Optimal sample allocation in multivariate stratified sampling: a comparison of deterministic and stochastic optimization algorithms

Dalius Pumputis

doi:https://doi.org/10.59139/stattrans-2026-001

Optimal sample allocation in multivariate stratified sampling: a comparison of deterministic and stochastic optimization algorithms

Dalius Pumputis 1Vilnius Gediminas Technical University (VILNIUS TECH), Lithuania ORCID:https://orcid.org/0000-0003-0954-0663 Statistics in Transition new series, vol. 27, 2026, 1, pages: 1-20 Published online: 11 March 2026 https://doi.org/10.59139/stattrans-2026-001 Citation: Pumputis D., 2026. Optimal sample allocation in multivariate stratified sampling: a comparison of deterministic and stochastic optimization algorithms. Statistics in Transition new series, 27(1), pp. 1-20 https://doi.org/10.59139/stattrans-2026-001

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ABSTRACT

This study addresses the problem of optimal sample allocation in multivariate stratified sampling, where survey accuracy and cost-efficiency are the key concerns. Two optimization formulations are examined: one aims to minimize the total survey cost subject to constraints on the precision of the estimators of the population totals, while the other seeks to minimize a weighted sum of the relative variances of these estimators, given a fixed total survey budget. Classical and modern optimization approaches are reviewed and evaluated, including Integer Programming Algorithms (IPA), Bethel’s Algorithm (BA), Constrained Optimization by Linear Approximations (COBYLA), and three stochastics, namely Generalized Simulated Annealing Algorithm (GSAA), Particle Swarm Optimization (PSOA) and Biased Random- Key Genetic Algorithm (BRKGA). Using synthetic and real-world populations, numerical experiments demonstrate that IPA consistently achieves the global minimum and serves as the benchmark. While BA underperforms, BRKGA emerges as a competitive alternative, closely matching IPA in most scenarios. Results also highlight the impact of variable skewness on allocation efficiency, with real-world datasets being more complex and thus having higher sampling demands. The findings underscore the importance of adaptive, integerfeasible optimization methods for accurate and cost-effective survey design.

KEYWORDS

constrained optimization by linear approximations, integer programming, multivariate stratified sampling, optimal sample allocation, stochastic optimization

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