStrata, sampleSize, cumTotal, sumSquares, c, dd, nocrom, fitp1, fit, N, means, s, n, vars, mas, NN, k, p, t)

Arguments

randomGeneration

The generation which a fitness function will be applied and a fitness value willbe calculated. This is initially a random generation and after each iteration it isthe mutated, crossovered and selected generation.




cumTotal An array: The cumulative total of the data elements from i=1 to i=N

sumSquares An array: The cumulative total of the squares of the data elements from i=1 toi=N

c An integer: The length of the data.

dd An array (nocrom X 1): The minimum of the difference in between the size ofeach stratum and the sample size to be drawn from that stratum.

nocrom An integer: The number of the chromosomes in the generation.

fitp1 An array (1 X nocrom): The fitness value for each chromosome in the genera-tion.

fit An array (nocrom X 1): The fitness value for each chromosome in the genera-tion.

N An array (nocrom X nofstrata): The number of the elements in each stratum foreach chromosome in the generation.

means An array (nocrom X nofstrata): The mean of the elements in each stratum foreach chromosome in the generation.

s An array (nocrom X nofstrata): The standart deviation of the elements in eachstratum for each chromosome in the generation.

n An array (nocrom X nofstrata): The number of the sample size to be drawn fromeach stratum for each chromosome in the generation.

vars An array (nocrom X nofstrata): The variance of the estimate in each stratum foreach chromosome in the generation.

mas An array (nocrom X nofstrata): The indice of each stratum for each chromosomein the generation.

NN An array (nocrom X nofstrata): The cumulative sum of the number of the ele-ments in each stratum.

k An array (nocrom X nofstrata): The difference between the number of the ele-ments and the sample sizes in each stratum.

t An array (nocrom X nofstrata): The maximum of the k

p An array (nocrom X nofstrata): The indice of the element where k is equal to t


Note


Author(s)



References



See Also

GA4StratificationP1 GA4StratificationP1fitt GA4StratificationP1m GA4StratificationP1x


Examples

## The function is currently defined asfunction(randomGeneration,dataName,numberOfStrata,sampleSize,cumTotal,sumSquares,c,dd,nocrom,fitp1,fit,N,means,s,n,vars,mas,NN,k,p,t){

for ( i in 1:nocrom ){mas[i,]=which(randomGeneration[i,]==1,arr.ind=TRUE)N[i,1]=min(mas[i,])means[i,1]=cumTotal[mas[i,1],]/N[i,1]

if(N[i,1]==1){s[i,1]=0} else{

s[i,1]=((N[i,1]/(N[i,1]-1))*(sumSquares[N[i,1]]/N[i,1]-means[i,1]^2))^.5}

for ( j in 2:numberOfStrata ){

N[i,j]=mas[i,j]-mas[i,(j-1)]means[i,j]=(cumTotal[mas[i,j],]-cumTotal[mas[i,j-1],])/N[i,j]

if(N[i,j]==1){s[i,j]=0} else

{s[i,j]=((N[i,j]/(N[i,j]-1))*((sumSquares[mas[i,j]]-sumSquares[mas[i,j-1]])/N[i,j]-means[i,j]^2))^.5}}


n[i,j]=sampleSize/numberOfStrata}

GA4StratificationP1fitt 13


vars[i,j]=((N[i,j]-n[i,j])*s[i,j]^2*N[i,j]^2)/(c^2*n[i,j]*N[i,j])}

kl=0

fit[i,]=sum(vars[i,])dd[i,]=min(N[i,]-n[i,])

if ( dd[i]<0 ){fit[i]= 999999999999999999999}

p1fit=array(-fit,dim=c(nocrom,1))

}return(p1fit)}

GA4StratificationP1fitt

The genetic algorithm fitness function to calculate the variance of theestimate of each chromosome in the generation with an Equal SampleAllocation Scheme

Description

This is the fitness function in Genetic Algorithm that calculates the variance of the estimate accord-ing to the boundaries obtained with GA and sample sizes obtained with Equal Allocation for thefinal chromosome.

Usage

GA4StratificationP1fitt(bestGeneration, dataName, numberOfStrata, sampleSize, bestValue, cumTotal, sumSquares)

Arguments

bestGeneration The generation that has the smallest fitness value is the best generation that willbe delivered to the next step.


numberOfStrata An integer: The number of strata.sampleSize An integer: The total sample size.bestValue A numeric: The best fitness value that is the minimum variance of the estimate

for the best generation.cumTotal An array: The cumulative total of the data elements from i=1 to i=NsumSquares An array: The cumulative total of the squares of the data elements from i=1 to

i=N

14 GA4StratificationP1fitt

Note


Author(s)



References



See Also

GA4StratificationP1 GA4StratificationP1fit GA4StratificationP1m GA4StratificationP1x


Examples

## The function is currently defined asfunction(bestGeneration,dataName,numberOfStrata,sampleSize,bestValue,cumTotal,sumSquares){

c=nrow(dataName)nocrom=length(bestGeneration)/cbestGeneration=array(bestGeneration,dim=c(length(bestGeneration)/c,c))fitp1=array(0,dim=c(1,nocrom))fit=array(0,dim=c(nocrom,1))N=means=s=n=vars=mas=NN=k=p=t=array(0,dim=c(nocrom,numberOfStrata))

dd=array(0,dim=c(nocrom,1))

for ( i in 1:nocrom ){

mas[i,]=which(bestGeneration[i,]==1,arr.ind=TRUE)N[i,1]=min(mas[i,])means[i,1]=cumTotal[mas[i,1],]/N[i,1]s[i,1]=((N[i,1]/(N[i,1]-1))*(sumSquares[N[i,1]]/N[i,1]-means[i,1]^2))^.5


