This paper introduces a heuristic framework for the Best Secretary Problem, where one item must be selected using rank information only. We develop five data-responsive rules extending classical fixed-cutoff methods: an expected-record threshold, an adaptive deviation correction, a probabilistic early-accept rule, a two-phase relaxation, and a local dynamic programming approximation. These rules adjust thresholds sequentially as information accumulates. Simulations across diverse sample sizes, distributions, and autocorrelated settings show that the heuristics match or exceed traditional optimal rules in stability and efficiency. The expected-record rule remains strong despite its simplicity, the adaptive correction performs well under asymmetry, and the adaptive and probabilistic rules reduce average stopping times. An ensemble combining multiple rules yields the most stable performance. Overall, a few intuitive parameters achieve near-optimal results, demonstrating that data-responsive heuristics can effectively extend rank-based optimal stopping to dynamic decision environments.

翻译：本文针对仅依赖排序信息进行单次选择的最佳秘书问题，提出了一种启发式求解框架。我们基于经典固定阈值方法扩展了五种数据响应式规则：期望记录阈值、自适应偏差校正、概率性提前接受规则、两阶段松弛方法以及局部动态规划近似。这些规则能够随着信息积累动态调整决策阈值。通过在不同样本规模、分布类型及自相关场景下的仿真实验表明，所提启发式方法在稳定性与效率方面均达到或超越了传统最优规则。其中期望记录规则虽形式简洁但性能稳健，自适应校正规则在非对称场景下表现优异，自适应与概率性规则有效降低了平均停止时间。融合多种规则的集成策略实现了最优的稳定性表现。总体而言，仅需少量直观参数即可获得接近最优的结果，这证明数据响应式启发式方法能够有效将基于排序的最优停止理论扩展至动态决策环境。