stratbr {stratbr}

Optimization Algorithm to solve stratification problem

Description

This function aims at constructing optimal strata with an optimization algorithm based on a global optimisation technique called Biased Random Key Genetic Algorithms(BRKGA). The optimization algorithm is applied to solve the one dimensional case, which reduces the stratification problem to just determining strata boundaries. Assuming that the number H of strata and the total sample size n are fixed, it is possible to produce the strata boundaries by taking into consideration an objective function associated with the variance. This function determines strata boundaries so that the elements in each stratum are more homogeneous among themselves.

Usage

stratbr(X, H = 3, n = 30, nmin = 2, takeall = FALSE, tampop = 100,
  totgen = 1500, pelite = 0.2, pmutant = 0.3, rc = 0.6, cores = 2)

Arguments

X

Stratification variable.

H

Number of strata.

n

Sample size.

nmin

Minimum sample size (smallest possible sample size in any stratum).

takeall

Take-all stratum (takeall=TRUE) => nH=NH.

tampop

Number of chromosomes BRKGA.The default is 100.

totgen

Maximum number of generations BRKGA.The default is 1500.

pelite

Percentage elite solutions BRKGA.The default is 0.2.

pmutant

Percentage mutant solutions BRKGA.The default is 0.3.

rc

Crossover probability BRKGA. The default is 0.6.

cores

Numerical amount of CPUs requested for the cluster.

Value

cvtot

Coefficient of variation for the estimator of total of the stratification variable considered.

nh

Number of sample elements, or sample size, in stratum h.

Nh

Number of population elements, or population size, in stratum h.

Sh2

Population variance of the stratification variable x in stratum h.

bk

Strata boundaries

cputime

Time consumed by the algorithm in seconds.

Author(s)

Jose Brito ([e-mail]), Pedro Luis and Tomas Veiga.

References

Brito, J.A.M, Silva, P.L.N.,Semaan, G.S. and Maculan, N. (2015). Integer Programming Formulations Applied to Optimal Allocation in Stratified Sampling. Survey Methodology, 41: 427-442.

Brito, J.A.M, Semaan, G.S., Fadel, A.C. and Brito, L.R.(2017). An optimization approach applied to the optimal stratification problem, Communications in Statistics - Simulation and Computation.

Gonçalves, J.R. and Resende, M.G.C. (2011). Biased random-key genetic algorithms for combinatorial optimization, Journal of Heuristics, 17: 487-525.

Examples

data(Sweden)
REV84<-Sweden[,9]
solution1<-stratbr(REV84,H=3,n=50,nmin=10,totgen=2,cores=4)
data(USbanks)
solution2<-stratbr(USbanks,H=3,n=50,totgen=2,cores=4,takeall=TRUE)