N[i,j]=mas[i,j]-mas[i,(j-1)]N

means[i,j]=(cumTotal[mas[i,j],]-cumTotal[mas[i,j-1],])/N[i,j]means

s[i,j]=((N[i,j]/(N[i,j]-1))*((sumSquares[mas[i,j]]-sumSquares[mas[i,j-1]])/N[i,j]-means[i,j]^2))^.5s}

GA4StratificationP1m 15


n[i,j]=(sampleSize/numberOfStrata)}

}

return(array(c(N,n,bestValue),dim=c(numberOfStrata,3)))}

GA4StratificationP1m The mutation operation in genetic algorithm for the determination ofstratum boundaries and sample sizes of each stratum in stratified sam-pling

Description

This is the mutation operation in the Genetic Algorithm approach for the determination of thestratum boundaries and sample sizes in each stratum in stratified sampling with an Equal SampleAllocation Scheme.

Usage

GA4StratificationP1m(mutationGeneration, mutationRate, it)

Arguments

mutationGeneration

The generation that will be crossovered and transfered to the next generation.


it An integer: The number of the iteration

Note


Author(s)



References



16 GA4StratificationP1m

See Also

GA4StratificationP1 GA4StratificationP1fit GA4StratificationP1fitt GA4StratificationP1x


Examples

## The function is currently defined asfunction(mutationGeneration,mutationRate,it)

{

rowOfMutationGeneration=nrow(mutationGeneration)for ( i in 1:rowOfMutationGeneration ){

for ( k in 1:5 ){

if ( runif(1,0,1) < mutationRate ){

if ( runif(1,0,1) < mutationRate ){if ( it<50 )

{ones=which(mutationGeneration[i,]==1,arr.ind=TRUE)zeros=which(mutationGeneration[i,]==0,arr.ind=TRUE)mutationPoint=ones[sample((length(ones)-1),1)]

mutationPoint1=zeros[sample(length(zeros),1)]mutationGeneration[i,mutationPoint]=0mutationGeneration[i,mutationPoint1]=1} else

{ones=which(mutationGeneration[i,]==1,arr.ind=TRUE)mutationPoint=ones[sample((length(ones)-1),1)]

if ( runif(1,0,1)<0.51 ){

if ( mutationGeneration[i,(mutationPoint+1)]==0 ){mutationGeneration[i,mutationPoint]=0

mutationGeneration[i,(mutationPoint+1)]=1}

} else if ( mutationPoint>1){

if ( mutationGeneration[i,(mutationPoint-1)]==0 ){

mutationGeneration[i,mutationPoint]=0;mutationGeneration[i,mutationPoint-1]=1;

}}

}}

}}}return(mutationGeneration)

GA4StratificationP1x 17

}

GA4StratificationP1x The crossover operation in genetic algorithm for the determinationof stratum boundaries and sample sizes of each stratum in stratifiedsampling

Description

This is the crossover operation in the Genetic Algorithm approach for the determination of thestratum boundaries and sample sizes in each stratum in stratified sampling with an Equal SampleAllocation Scheme.

Usage

GA4StratificationP1x(crossoverGeneration,bestGeneration,dataName,numberOfStrata,sampleSize,fitnessValueGeneration,cumTotal,sumSquares,lengthData,dd,nocrom,fitp1,fit,N,means,s,n,vars,mas,NN,k,p,t,randomNumbersX,tableData,randomnumRange,lengthRandomnum)

Arguments

crossoverGeneration


bestGeneration The generation that has the best fitness value after the selection process.



sampleSize An integer: The total sample size.fitnessValueGeneration

The fitness value -the variance of the estimate- of the best generation after se-lection



lengthData An integer: The size of the data.






18 GA4StratificationP1x










randomNumbersX An integer: The number of random numbers.

tableData The frequency table of the data.

randomnumRange An array: The range of the data where different random numbers will be chosen.

lengthRandomnum

An integer: The number of random numbers that are different from eachother.

Note


Author(s)



References



See Also

GA4StratificationP1 GA4StratificationP1fit GA4StratificationP1fitt GA4StratificationP1m



Examples

## The function is currently defined asfunction(crossoverGeneration,bestGeneration,dataName,numberOfStrata,sampleSize,fitnessValueGeneration,cumTotal,sumSquares,lengthData,dd,nocrom,fitp1,fit,N,means,s,n,vars,mas,NN,k,p,t,randomNumbersX,tableData,randomnumRange,lengthRandomnum){

fitnessValueParents=fitnessValueGenerationparents=cbind(crossoverGeneration,fitnessValueParents)crossoverGenerationp=crossoverGenerationrowCrossoverGenerationp=nocrom

for (i in 1:rowCrossoverGenerationp){

randomNumbersX[i,]=randomnumGenerator((1:rowCrossoverGenerationp),(rowCrossoverGenerationp+1),2)}

mother=father=NULL

for (i in 1:rowCrossoverGenerationp){mother=randomNumbersX[i,1]father=randomNumbersX[i,2]

crossoverPoint=sample((randomnumRange[1:lengthRandomnum-1]),1)while ( sum(crossoverGenerationp[mother,c(1:crossoverPoint)])!=sum(crossoverGenerationp[father,c(1:crossoverPoint)]) ){

crossoverPoint=sample((randomnumRange[1:lengthRandomnum-1]),1)

