A grouping genetic algorithm for joint stratification and sample allocation designs
Section 1. Introduction

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In this paper we address the optimization problem of jointly determining stratification and sample allocation for univariate and mulitivariate scenarios. To serve this purpose, we refer to (Ballin and Barcaroli, 2013). In principle the optimal stratification (i.e., that which yields the smallest sample size) can be found by testing all possible partitionings of atomic strata, but the number of possible partitionings grows exponentially with the number of atomic strata.

An efficient search algorithm is necessary to avoid evaluating each possible partitioning. Genetic algorithms (GAs) often converge quickly to optimal or near optimal solutions, and are particularly good at navigating rugged search spaces containing many local minima. The Bethel-Chromy algorithm combines similar algorithms from (Bethel, 1985, 1989) and (Chromy, 1987) and is suitable for univariate and mulitivariate cases. It uses lagrangian multipliers to find the minimum sample size that meets precision constraints for a given stratification. (Ballin and Barcaroli, 2013) combine a GA with this algorithm to search for the minimum sample size. It is used to evaluate each partitioning created by the GA. A full description of the methodology and problem statement is found in (Ballin and Barcaroli, 2013). However, they use a classical GA which is known to be unsuitable for partitioning problems.

In this paper we propose to apply genetic operators to the GA that are better suited to this application. It is an example of the class of evolutionary algorithms called Grouping Genetic Algorithms (GGAs). The GA has been updated following this work (Barcaroli, 2019). Section 2 motivates the work and introduces GGAs. Section 2.3 describes our GGA for the problem. Section 3 compares the original GA with our GGA on publicly-available test data. Section 4 describes a version of our GGA with enhanced performance, using a fast C++ implementation of the bethel.r function which we integrated into R using the Rcpp package. Section 5 concludes the paper.

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. Classical vs grouping genetic algorithms
Section 3. Comparing the genetic algorithms
Section 4. An improved Bethel implementation
Section 5. Conclusion and further work
Acknowledgements
References

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