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An optimisation algorithm applied to the one-dimensional stratification problem

机译：一维分层问题的优化算法

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This paper presents a new algorithm to solve the one-dimensional optimal stratification problem, which reduces to just determining stratum boundaries. When the number of strata H and the total sample size n are fixed, the stratum boundaries are obtained by minimizing the variance of the estimator of a total for the stratification variable. This algorithm uses the Biased Random Key Genetic Algorithm (BRKGA) metaheuristic to search for the optimal solution. This metaheuristic has been shown to produce good quality solutions for many optimization problems in modest computing times. The algorithm is implemented in the R package stratbr available from CRAN (de Moura Brito, do Nascimento Silva and da Veiga, 2017a). Numerical results are provided for a set of 27 populations, enabling comparison of the new algorithm with some competing approaches available in the literature. The algorithm outperforms simpler approximation-based approaches as well as a couple of other optimization-based approaches. It also matches the performance of the best available optimization-based approach due to Kozak (2004). Its main advantage over Kozak's approach is the coupling of the optimal stratification with the optimal allocation proposed by de Moura Brito, do Nascimento Silva, Silva Semaan and Maculan (2015), thus ensuring that if the stratification bounds obtained achieve the global optimal, then the overall solution will be the global optimum for the stratification bounds and sample allocation.
机译：本文提出了一种解决一维最优分层问题的新算法，该算法简化为仅确定层边界。当层数H的数量和总样本大小n固定时，可通过最小化分层变量的总估计量的方差来获得层边界。该算法使用偏向随机密钥遗传算法（BRKGA）元启发式算法来搜索最佳解。已经证明，这种元启发法可以在适度的计算时间内为许多优化问题提供高质量的解决方案。该算法在可从CRAN获得的R包stratbr中实现（de Moura Brito，dos Nascimento Silva和da Veiga，2017a）。提供了一组27个总体的数值结果，从而可以将新算法与文献中提供的一些竞争方法进行比较。该算法的性能优于简单的基于逼近的方法以及其他几种基于优化的方法。由于Kozak（2004），它也与最佳的基于优化的方法的性能相匹配。与Kozak方法相比，它的主要优势是将最佳分层与de Moura Brito，Nascimento Silva，Silva Semaan和Maculan（2015）提出的最优分配相结合，从而确保如果获得的分层界限达到全局最优，则总体解决方案将是分层边界和样本分配的全局最优。

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