AI 中文总结
针对固定入样概率下最均衡抽样设计的组合难题，提出基于遗传算法的启发式方法，可显著提升均衡性，适用于调查抽样与实验设计。
AI 中文摘要
均衡抽样旨在选取随机样本，使得辅助变量的估计总量（由入样概率的倒数加权）尽可能接近已知的总体总量。尽管已提出拒绝抽样、再随机化、立方方法等多种提升均衡性的方法，但在固定入样概率下识别最均衡的抽样设计仍是具有挑战性的组合问题。该问题可被表述为定义在所有可能样本集合上的线性规划，但样本数量随总体规模呈指数增长，仅在总体极小时 exact optimization（精确优化）才可行。为解决此问题，我们提出一种基于遗传算法的启发式方法，通过将最小支持设计与高均衡性候选样本相结合，迭代改进抽样设计的均衡性。虽无法保证最优性，但该方法相较于立方方法等标准程序可显著提升均衡性，且适用于调查抽样与实验设计。
英文摘要
Balanced sampling aims to select random samples in which the estimated totals of the auxiliary variables, weighted by the inverse of the inclusion probabilities, correspond as closely as possible to the known population totals. While several methods, such as rejective sampling, rerandomization, and the cube method, have been proposed to improve balance, identifying the most balanced sampling design under fixed inclusion probabilities remains a challenging combinatorial problem. This problem can be formulated as a linear program defined over the set of all possible samples, but the number of samples grows exponentially with population size, making exact optimization infeasible except for very small populations. To address this issue, we propose a heuristic approach based on a genetic algorithm that iteratively improves the balance of sampling designs by combining minimum support designs with highly balanced candidate samples. Although optimality cannot be guaranteed, the proposed method can substantially improve balance relative to standard procedures such as the cube method. The approach is applicable to both survey sampling and experimental design.