}crossoverGeneration[i,c(1:crossoverPoint)]=crossoverGenerationp[mother,c(1:crossoverPoint)]crossoverGeneration[i,c((crossoverPoint+1):lengthData)]=crossoverGenerationp[father,c((crossoverPoint+1):lengthData)]

}s=GA4StratificationP1fit(crossoverGeneration,dataName,numberOfStrata,sampleSize,cumTotal,sumSquares,lengthData,dd,nocrom,fitp1,fit,N,means,s,n,vars,mas,NN,k,p,t)crossoverGenerationx=cbind(crossoverGeneration,s)GA4StratificationP1x=rbind(parents, crossoverGenerationx)GA4StratificationP1x=GA4StratificationP1x[order(GA4StratificationP1x[,(lengthData+1)]),]GA4StratificationP1x=GA4StratificationP1x[c((rowCrossoverGenerationp+1):(rowCrossoverGenerationp*2)),c(1:lengthData)]

return(GA4StratificationP1x)}

GA4StratificationP2 The genetic algorithm function to determine the stratum boundariesand sample sizes of each stratum in stratified sampling with Propor-tional Sample Allocation Scheme

Description



Usage


Arguments







Note


Author(s)



References



See Also



Examples


dataName=data.frame(dataName)dataName=data.frame(dataName[order(dataName[,1]),])lengthData=nrow(dataName)randomGeneration=array(0,dim=c(GAgenerationSize,lengthData))randomNumbers=array(0,dim=c(GAgenerationSize,numberOfStrata-1))cumTotal=cumsum(dataName)sumSquares=cumsum(dataName^2)


nocrom=GAgenerationSizefitp1=array(0,dim=c(1,nocrom))fit=array(0,dim=c(nocrom,1))N=means=s=n=vars=mas=NN=k=p=t=array(0,dim=c(nocrom,numberOfStrata))


tableData=as.data.frame(table(dataName))randomnumRange=cumsum(tableData[,2])

lengthRandomnum=length(randomnumRange)



}


for(i in 2:(numberOfStrata+1)){randomGeneration[indis[,c(1,i)]]=1}




}


randomGeneration=GA4StratificationP2x(randomGeneration,bestGeneration,dataName,numberOfStrata,sampleSize,fitnessValueGeneration,cumTotal,sumSquares,lengthData,dd,nocrom,fitp1,fit,N,means,s,n,vars,mas,NN,k,p,t)






} else{randomGeneration[sample(GAgenerationSize,1),]=bestGeneration}


}GA4StratificationP2fitt(bestGeneration,dataName,numberOfStrata,sampleSize,-bestValue,cumTotal,sumSquares)

}


The genetic algorithm (GA) fitness function that calculates the vari-ance of the estimate of each chromosome in the GA generation withan Proportional Sample Allocation Scheme

Description

This is the fitness function in GA that calculates the variance of the estimate according to theboundaries obtained with GA and sample sizes obtained with Proportional Allocation.

Usage


Arguments

randomGeneration























Note


Author(s)



References



See Also




Examples


for ( i in 1:nocrom ){mas[i,]=which(randomGeneration[i,]==1,arr.ind=TRUE)N[i,1]=min(mas[i,])means[i,1]=cumTotal[mas[i,1],]/N[i,1]if(N[i,1]==1)

{s[i,1]=0} else{



N[i,j]=mas[i,j]-mas[i,(j-1)]means[i,j]=(cumTotal[mas[i,j],]-cumTotal[mas[i,j-1],])/N[i,j]if(N[i,j]==1)

{s[i,j]=0} else{

s[i,j]=((N[i,j]/(N[i,j]-1))*((sumSquares[mas[i,j]]-sumSquares[mas[i,j-1]])/N[i,j]-means[i,j]^2))^.5}}


n[i,j]=max(1,floor(sampleSize*N[i,j]/sum(N[i,])))n[i,j]=min(n[i,j],N[i,j])

}if ( sampleSize-sum(n[i,])>0 ){

k[i,]=N[i,]-n[i,]t[i,]=max(k[i,])p[i,]=which(k[i,]==t[i,],arr.ind=TRUE)[1]n[i,p[i,1]]=min(n[i,p[i,1]]+sampleSize-sum(n[i,]),N[i,p[i,1]])

}



dd[i,]=min((N[i,]-n[i,]))NN[i,]=cumsum(N[i,])kl=0

fit[i,]=sum(vars[i,])


if ( dd[i]<0 ){fit[i]= 9999999999999999

} else if (!all(N[i,]!=1)){fit[i]= 999999999999999999

} else if (!all(N[i,]!=0)){fit[i]= 999999999999999999} else{fit[i]=fit[i]}

for ( j in 1:(numberOfStrata-1) ){

kl=kl+dataName[(NN[i,j]+1),]-dataName[NN[i,j],]}


}return(p2fit)

}


The genetic algorithm fitness function to calculate the variance of theestimate of each chromosome in the generation with an ProportionalSample Allocation Scheme

Description

This is the fitness function in Genetic Algorithm that calculates the variance of the estimate accord-ing to the boundaries obtained with GA and sample sizes obtained with Proportional Allocation forthe final chromosome.

Usage


Arguments






bestValue A numeric: The best fitness value that is the minimum variance of the estimatefor the best generation.



