Heuristic Algorithm for Univariate Stratification Problem

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.Comment: 25 pages and 7 figure

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The effective BRKGA algorithm for the

This paper presents a biased random-key genetic algorithm for k-medoids clustering problem. A novel heuristic operator was implemented and combined with a parallelized local search procedure. Experiments were carried out with fifty literature data sets with small, medium, and large sizes, considering several numbers of clusters, showed that the proposed algorithm outperformed eight other algorithms, for example, the classics PAM and CLARA algorithms. Furthermore, with the results of a linear integer programming formulation, we found that our algorithm obtained the global optimal solutions for most cases and, despite its stochastic nature, presented stability in terms of quality of the solutions obtained and the number of generations required to produce such solutions. In addition, considering the solutions (clusterings) produced by the algorithms, a relative validation index (average silhouette) was applied, where, again, was observed that our method performed well, producing cluster with a good structure

Heuristic algorithm for univariate stratification problem

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