多重因素约束下的网格搜索对策问题研究  

Research on the Problem of Search Games on a Lattice Under The Constraint of Multiple Factors

作　　者：赵玉亮[1] 张建军[1] 宋业新[1] 

机构地区：[1]海军工程大学理学院,湖北武汉430033

出　　处：《数学的实践与认识》2017年第11期135-141,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71171198)

摘　　要：首次基于搜索成本及搜索资源等限制因素,构造局中人面向多重约束条件的可行策略集合,建立相应的搜索空间;在给定搜索点权值的基础上,考虑搜索成本与搜索成功概率等因素,构造相应的支付函数,建立多重因素约束下的网格搜索对策模型.为简化模型求解,将对策论问题转化为约束最优化问题,求解约束问题获得最优值,转化为模型的对策值,并给出双方最优混合策略.最后,给出军事想定实例,说明上述模型的实用性及方法的有效性.Based on the constraints such as search costs and search resources for the firsttime, the feasible strategy sets of the players for multi-constraint were constructed, andthe corresponding search space was established. Considering factors such as search costsand the probability of the successful search with the given weights of search points, thecorresponding payoff function was constructed, and the search game model on a latticeunder the constraints of multiple factors was established. To simplify the model solving, thegame theory problem was transformed into constrained optimization problem. Solving theconstrained optimization ：problem, the optimal value of constrained optimization problemwas obtained and converted into the value of the search game model, and the optimal mixedstrategy was given. Finally, a military example was provided, to illustrate the practicalityand effectiveness of the model. .

关 键 词：搜索对策 网格 搜索资源 搜索成本 搜索成功概率 

分 类 号：O225[理学—运筹学与控制论]