Key points are not available for this paper at this time.
This study addresses the multivariate sample allocation problem in stratified sampling under realistic survey conditions, where only auxiliary variables are available. Seven optimization algorithms are compared: integer programming (IPA), Bethel's algorithm (BA), generalized simulated annealing algorithm (GSAA), constrained optimization by linear approximations (COBYLA), particle swarm optimization (PSO), biased random key genetic algorithm (BRKGA), and differential evolution optimization (DEO). For the first time, several of these algorithms are applied to this problem and systematically evaluated through numerical analysis using both artificial and real survey data. To ensure fair and effective comparisons, optimal hyperparameter values are determined for each algorithm via structured grid search.The performance of each method is assessed not only by accuracy in attaining the global minimum sample cost but also through a detailed computational efficiency analysis – measuring runtime, memory usage, and convergence behavior. IPA consistently achieves the global minimum, while DEO proves to be the most effective approximation method in terms of accuracy and stability, followed closely by BRKGA and PSO. Additionally, the study explores the impact of skewed distributions and weak correlations between auxiliary and study variables, which significantly increase the required sample sizes, whereas normally distributed variables and strong correlations improve allocation efficiency.Furthermore, the study incorporates a robust approach to handling multivariate outliers in auxiliary data using the Isolation Forest algorithm. This pre-processing step improves allocation robustness and cost-efficiency, albeit with a moderate trade-off in estimator precision. Overall, the findings highlight the critical role of auxiliary variable quality and establish DEO as a strong, practical alternative for multivariate stratified sampling under complex survey conditions.
Pumputis et al. (Mon,) studied this question.