Heuristic algorithm for univariate stratification problem

¹ National School of Statistical Sciences, Rio de Janeiro, Brazil
² Fluminense Federal University, Rio de Janeiro, Brazil
³ Federal University of Paraná, Curitiba, Brazil
⁴ Brazilian Institute of Geography and Statistics, Rio de Janeiro, Brazil

^* Corresponding author: jambrito@gmail.com

Received: 13 March 2023
Accepted: 26 September 2023

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 algorithm of Lavallée–Hidiroglou.