STRATVNS {stratvns}

Vns Algorithm

Description

This function aims at constructing optimal strata with an optimization algorithm based on a global optimisation technique called Variable neighborhood search (VNS). 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 L of strata and the coefficient of variation are fixed, it is possible to produce the strata boundaries by taking into consideration an objective function associated with the sample size. This function determines strata boundaries so that the elements in each stratum are more homogeneous among themselves and produce minimum sample size applying an integer formulation proposed by Brito et al (2015).

Usage

STRATVNS(
  X,
  L = 3,
  cvt = 0.1,
  nhmin = 2,
  maxstart = 3,
  imax = 3,
  kmax = 3,
  s = 30,
  sl = 50,
  tmax = 15,
  nsols = 20,
  cputime = 3600,
  nIterWithNoImpMax = 5,
  parallelize = TRUE
)

Arguments

X

Stratification Variable

L

Number of strata

cvt

Target cv

nhmin

Mininum sample size by stratum

maxstart

Number of iterations in multstart

imax

Maximum Number Iterations - VNS

kmax

Maximum Neighborhoods = number of cut points selected to apply shaking and local search

s

Range of shaking procedure

sl

Range of RVNS procedure

tmax

Maximum number cut points in neighborhoods

nsols

Number of initial solutions generated

cputime

Maximum cpu time in seconds

nIterWithNoImpMax

Maximum number of iterations without improvement in VNS

parallelize

TRUE = Performs multiple vns calls in parallel

Details

STRATVNS

Value

bk

Cut points

n

Minimum sample size

nh

Sample size by strata

cv

coefficient of variation

Nh

Strata sizes

Vh

Strata variances

cputime

Runtime in seconds

Author(s)

Leonardo de Lima, Jose Brito, Pedro Gonzalez and Breno Oliveira

References

1. Hansen, P., Mladenovi´c, N., 2001. Variable neighborhood search: Principles and applications. European Journal of Operational Research 130, 3, 449 – 467.

2. Brito, J.A.M., Silva, P.L.N., Semaan, G.S., Maculan, N., 2015. Integer programming formulations applied to optimal allocation in stratified sampling. Survey Methodology 41, 2, 427–442.

Examples

## Not run: 
Example1:
s<-STRATVNS(U1,L=4,cvt=0.05,nhmin=3)
Example2:
s<-STRATVNS(U15,L=3)
#'Example3:
s<-STRATVNS(U21,L=5)
Example4:
s<-STRATVNS(U1,L=3,nhmin=4)

## End(Not run)