摘要
综合考虑物品数量以及列容量约束,将隐藏成本与检查概率引入支付函数.建立一种新的多约束的网格检查对策模型.根据矩阵对策性质及Holder不等式,将对策论问题转化为非线性整数规划问题.提出一个基于遗传算法的模型求解方法,将归一化处理得到的变量进行二进制编码,通过数据变换将问题转化为无约束问题,采用轮盘赌选择、多点交叉及单点变异操作求解模型.仿真结果表明了模型及所提算法的有效性.
Considering the constraints such as the quantities of objects and the capacity of each column,and introducing hidden costs and the inspection probability into the payoff function,the inspection game model on a lattice under the constraints of multiple factors was established.According to properties of the matrix game and Holder inequality,the game theory problem was transformed into a nonlinear integer programming problem.A genetic algorithm based method of solving the model was proposed,in which a binary encoding method for variables after normalization processing was designed and the problem was transferred to an unconstrained one through data transformation,and thus the roulette wheel selection method,multi-point crossover and single point mutation can be used to solve the model.The simulation results showed the effectiveness of the model and the proposed algorithm.
作者
张建军
赵玉亮
王玉琢
ZHANG Jian-jun;ZHAO Yu-liang;WANG Yu-zhuo(Department of Basic Courses Teaching,Naval University of Engineering,Wuhan 430033,China)
出处
《数学的实践与认识》
北大核心
2018年第24期195-202,共8页
Mathematics in Practice and Theory
基金
国家自然科学基金(71171198)
海军工程大学基础部自然科学基金(HGDJCB17ZK001)
关键词
网格检查对策
多重约束
非线性整数规划遗传算法
HOLDER不等式
Inspection game on a lattice
Multi-constraints
Nonlinear integer programming
Genetic algorithm
Holder inequality