Non‐zero‐sum nonlinear network path interdiction with an application to inspection in terror networks

A simultaneous non‐zero‐sum game is modeled to extend the classical network interdiction problem. In this model, an interdictor (e.g., an enforcement agent) decides how much of an inspection resource to spend along each arc in the network to capture a smuggler. The smuggler (randomly) selects a commodity to smuggle—a source and destination pair of nodes, and also a corresponding path for traveling between the given pair of nodes. This model is motivated by a terrorist organization that can mobilize its human, financial, or weapon resources to carry out an attack at one of several potential target destinations. The probability of evading each of the network arcs nonlinearly decreases in the amount of resource that the interdictor spends on its inspection. We show that under reasonable assumptions with respect to the evasion probability functions, (approximate) Nash equilibria of this game can be determined in polynomial time; depending on whether the evasion functions are exponential or general logarithmically‐convex functions, exact Nash equilibria or approximate Nash equilibria, respectively, are computed. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 139–153, 2017     

基于微分对策理论的信息战模型

基于兰彻斯特作战理论,提出了一个新的微分对策模型来研究在交战双方均有信息战系统协助作战的条件下的最优火力分配策略。又运用微分对策理论对该模型进行分析和求解,并对所得到的结论作出符合战术意义的解释。     

相依目标群状态转移概率矩阵的特性及其应用

本文对相依目标群的状态转移概率矩阵的性质进行了深入的分析,得到了若干重要结论,并在此基础上讨论了相依目标群系统的火力分配模型     

遗传算法及其在导弹火力分配上的应用

遗传算法是一种近年来新发展起来的优化算法,目前它已被广泛应用于解决许多实际问题,如函数优化、图像识别、机器学习、人工神经网络、人工生命、优化调度等许多领域。通过对一种遗传算法的研究,阐述其在导弹武器火力分配上的应用。首先设计和实现了一种遗传算法;然后描述了导弹火力分配优化问题,建立了其数学模型;最后运用遗传算法求解了该问题。     

坦克分队在进攻战斗中的最佳火力分配

运用兰切斯特方程和极值理论就坦克分队在进攻战斗中如何分配火力及使火力分配最佳进行了研究。给出了最佳方案的计算方法     

基于AHP和模糊数学的课程评估系统初探

给出课程评估的因素和指标体系,提出模糊数学与AHP相结合进行课程综合评价的原理与方法,使对问题的定性分析与定量分析得到有机结合,评估结果科学合理.     

超高分子量聚碳硅烷的合成及其表征

采用正交设计的方法从常压合成得到的中低分子量PCS出发进行热压合成制备超高分子量PCS;并运用红外、GPC、核磁共振等分析测试手段对其结构和性能进行了表征。研究表明:控制热压反应温度在460~470℃、预加压力1~2MPa、反应6h时得到超高分子量PCS的重均分子量在6400~8500;通过控制热压反应时间可以较好的调控超高分子PCS的分子量大小;热压合成后制得的超高分子量PCS的支化度和Si-H键含量有所降低。     

基于灰色聚类的管道电伴热系统安全评价

虽然管道电伴热系统在国防工业领域有着十分广泛的应用,但在实际使用过程中也经常会出现各种问题.本文针对管道电伴热系统安全性的评价问题,在分析总结管道电伴热系统常见故障的基础上,从系统设计、安装施工、电气连接与操作使用4个方面,选取17个影响因素构建管道电伴热系统安全评价指标体系,通过改进层次分析法计算得到各方案层的权重值...     

高压合成聚碳硅烷的沉淀与复配

研究了沉淀与复配两种调控高压合成聚碳硅烷(PCS)分子量及其分布的方法。研究表明,在PCS的良溶剂(如二甲苯)溶液中加入沉淀剂(如丙酮)比例超过临界点后,PCS中分子量越高的部分越先沉淀出来,从而降低了PCS的软化点、分子量和分散系数,PCS的高、中、低分子量的比例得到调节。复配是将不同分子量分布的PCS均匀地混合在一起,其分子量、软化点和高、中、低各部分的含量基本符合混合率的关系。因此,可以按照混合率来设计所需PCS的软化点、分子量及高、中、低分子含量。     

A specially structured nonlinear integer resource allocation problem

We present an algorithm for solving a specially structured nonlinear integer resource allocation problem. This problem was motivated by a capacity planning study done at a large Health Maintenance Organization in Texas. Specifically, we focus on a class of nonlinear resource allocation problems that involve the minimization of a convex function over one general convex constraint, a set of block diagonal convex constraints, and bounds on the integer variables. The continuous variable problem is also considered. The continuous problem is solved by taking advantage of the structure of the Karush‐Kuhn‐Tucker (KKT) conditions. This method for solving the continuous problem is then incorporated in a branch and bound algorithm to solve the integer problem. Various reoptimization results, multiplier bounding results, and heuristics are used to improve the efficiency of the algorithms. We show how the algorithms can be extended to obtain a globally optimal solution to the nonconvex version of the problem. We further show that the methods can be applied to problems in production planning and financial optimization. Extensive computational testing of the algorithms is reported for a variety of applications on continuous problems with up to 1,000,000 variables and integer problems with up to 1000 variables. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 770–792, 2003.