攻防对抗中指数射击策略最优性分析

研究了红蓝攻防对抗中的射击策略优化问题，即研究红方面对多个蓝方目标，如何射击能获得最大收益的问题。基于以往研究的局限性，为平衡红方射击收益和自身存活概率，引入和拓展Gittins指数应用于射击决策问题，考虑了蓝方目标退出战斗的可能性，以红方在自身被摧毁之前最大化杀伤蓝方目标的收益（或数量）为目标，对指数射击策略的最优性进行了讨论，拓展了定理1、定理2，给出推论1. 为进行比较，引入近视策略、完全策略和循环策略3种截然不同的射击策略，并给出近视策略最优性定理3. 实例设置了两个射击场景，在4种射击策略下计算红方的收益情况、杀伤目标情况和自身被摧毁情况，验证了指数射击策略的最优性。

Optimality Analysis of Index Policy for Offense-defense Shooting Process

The index policy for offense-defense shooting process, namely, how a single red shoots at a collection of blue targets to maximize the return obtained from killed blue targets, is discussed. In consideration of the limitations of previous research and the balance of the red’s excepted return and survival probability, Gittins index is introduced and expanded to solve the shooting problems. The optimality of index shooting policy is discussed. Theorem 1 and 2 are extended, and Lemma 1 is presented. Three different shooting policies, such as myopic policy, exhaustive policy and round-robin policy, are introduced for comparison, and the optimality theorem 3 of myopic policy is proposed. 2 shooting scenes are set in numerical study. The red’s mean return, mean numbers of killed blue targets and red’s death rate are calculated for 4 policies. Simulation study outcome verified the optimality of index policy.