Note


Author(s)



References



See Also



Examples


c=nrow(dataName)nocrom=length(bestGeneration)/cbestGeneration=array(bestGeneration,dim=c(length(bestGeneration)/c,c))fitp1=array(0,dim=c(1,nocrom))fit=array(0,dim=c(nocrom,1))N=means=s=n=vars=mas=NN=k=p=t=array(0,dim=c(nocrom,numberOfStrata))










n[i,j]=max(1,floor(sampleSize*N[i,j]/sum(N[i,])))n[i,j]=min(n[i,j],N[i,j])

}if ( sampleSize-sum(n[i,])>0 ){

k[i,]=N[i,]-n[i,]t[i,]=max(k[i,])p[i,]=which(k[i,]==t[i,],arr.ind=TRUE)n[i,p[i,1]]=min(n[i,p[i,1]]+sampleSize-sum(n[i,]),N[i,p[i,1]])

}}



Description

This is the mutation operation in the Genetic Algorithm approach for the determination of thestratum boundaries and sample sizes in each stratum in stratified sampling with an ProportionalSample Allocation Scheme.

Usage


Arguments

mutationGeneration





Note


Author(s)



References



See Also



Examples


{

rowOfMutationGeneration=nrow(mutationGeneration)for ( i in 1:rowOfMutationGeneration ){

for ( k in 1:5 ){if ( runif(1,0,1) < mutationRate )

{if ( runif(1,0,1) < mutationRate ){if ( it<50 )

{ones=which(mutationGeneration[i,]==1,arr.ind=TRUE)zeros=which(mutationGeneration[i,]==0,arr.ind=TRUE)mutationPoint=ones[sample((length(ones)-1),1)]



if ( runif(1,0,1)<0.51 ){







}}

}}

}}}return(mutationGeneration)}


Description

This is the crossover operation in the Genetic Algorithm approach for the determination of thestratum boundaries and sample sizes in each stratum in stratified sampling with an ProportionalSample Allocation Scheme.

Usage

GA4StratificationP2x(crossoverGeneration,bestGeneration,dataName,numberOfStrata,sampleSize,fitnessValueGeneration,cumTotal,sumSquares,lengthData,dd,nocrom,fitp1,fit,N,means,s,n,vars,mas,NN,k,p,t)

Arguments

crossoverGeneration







fitnessValueGeneration



















Note


Author(s)




References



See Also



Examples

## The function is currently defined asfunction(crossoverGeneration,bestGeneration,dataName,numberOfStrata,sampleSize,fitnessValueGeneration,cumTotal,sumSquares,lengthData,dd,nocrom,fitp1,fit,N,means,s,n,vars,mas,NN,k,p,t){fitnessValueParents=fitnessValueGenerationparents=cbind(crossoverGeneration,fitnessValueParents)crossoverGenerationp=crossoverGenerationrowCrossoverGenerationp=nocrom



randomNumbers=array(0,dim=c(rowCrossoverGenerationp,2))


randomNumbers[i,]=randomnumGenerator((1:rowCrossoverGenerationp),(rowCrossoverGenerationp+1),2)}mother=father=NULLfor (i in 1:rowCrossoverGenerationp){mother=randomNumbers[i,1]father=randomNumbers[i,2]

crossoverPoint=sample((randomnumRange[1:lengthRandomnum-1]),1)while ( sum(crossoverGenerationp[mother,c(1:crossoverPoint)])!=sum(crossoverGenerationp[father,c(1:crossoverPoint)]) ){

crossoverPoint=sample((randomnumRange[1:lengthRandomnum-1]),1)}

crossoverGeneration[i,c(1:crossoverPoint)]=crossoverGenerationp[mother,c(1:crossoverPoint)]crossoverGeneration[i,c((crossoverPoint+1):lengthData)]=crossoverGenerationp[father,c((crossoverPoint+1):lengthData)]




GA4StratificationP3 The genetic algorithm function to determine the stratum boundariesand sample sizes of each stratum in stratified sampling with NeymanSample Allocation Scheme

Description


Usage


Arguments







Note


Author(s)



References




See Also



Examples


dataName=data.frame(dataName)dataName=data.frame(dataName[order(dataName[,1]),])lengthData=nrow(dataName)randomGeneration=array(0,dim=c(GAgenerationSize,lengthData))randomNumbers=array(0,dim=c(GAgenerationSize,numberOfStrata-1))cumTotal=cumsum(dataName)sumSquares=cumsum(dataName^2)

nocrom=GAgenerationSizefitp1=array(0,dim=c(1,nocrom))fit=array(0,dim=c(nocrom,1))N=means=s=n=vars=mas=NN=k=p=t=array(0,dim=c(nocrom,numberOfStrata))dd=array(0,dim=c(nocrom,1))


lengthRandomnum=length(randomnumRange)-1



}





bestValue=max(fitnessValueGeneration)


bestGeneration=randomGeneration[max(which(fitnessValueGeneration==bestValue)),]}










}


The genetic algorithm (GA) fitness function that calculates the vari-ance of the estimate of each chromosome in the GA generation withan Neyman Sample Allocation Scheme

Description

This is the fitness function in GA that calculates the variance of the estimate according to theboundaries obtained with GA and sample sizes obtained with Neyman Allocation.

