Survey Methodology
An optimisation algorithm applied to the one-dimensional stratification problem

by José André de Moura Brito, Tomás Moura da Veiga and Pedro Luis do Nascimento SilvaNote 1

  • Release date: June 27, 2019
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Abstract

This paper presents a new algorithm to solve the one-dimensional optimal stratification problem, which reduces to just determining stratum boundaries. When the number of strata H and the total sample size n are fixed, the stratum boundaries are obtained by minimizing the variance of the estimator of a total for the stratification variable. This algorithm uses the Biased Random Key Genetic Algorithm (BRKGA) metaheuristic to search for the optimal solution. This metaheuristic has been shown to produce good quality solutions for many optimization problems in modest computing times. The algorithm is implemented in the R package stratbr available from CRAN (de Moura Brito, do Nascimento Silva and da Veiga, 2017a). Numerical results are provided for a set of 27 populations, enabling comparison of the new algorithm with some competing approaches available in the literature. The algorithm outperforms simpler approximation-based approaches as well as a couple of other optimization-based approaches. It also matches the performance of the best available optimization-based approach due to Kozak (2004). Its main advantage over Kozak’s approach is the coupling of the optimal stratification with the optimal allocation proposed by de Moura Brito, do Nascimento Silva, Silva Semaan and Maculan (2015), thus ensuring that if the stratification bounds obtained achieve the global optimal, then the overall solution will be the global optimum for the stratification bounds and sample allocation.

Key Words:      Optimal stratification; Genetic algorithm; Integer programming; Nonlinear optimization; BRKGA Metaheuristic.

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How to cite

de Moura Brito, J.A., da Veiga, T.M. and do Nascimento Silva, P.L. (2019). An optimisation algorithm applied to the one-dimensional stratification problem. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 45, No. 2. Paper available at https://www150.statcan.gc.ca/n1/pub/12-001-x/2019002/article/00006-eng.htm.

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ISSN : 1492-0921

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Survey Methodology publishes articles dealing with various aspects of statistical development relevant to a statistical agency, such as design issues in the context of practical constraints, use of different data sources and collection techniques, total survey error, survey evaluation, research in survey methodology, time series analysis, seasonal adjustment, demographic studies, data integration, estimation and data analysis methods, and general survey systems development. The emphasis is placed on the development and evaluation of specific methodologies as applied to data collection or the data themselves. All papers will be refereed. However, the authors retain full responsibility for the contents of their papers and opinions expressed are not necessarily those of the Editorial Board or of Statistics Canada.

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Published by authority of the Minister responsible for Statistics Canada.

© Her Majesty the Queen in Right of Canada as represented by the Minister of Industry, 2019

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Catalogue No. 12-001-X

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. Stratified sampling
Section 3. The one-dimensional stratification problem
Section 4. Biased Random-Key Genetic Algorithm
Section 5. Computational results
Section 6. Conclusions
Appendix A
References

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