发表机构
The University of Texas at Dallas（德克萨斯大学达拉斯分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对多空中威胁的多拦截器分配问题，严格证明均匀分配策略A优于随机分配策略B且为最优策略，该结论在拦截器数量不少于或少于威胁数量时均成立。
AI 中文摘要
本文研究多枚相同拦截器对多枚相同空中威胁的分配问题，所有拦截器均以齐射方式发射。针对该问题，文献中已研究两种策略：策略A为将所有拦截器尽可能均匀分配给所有威胁；策略B为将所有拦截器随机分配给各威胁。本文主要贡献如下：其一，文献中存在经验证据表明，当拦截器数量不少于威胁数量时，策略A在漏检威胁的均值数量方面比策略B更高效，本文对该结论给出严格证明；其二，通过数值计算表明，策略A的效率可显著高于策略B；其三，本文证明策略A不仅优于策略B，还是真正的最优策略；最后，本文证实上述结论在拦截器数量少于威胁数量时同样成立。
英文摘要
This article investigates the problem of assigning multiple identical interceptors over multiple identical aerial threats, where all interceptors are launched in a single salvo. For this problem, two strategies have been studied in the literature: (A) to spread all interceptors as evenly as possible over all threats, and (B) to randomly assign all interceptors over the threats. The main contributions of this article are as follows. First, the literature contains empirical evidence that Strategy A is more efficient than Strategy B in terms of the mean number of missed threats, when the number of interceptors is no less than the number of threats. This article gives a rigorous proof of this fact. Secondly, it demonstrates numerically that Strategy~A can be significantly more efficient than Strategy B. Thirdly, it shows that Strategy~A is not only superior to Strategy B, but also the bona fide optimal strategy. Finally, this article establishes that these conclusions also hold when the number of interceptors is less than the number of threats.
