Heuristic Algorithm for Univariate Stratification Problem

TL;DR

This paper introduces a heuristic algorithm for the univariate stratification problem in survey sampling, aiming to optimize the number and limits of strata to reduce sample size while maintaining precision, outperforming existing algorithms in most cases.

Contribution

It develops a novel heuristic combining stochastic and exact optimization methods for univariate stratification, improving solution quality over previous algorithms.

Findings

Heuristic outperformed four existing algorithms in over 94% of cases.

The method effectively reduces sample size while maintaining desired precision.

Performance was validated across 20 diverse population scenarios.

Abstract

In sampling theory, stratification corresponds to a technique used in surveys, which allows segmenting a population into homogeneous subpopulations (strata) to produce statistics with a higher level of precision. In particular, this article proposes a heuristic to solve the univariate stratification problem - widely studied in the literature. One of its versions sets the number of strata and the precision level and seeks to determine the limits that define such strata to minimize the sample size allocated to the strata. A heuristic-based on a stochastic optimization method and an exact optimization method was developed to achieve this goal. The performance of this heuristic was evaluated through computational experiments, considering its application in various populations used in other works in the literature, based on 20 scenarios that combine different numbers of strata and levels of precision. From the analysis of the obtained results, it is possible to verify that the heuristic had a performance superior to four algorithms in the literature in more than 94% of the cases, particularly concerning the known algorithms of Kozak and Lavallee-Hidiroglou.