多重因素约束下的网格检查对策问题研究  

Research on the Problem of Inspection 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15期202-209,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71171198)

摘　　要：基于物品数量及每列容量等限制因素,构造局中人的可行策略集合;考虑隐藏成本,处罚规则与检查成功概率等因素,构造相应的支付函数,建立多重因素约束下的网格检查对策模型.根据矩阵对策性质,将对策论问题转化为非线性整数规划问题,利用H(o|¨)lder不等式获得实数条件下的规划问题的解,然后转化为整数解,得到特定条件下的模型的对策值及局中人的最优混合策略.最后,给出一个实例,说明上述模型的实用性及方法的有效性.Based on the constraints such as the quantity of objects and the capacity of each column, the feasible strategy sets of the players were constructed. Considering factors such as hidden costs, the rules of punishment and the probability of the successful inspection, the corresponding payoff function was constructed, and so the inspection game model on a lattice under the constraints of multiple factors was established. According to property of the matrix game, the game theory problem was transformed into nonlinear integer programming. By using Holder inequality the solution of programming under the condition of real numbers was obtained and then converted into integral solution, the value of the search game model and the optimal mixed strategies under given conditions were obtained. Finally, an example was provided to illustrate the practicality and effectiveness of the model.

关 键 词：网格检查对策 多重约束 非线性整数规划 HOLDER不等式 

分 类 号：O225[理学—运筹学与控制论]