搜索路径给定时的搜索对策问题及其应用

Search Game and Application When a Search Path Given

搜索路径给定时的最优搜索方案问题,也可以理解为是关于搜索者和目标的二人对策问题,主要讨论了当搜索路径给定时的单个搜索者和单个目标的搜索对策问题。首先根据问题的特点,利用动态规划和迭代的方法,确定关于目标逃逸路径混合策略的最优分区,证明该分区是多面体凸集;针对目标不同逃逸路径的分区,求出搜索者的最大期望收益,再将问题转化为二人有限零和对策,计算出搜索者的支付矩阵,确定最优搜索策略。最后结合海军护航行动,对我舰载直升机搜索小型海盗船进行分析和计算,说明搜索路径给定时的最优搜索对策对于双方的资源分配和提高搜索效率具有一定的应用价值。

A searcher is given a search path in advance and a target selects a path from someoptions.In this paper we consider the search problem,describe our model and formulate it.Based on thetwo-person zero-sum strategies and the search theory,we discuss the search game with a singlesearcher and a single target when the search path is given in advance.The target selects an escape pathfrom some options.Firstly,according to the characteristics of the problem,using the dynamicprogramming and the iterative approach,the searcher gains a value on the detection of the target butexpends search cost by the look.A pay-off function of the game for the searcher is the expected rewardwhich is defined as the expected value minus the expected search cost.Then the most optimal searchstrategy is determined.Finally,the method is combined with the helicopter searching the small pirateships in the naval practical action,the study results do have the military application value for resourcedistribution and improving searching effectiveness.