求解输出为有界随机数的排序择优问题

目的/意义排序择优问题是仿真优化领域的经典研究问题。该问题的目标是设计统计采样算法，通过在有限个统计分布中进行采样并观测随机采样结果从而找到真实均值最大的分布。在该问题的研究中，现有文献大多假设对不同分布进行采样时输出为正态分布随机数，进而基于正态分布随机数相关性质进行算法设计。但在现实中，该假设通常不成立，一旦假设不成立，现有算法的统计有效性将会大受影响。设计/方法将正态假设进行拓展，即假设对不同分布为有界域分布，进而开展算法设计。结论/发现设计出一类顺序淘汰式算法求解输出为有界域随机数的排序择优问题，数值实验验证，此算法效率远高于现有的SE、ME和lil′DCB算法。

Review on ranking and selection: a new perspective

[Purpose/Significance] Ranking and selection is a fundamental research problem in the area of simulation optimization. The problem aims to select the statistical population with the largest mean from a finite set of statistical populations by taking samples and observing the random outputs. In the existing literature, while designing procedures to solve the problem, one often assumes that the outputs follow normal distributions and develop procedures based on the statistical properties of normal random variables. However, in practice, the normality assumption on the outputs may sometimes fail to hold. Once the normality assumption is violated, a procedure’s finite-time statistical validity may no longer hold. [Design/Methodology] To overcome this issue, this paper focuses on solving the problem where the outputs are drawn from bounded distributions and develop a fully-sequential procedure. [Conclusions/Findings] A class of sequential elimination algorithms is designed to solve the ranking problem where the output is a random number with bounded domain, and numerical experiments verify that the efficiency of this paper is much higher than the existing SE, ME and lil′DCB algorithms.