Heuristic approach applied to the optimum stratification problem

¹ National School of Statistical Sciences, Rio de Janeiro, Brazil
² Federal University of Paraná, Curitiba, Brazil
³ Federal Center for Technological Education of Rio de Janeiro, Rio de Janeiro, Brazil
⁴ Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

^* Corresponding author: leonardo.delima@ufpr.br

Received: 5 August 2020
Accepted: 30 March 2021

Abstract

The problem of finding an optimal sample stratification has been extensively studied in the literature. In this paper, we propose a heuristic optimization method for solving the univariate optimum stratification problem to minimize the sample size for a given precision level. The method is based on the variable neighborhood search metaheuristic, which was combined with an exact method. Numerical experiments were performed over a dataset of 24 instances, and the results of the proposed algorithm were compared with two very well-known methods from the literature. Our results outperformed 94% of the considered cases. Besides, we developed an enumeration algorithm to find the optimal global solution in some populations and scenarios, which enabled us to validate our metaheuristic method. Furthermore, we find that our algorithm obtained the optimal global solutions for the vast majority of the cases.