Usage


Arguments

randomGeneration























Note


Author(s)




References



See Also



Examples


for ( i in 1:nocrom ){mas[i,]=which(randomGeneration[i,]==1,arr.ind=TRUE)N[i,1]=min(mas[i,])means[i,1]=cumTotal[mas[i,1],]/N[i,1]

if(N[i,1]==1){s[i,1]=0} else

s[i,1]=((N[i,1]/(N[i,1]-1))*(sumSquares[N[i,1]]/N[i,1]-means[i,1]^2))^.5


N[i,j]=mas[i,j]-mas[i,(j-1)]

means[i,j]=(cumTotal[mas[i,j],]-cumTotal[mas[i,j-1],])/N[i,j]if(N[i,j]==1){s[i,j]=0} else

s[i,j]=((N[i,j]/(N[i,j]-1))*((sumSquares[mas[i,j]]-sumSquares[mas[i,j-1]])/N[i,j]-means[i,j]^2))^.5

}


n[i,j]=max(1,round(sampleSize*N[i,j]*s[i,j]/sum(N[i,]*s[i,])))n[i,j]=min(n[i,j],N[i,j])

}if ( (sampleSize-sum(n[i,]))>0 ){


}




dd[i,]=min((N[i,]-n[i,]))NN[i,]=cumsum(N[i,])kl=0


if ( dd[i]<0 ){fit[i]= 9999999999999999



for ( j in 1:(numberOfStrata-1) ){

kl=kl+dataName[(NN[i,j]+1),]-dataName[NN[i,j],]}


}return(p3fit)

}


The genetic algorithm fitness function to calculate the variance of theestimate of each chromosome in the generation with an Neyman Sam-ple Allocation Scheme

Description

This is the fitness function in Genetic Algorithm that calculates the variance of the estimate accord-ing to the boundaries obtained with GA and sample sizes obtained with Neyman Allocation for thefinal chromosome.


Usage


Arguments








Note


Author(s)



References



See Also



Examples


c=nrow(dataName)nocrom=length(bestGeneration)/cbestGeneration=array(bestGeneration,dim=c(length(bestGeneration)/c,c))fitp1=array(0,dim=c(1,nocrom))fit=array(0,dim=c(nocrom,1))


N=means=s=n=vars=mas=NN=k=p=t=array(0,dim=c(nocrom,numberOfStrata))dd=array(0,dim=c(nocrom,1))




N[i,j]=mas[i,j]-mas[i,(j-1)]means[i,j]=(cumTotal[mas[i,j],]-cumTotal[mas[i,j-1],])/N[i,j]s[i,j]=((N[i,j]/(N[i,j]-1))*((sumSquares[mas[i,j]]-sumSquares[mas[i,j-1]])/N[i,j]-means[i,j]^2))^.5

}


n[i,j]=max(1,round(sampleSize*N[i,j]*s[i,j]/sum(N[i,]*s[i,])))n[i,j]=min(n[i,j],N[i,j])

}if ( (sampleSize-sum(n[i,]))>0 ){


}

}



Description

This is the mutation operation in the Genetic Algorithm approach for the determination of thestratum boundaries and sample sizes in each stratum in stratified sampling with an Neyman SampleAllocation Scheme.


Usage


Arguments

mutationGeneration




Note


Author(s)



References



See Also



Examples


{

rowOfMutationGeneration=nrow(mutationGeneration)for ( i in 1:rowOfMutationGeneration){

for ( k in 1:5 ){if ( runif(1,0,1) < mutationRate )

{if ( runif(1,0,1) < mutationRate ){if ( it<50 )

{


ones=which(mutationGeneration[i,]==1,arr.ind=TRUE)zeros=which(mutationGeneration[i,]==0,arr.ind=TRUE)mutationPoint=ones[sample((length(ones)-1),1)]



if ( runif(1,0,1)<0.51 ){






}}

}}

}}}return(mutationGeneration)}


Description

This is the crossover operation in the Genetic Algorithm approach for the determination of thestratum boundaries and sample sizes in each stratum in stratified sampling with an Neyman SampleAllocation Scheme.

Usage



Arguments

crossoverGeneration

























Note


Author(s)



References



See Also



Examples

## The function is currently defined asfunction(crossoverGeneration,bestGeneration,dataName,numberOfStrata,sampleSize,fitnessValueGeneration,cumTotal,sumSquares,lengthData,dd,nocrom,fitp1,fit,N,means,s,n,vars,mas,NN,k,p,t){fitnessValueParents=fitnessValueGenerationparents=cbind(crossoverGeneration,fitnessValueParents)crossoverGenerationp=crossoverGenerationrowCrossoverGenerationp=nocrom






crossoverPoint=sample((randomnumRange[1:lengthRandomnum-1]),1)while ( sum(crossoverGenerationp[mother,c(1:crossoverPoint)])!=sum(crossoverGenerationp[father,c(1:crossoverPoint)]) ){crossoverPoint=sample((randomnumRange[1:lengthRandomnum-1]),1)


}crossoverGeneration[i,c(1:crossoverPoint)]=crossoverGenerationp[mother,c(1:crossoverPoint)]crossoverGeneration[i,c((crossoverPoint+1):lengthData)]=crossoverGenerationp[father,c((crossoverPoint+1):lengthData)]



GA4StratificationP4 The genetic algorithm function to determine the stratum boundariesand sample sizes of each stratum in stratified sampling with GA Sam-ple Allocation Scheme

Description


Usage


Arguments







Note



Author(s)



References



See Also



Examples


dataName=data.frame(dataName)dataName=data.frame(dataName[order(dataName[,1]),])lengthData=nrow(dataName)randomGeneration=array(0,dim=c(GAgenerationSize,lengthData+numberOfStrata))

nocrom=GAgenerationSizefitp1=array(0,dim=c(1,nocrom))fit=array(0,dim=c(nocrom,1))N=means=s=n=vars=mas=NN=k=p=t=array(0,dim=c(nocrom,numberOfStrata))dd=array(0,dim=c(nocrom,1))

randomNumbers=array(0,dim=c(GAgenerationSize,numberOfStrata-1))samples=sumSamples=array(0,dim=c(GAgenerationSize,numberOfStrata))aftermut=array(0,dim=c(GAgenerationSize,lengthData+numberOfStrata+1))cumTotal=cumsum(dataName)sumSquares=cumsum(dataName^2)




randomNumbers[i,]=randomnumGenerator(randomnumRange,lengthRandomnum,numberOfStrata-1)samples[i,]=floor(runif(numberOfStrata,1,10))sumSamples[i,]=sum(samples[i,])

