A Tabu Search Algorithm for the Optimal Stratification Problem

An algorithm to solve the optimal univariate stratification problem is proposed that consistently outperforms competing algorithms in a range of numerical experiments. Here the number of strata L and the sample size n are pre-specified, and the algorithm seeks the boundaries for the strata that minimize the variance of the estimator for the total of the stratification variable, under exact optimal allocation of the sample to the resulting strata. The algorithm combines ideas from the Tabu Search metaheuristic with an exact method for allocating the sample to the strata. Numerical experiments were carried out with 40 populations, varying numbers of strata (6) and sample sizes (2) - yielding a total of $ 40 \times 6 \times 2 = 480 $ 40x6x2=480 scenarios. Our results were compared to those obtained by four competing algorithms, including the well-known algorithm by Kozak and two algorithms based on alternative metaheuristics. The comparison showed that our proposed algorithm outperformed all the competitors considered, producing a high percentage of good-quality solutions.