BRKGA ALGORITHM APPLIED TO THE UNIVARIATE STRATIFICATION PROBLEM

Official statistical agencies conduct surveys using complex designs that combine sampling techniques. Sample design must reconcile effectiveness and efficiency, related respectively to estimate quality and optimizing resources such as time and budget. Stratified sampling can improve precision at lower cost while ensuring population representation. In this method, a population is divided into H mutually exclusive and exhaustive strata, defined by H-1 cutoff points on a stratification variable, from which samples are selected. A key challenge is determining these points to ensure internal homogeneity within strata and thereby reduce total variance. This task, known as the optimal stratum boundaries problem, has high computational complexity. Despite its relevance, few methods jointly address stratum boundaries and optimal sample allocation. Existing approaches often rely on simple heuristics and remain limited to local optima of moderate quality. To address this gap, this study proposes an algorithm based on the Biased Random-Key Genetic Algorithm (BRKGA) metaheuristic. BRKGA represents solutions as random keys, which a problem-specific decoder transforms into feasible solutions. The proposed decoder constructs the strata, determines cutoff points, and enables sample allocation. The algorithm was implemented using a specialized BRKGA package that provides the framework, allowing development to focus on problem modeling and decoder design. Computational experiments were conducted with 20 populations, comparing the proposed algorithm with a method from the literature. Based on solution quality in terms of variance, results show that the algorithm is a competitive alternative for stratification and produces quality solutions.