}samples=floor(samples/sumSamples*sampleSize)son=array(lengthData,dim=c(GAgenerationSize,1))indis=array(c(1:GAgenerationSize,randomNumbers,son),dim=c(GAgenerationSize,(numberOfStrata+1)))



for ( i in 1:GAgenerationSize ){

samples[i,numberOfStrata]=samples[i,numberOfStrata]+sampleSize-sum(samples[i,])}

randomGeneration[,(lengthData+1):(lengthData+numberOfStrata)]=samples




}



randomGeneration=GA4StratificationP4m(randomGeneration,numberOfStrata,mutationRate,i)







}



The genetic algorithm (GA) fitness function that calculates the vari-ance of the estimate of each chromosome in the GA generation withan GA Sample Allocation Scheme

Description

This is the fitness function in GA that calculates the variance of the estimate according to theboundaries obtained with GA and sample sizes obtained with GA Allocation.

Usage


Arguments

randomGeneration























Note


Author(s)



References



See Also



Examples


for ( i in 1:nocrom ){mas[i,]=which(randomGeneration[i,1:c]==1,arr.ind=TRUE)N[i,1]=min(mas[i,])means[i,1]=cumTotal[mas[i,1],]/N[i,1]if(N[i,1]==1)

{s[i,1]=0} else{



n[i,]=randomGeneration[i,(c+1):(c+numberOfStrata)]


N[i,j]=mas[i,j]-mas[i,(j-1)]means[i,j]=(cumTotal[mas[i,j],]-cumTotal[mas[i,j-1],])/N[i,j]means

if(N[i,j]==1){s[i,j]=0} else{

s[i,j]=((N[i,j]/(N[i,j]-1))*((sumSquares[mas[i,j]]-sumSquares[mas[i,j-1]])/N[i,j]-means[i,j]^2))^.5}}



dd[i,]=min((N[i,]-n[i,]))NN[i,]=cumsum(N[i,])


if ( dd[i]<0 ){fit[i]= 99999999999999999999999




}return(p4fit)

}


The genetic algorithm fitness function to calculate the variance of theestimate of each chromosome in the generation with an GA SampleAllocation Scheme


Description

This is the fitness function in Genetic Algorithm that calculates the variance of the estimate accord-ing to the boundaries obtained with GA and sample sizes obtained with GA Allocation for the finalchromosome.

Usage


Arguments








Note


Author(s)



References



See Also




Examples


c=nrow(dataName)nocrom=length(bestGeneration)/(c+numberOfStrata)bestGeneration=array(bestGeneration,dim=c(length(bestGeneration)/(c+numberOfStrata),(c+numberOfStrata)))fitp1=array(0,dim=c(1,nocrom))fit=array(0,dim=c(nocrom,1))N=means=s=n=vars=mas=NN=k=p=t=array(0,dim=c(nocrom,numberOfStrata))dd=array(0,dim=c(nocrom,1))


mas[i,]=which(bestGeneration[i,1:c]==1,arr.ind=TRUE)N[i,1]=min(mas[i,])means[i,1]=cumTotal[mas[i,1],]/N[i,1]s[i,1]=((N[i,1]/(N[i,1]-1))*(sumSquares[N[i,1]]/N[i,1]-means[i,1]^2))^.5n[i,]=bestGeneration[i,(c+1):(c+numberOfStrata)]





}



Description

This is the mutation operation in the Genetic Algorithm approach for the determination of thestratum boundaries and sample sizes in each stratum in stratified sampling with an GA SampleAllocation Scheme.


Usage

GA4StratificationP4m(mutationGeneration, numberOfStrata, mutationRate, it)

Arguments

mutationGeneration





Note


Author(s)



References



See Also



Examples

## The function is currently defined asfunction(mutationGeneration,numberOfStrata,mutationRate,it)

{

rowOfMutationGeneration=nrow(mutationGeneration)colOfMutationGeneration=ncol(mutationGeneration)

c=colOfMutationGeneration-numberOfStratafor ( i in 1:rowOfMutationGeneration){

if ( runif(1,0,1) < mutationRate ){

for ( k in 1:2 ){

if ( runif(1,0,1) < 0.35 )


{if ( it<100 ){

ones=which(mutationGeneration[i,1:c]==1,arr.ind=TRUE)zeros=which(mutationGeneration[i,1:c]==0,arr.ind=TRUE)mutationPoint=ones[sample(1:(length(ones)-1),1)]mutationPoint1=zeros[sample(1:length(zeros),1)]mutationGeneration[i,mutationPoint]=0mutationGeneration[i,mutationPoint1]=1

