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An optimisation algorithm applied to the one-dimensional stratification problem

机译：一种应用于一维分层问题的优化算法

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摘要

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：本文介绍了解决一维最优分层问题的新算法，这减少了仅确定层面边界。当STRATA H和总样本大小N的数量是固定时，通过最小化分层变量的总估计器的方差来获得层边界。该算法使用偏置随机键遗传算法（BRKGA）Metaheuristic来搜索最佳解决方案。在适度的计算时间内，已显示这种成交型态度在许多优化问题中产生了良好的质量解决方案。该算法在r封装Stratbr中实现，可从Cran（de Moura Brito，Do Nascimento Silva和Da Veiga，2017a）中。为一组27种群体提供了数值结果，使得具有文献中可用的一些竞争方法的新算法的比较。该算法优于基于近似的近似的方法以及基于其他优化的方法。由于Kozak（2004），它还符合基于最佳优化的方法的性能。它的主要优势在Kozak的方法中是通过De Moura Brito提出的最佳分配，Do Moura Brito，Do Nascimento Silva，Silva Semaan和Maculan（2015）的最佳分配耦合，从而确保如果获得的分层界限实现全球最佳，那么整体解决方案将是分层边界和样品分配的全局最优。

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