} else{

ones=which(mutationGeneration[i,1:c]==1,arr.ind=TRUE)mutationPoint=ones[sample(1:(length(ones)-1),1)]

if ( runif(1,0,1)<0.51 ){





mutationGeneration[i,mutationPoint]=0mutationGeneration[i,mutationPoint-1]=1

}}

}} else

{mutationPoint=sample((c+1):(c+numberOfStrata),1)mutationPoint1=sample((c+1):(c+numberOfStrata),1)

while ( mutationPoint == mutationPoint1 ){

mutationPoint=sample((c+1):(c+numberOfStrata),1)mutationPoint1=sample((c+1):(c+numberOfStrata),1)}

if (mutationGeneration[i,mutationPoint]>2 & mutationGeneration[i,mutationPoint1]>2){

if (runif(1,0,1)< 0.51){mutationGeneration[i,mutationPoint]=mutationGeneration[i,mutationPoint]-1

mutationGeneration[i,mutationPoint1]=mutationGeneration[i,mutationPoint1]+1

} else{

mutationGeneration[i,mutationPoint]=mutationGeneration[i,mutationPoint]+1mutationGeneration[i,mutationPoint1]=mutationGeneration[i,mutationPoint1]-1

}


} else if (mutationGeneration[i,mutationPoint]==2 & mutationGeneration[i,mutationPoint1]>2){

mutationGeneration[i,mutationPoint]=mutationGeneration[i,mutationPoint]+1mutationGeneration[i,mutationPoint1]=mutationGeneration[i,mutationPoint1]-1

} else (mutationGeneration[i,mutationPoint]>2 & mutationGeneration[i,mutationPoint1]==2)

mutationGeneration[i,mutationPoint]=mutationGeneration[i,mutationPoint]-1mutationGeneration[i,mutationPoint1]=mutationGeneration[i,mutationPoint1]+1

}}

}}

return(mutationGeneration)}


Description

This is the crossover operation in the Genetic Algorithm approach for the determination of thestratum boundaries and sample sizes in each stratum in stratified sampling with an GA SampleAllocation Scheme.

Usage


Arguments

crossoverGeneration

























Note


Author(s)



References




See Also



Examples

## The function is currently defined asfunction(crossoverGeneration,bestGeneration,dataName,numberOfStrata,sampleSize,fitnessValueGeneration,cumTotal,sumSquares,lengthData,dd,nocrom,fitp1,fit,N,means,s,n,vars,mas,NN,k,p,t){fitnessValueParents=fitnessValueGenerationparents=cbind(crossoverGeneration,fitnessValueParents)crossoverGenerationp=crossoverGenerationrowCrossoverGenerationp=nrow(crossoverGenerationp)colCrossoverGenerationp=ncol(crossoverGenerationp)






crossoverPoint=sample((randomnumRange[1:lengthRandomnum-1]),1)while ( sum(crossoverGenerationp[mother,c(1:crossoverPoint)])!=sum(crossoverGenerationp[father,c(1:crossoverPoint)]) ){crossoverPoint=sample((randomnumRange[1:lengthRandomnum-1]),1)

}crossoverGeneration[i,c(1:crossoverPoint)]=crossoverGenerationp[mother,c(1:crossoverPoint)]crossoverGeneration[i,c((crossoverPoint+1):colCrossoverGenerationp)]=crossoverGenerationp[father,c((crossoverPoint+1):colCrossoverGenerationp)]

}s=GA4StratificationP4fit(crossoverGeneration,dataName,numberOfStrata,sampleSize,cumTotal,sumSquares,lengthData,dd,nocrom,fitp1,fit,N,means,s,n,vars,mas,NN,k,p,t)crossoverGenerationx=cbind(crossoverGeneration,s)GA4StratificationP4x=rbind(parents, crossoverGenerationx)GA4StratificationP4x=GA4StratificationP4x[order(GA4StratificationP4x[,(colCrossoverGenerationp+1)]),]GA4StratificationP4x=GA4StratificationP4x[c((rowCrossoverGenerationp+1):(rowCrossoverGenerationp*2)),c(1:colCrossoverGenerationp)]


GA4StratificationSelection 57

GA4StratificationSelection

The selection operation in genetic algorithm for the determination ofstratum boundaries and sample sizes of each stratum in stratified sam-pling with Equal sample allocation scheme

Description

This is the selection operation in the Genetic Algorithm approach for the determination of thestratum boundaries and sample sizes in each stratum in stratified sampling with an Equal SampleAllocation Scheme.

Usage

GA4StratificationSelection(selectionGeneration, selectionGenerationFitness)

Arguments

selectionGeneration

The generation that selection operator will be applied.

selectionGenerationFitness

The fitness value of the generation that selection operator will be applied.

Note


Author(s)



References



See Also


randomnumGenerator

58 iso2004

Examples

## The function is currently defined asfunction(selectionGeneration,selectionGenerationFitness)

{rowSelectionGeneration=nrow(selectionGeneration)

colSelectionGeneration=ncol(selectionGeneration)selectionStrata=array(0,dim=c(rowSelectionGeneration,(colSelectionGeneration+1)))newSelectionGeneration=cbind(selectionGeneration, -selectionGenerationFitness)sortedSelectionGeneration=newSelectionGeneration[order(newSelectionGeneration[,colSelectionGeneration+1]),]sortedSelectionGenerationFitness=selectionGenerationFitness[order(-selectionGenerationFitness),]wheelOld = sortedSelectionGenerationFitness / sum(selectionGenerationFitness)

wheel=1:rowSelectionGeneration

for(i in rowSelectionGeneration:1){wheel[rowSelectionGeneration+1-i]=wheelOld[i]}wheel=cumsum(wheel)

for ( i in 1:rowSelectionGeneration ){

r = runif(1,0,1)for ( j in 1:rowSelectionGeneration ){if(r < wheel[j]){selectionStrata[i,] = sortedSelectionGeneration[j,]break;}}}randomGeneration=selectionStrata[,1:colSelectionGeneration]fitnessValueGeneration=selectionStrata[,(colSelectionGeneration+1)]return(randomGeneration)

}

iso2004 Net sales data of 487 Turkish manufacturing firms

Description

Net sales data of 487 Turkish manufacturing firms from the first 500 largest corporations belongingto the Istanbul Chamber of Industry ICI in year 2004

Usage

data(iso2004)

normal100_10 59

Format


V1 a numeric vector

Source

http://www.iso.org.tr/tr/web/statiksayfalar/index.aspx?ref=3

References


Examples

data(iso2004)

normal100_10 A randomly generated data

Description

normal100_10is a randomly generated data from normal distribution with mean 100 and standartdeviation 10.

Usage

data(normal100_10)

Format


V1 a numeric vector

References


Examples

data(normal100_10)

60 randomnumGenerator

P75 Population data of Swedish municipalities

Description

P75 is the 1975 population (in thousands) of 284 Swedish municipalities obtained from the paperof Hedlin (2003).

Usage

data(P75)

Format


V1 a numeric vector

Source

http://lib.stat.cmu.edu/datasets/mu284.txt

References

Hedlin, Dan (2003) Minimum variance stratification of a finite population. Southampton, UK,Southampton Statistical Sciences Research Institute, 30pp. (S3RI Methodology Working Papers,M03/07) : http://eprints.soton.ac.uk/7796/

Examples

data(P75)

randomnumGenerator Random number generator

Description

This function generates random variables that don’t repeat in a given range

Usage

randomnumGenerator(randomnumRange, lengthRandomnum, howManyRands)

randomnumGenerator 61

Arguments

randomnumRange This is the range of the random numbersrandomnumRange can be something given as: randomnumRange=1:487orrandomnumRange=c(6, 12, 36, 67, 87, 146, 267)therefore length of the randonnumRangein the first case is 487in the second case is 7, defining the index of the randomnumRange to be swapped

lengthRandomnum

This is the length of the random number range

howManyRands Number of random values

Value

An array of different random numbers

Author(s)

Sebnem Er

References

Swap method of Charlie Daly

Examples

randomnumGenerator(c(1,3,5,7,9,15,21),7,3)

function(randomnumRange,lengthRandomnum,howManyRands){

for (i in 1:(howManyRands)){

integer=sample(lengthRandomnum-1,1)tmp=randomnumRange[integer]randomnumRange[integer]=randomnumRange[i]randomnumRange[i]=tmp

}return(randomnumRange[1:howManyRands])

}

Index

∗Topic datasetsbeta10_3, 4chi1, 4chi10, 5chi15, 5chi5, 6iso2004, 58normal100_10, 59P75, 60

∗Topic differentrandomnumGenerator, 60

∗Topic randomNumbersrandomnumGenerator, 60

∗Topic stratificationGA4Stratification, 6GA4Stratification-package, 2GA4StratificationP1, 8GA4StratificationP1fit, 10GA4StratificationP1fitt, 13GA4StratificationP1m, 15GA4StratificationP1x, 17GA4StratificationP2, 19GA4StratificationP2fit, 22GA4StratificationP2fitt, 25GA4StratificationP2m, 27GA4StratificationP2x, 29GA4StratificationP3, 32GA4StratificationP3fit, 34GA4StratificationP3fitt, 37GA4StratificationP3m, 39GA4StratificationP3x, 41GA4StratificationP4, 44GA4StratificationP4fit, 47GA4StratificationP4fitt, 49GA4StratificationP4m, 51GA4StratificationP4x, 54GA4StratificationSelection, 57

beta10_3, 3, 4

chi1, 3, 4chi10, 3, 5chi15, 3, 5chi5, 3, 6

GA4Stratification, 6GA4Stratification-package, 2GA4StratificationP1, 3, 8, 12, 14, 16, 18, 57GA4StratificationP1fit, 3, 9, 10, 14, 16,

18, 57GA4StratificationP1fitt, 3, 9, 12, 13, 16,

18, 57GA4StratificationP1m, 3, 9, 12, 14, 15, 18,

57GA4StratificationP1x, 3, 9, 12, 14, 16, 17,

57GA4StratificationP2, 3, 19, 23, 26, 28, 31GA4StratificationP2fit, 3, 20, 22, 26, 28,

31GA4StratificationP2fitt, 3, 20, 23, 25, 28,

31GA4StratificationP2m, 3, 20, 23, 26, 27, 31GA4StratificationP2x, 3, 20, 23, 26, 28, 29GA4StratificationP3, 3, 32, 36, 38, 40, 43GA4StratificationP3fit, 3, 33, 34, 38, 40,


43GA4StratificationP3m, 3, 33, 36, 38, 39, 43GA4StratificationP3x, 3, 33, 36, 38, 40, 41GA4StratificationP4, 3, 44, 48, 50, 52, 56GA4StratificationP4fit, 3, 45, 46, 50, 52,


56GA4StratificationP4m, 3, 45, 48, 50, 51, 56GA4StratificationP4x, 3, 45, 48, 50, 52, 54GA4StratificationSelection, 3, 9, 12, 14,

16, 18, 20, 23, 26, 28, 31, 33, 36, 38,40, 43, 45, 48, 50, 52, 56, 57

62

INDEX 63

iso2004, 3, 58

normal100_10, 3, 59

P75, 3, 60

randomnumGenerator, 3, 9, 12, 14, 16, 18, 20,23, 26, 28, 31, 33, 36, 38, 40, 43, 45,48, 50, 52, 56, 57, 60

package ‘ga4stratiﬁcation’ fileauthor sebnem er, timur keskinturk, charlie daly maintainer...

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