基于遗传算法的武警捕歼战斗兵力优化指派建模与仿真

为进一步提高武警捕歼战斗用兵的精确性和科学性,针对武警捕歼战斗任务实际,考虑作战中队的行军距离、毁伤能力等多个因素,基于多目标规划建立了武警捕歼战斗兵力指派模型.借鉴遗传算法理论提出了两种改进算法,实验仿真结果表明,两种算法都能有效解决武警捕歼战斗的兵力指派问题,研究结果对武警捕歼战斗兵力指派具有一定现实意义.     

基于图论的防空兵力优化配置研究

应用图论将防空系统抽象成二维网络的拓扑结构图,通过指定点对间最小拦截概率的计算,得到防空拓扑图的子图,并应用复杂网络理论,建立了防空节点攻击价值的计算方法.在此基础上设计了防空兵力优化配置算法,给出了能够满足任务要求的兵力配置方案.     

水面舰队建立最佳防空编队的数学模型

防空反导是水面舰艇编队最重要的任务之一,我国南海海域辽阔,水面舰艇执行外围岛礁附近海域巡航任务时,往往超出了空中掩护的作战半径,需要自身的对空防御,这时,水面舰艇的编队阵型至关重要.同时,空中目标意图识别是战场态势分析的一个重要部分.以我海军在南海某开阔海域巡逻的水面舰艇编队为例,探究了最佳编队队形的数学模型,并根据所提供的战场空中目标信息,判断目标可能的意图,为威胁判断、火力分配和抗击来袭目标奠定基础.     

再论集中优势兵力原则

针对兰彻斯特平方定律,并结合现代作战的多目标要求,讨论了集中优势兵力原则中关于“优势”的计算问题,给出了具有实践指导意义和可操作性的计算方法.     

作战时耗指派矩阵取胜指派矩阵兵力耗损指派矩阵的一体构造

指派矩阵构造是指派问题应用研究的难点,在作战应用领域展开指派矩阵构造专题研究.文中回望了1914年Lanchester关于"兰氏"平方律作战过程取胜条件与剩余兵力的分析结果,以及1996年本文第一作者提出的关于"兰氏"平方律作战过程存在胜负的情况下其作战持续时间计算的数学模型,提出了关于"兰氏"平方律作战过程在作战双方势均力敌的情况下作战持续时间的数学模型.综合运用上述的已有理论与新建理论,建立了取胜矩阵、时耗矩阵、兵力耗损矩阵的一体构造模型.该一体构造模型从作战系统的4类可知数据出发,对于具体的多部队参战的作战过程均能构造出具体的取胜、时耗、兵力耗损数值矩阵.最后给出了取胜、时耗、兵力耗损矩阵的一个一体构造实例,并运用(n×m)-k缺省指派问题理论对该实例求得了其最多K胜条件下的最短时限最少耗费缺省指派最优解.     

"兰氏"平方律作战毁伤过程兵力损耗率系数战例求解理论

如何求得著名的“兰氏”平方律战斗动力学方程中双方兵力损耗率系数，这是作战模拟应用研究领域中一个久攻未克的难题。本文提出了以作战结果来逆向研究作战过程中双方兵力损耗率系数的思想。阐述了对于不变的作战双方在相同（相近）的作战环境与作战条件下相继进行的作战序列里，双方各自的兵力损耗率系数不变（波动不大）的公理，论证了揭示作战序列内部规律的两条定理。据此，建立了兵力损耗率系数的战例求解理论与方法。运用这一理论与方法，据以往发生的作战过程其数值特征可以求得未来相似或相同作战过程中双方兵力损耗率系数的具体取值，首次解决了作战模拟研究领域中兵力损耗率系数的具体取值这一难题。     

单兵种对双兵种作战模型

本文讨论了单兵种对双兵种作战的 Lanchester模型 ,分析研究了战斗进程中各方兵力的动态变化 ,给出了单兵种方的最优兵力分配原则 .     

飞行员数量的宏观估计与调控模型

本文提出一种估计与调控飞行员宏观数量的方法.文章给出了当航空兵的兵力规模保持稳定、只考虑飞行员年龄分布的情况下,战斗部队飞行员和航校教员总数量与每年的补充量、淘汰率、服役年限之间的函数关系;给出了当航空兵的兵力规模需要变更时,尽快达到变更目标的数学规划模型,模型考虑了每年的补充量、淘汰率、服役年限以及航校学制、规模和效率之间的关系.     

关于交战原则中的优势兵力问题

关于兰切斯特平方定律的研究很多，但是在目前的资料中基本上没有给出关于交战原则中的优势兵力问题的明确的、定量的解决方法。本根据现代作战的多目标要求，运用军事运筹学理论，在兰彻斯特平方定律和不同作战目的基础之上讨论了集中优势兵力原则中关于“优势”的计算和优化问题，给出了具有实践指导意义和可操作性的计算方法。     

空袭与防空作战的对策分析

假设在局部(常规)战争情况下,攻方要使用轰炸机袭击守方的要地(政治经济中心,交通枢纽等),守方使用高射炮、地空导弹和歼击机进行抗击。双方都知道对方的兵力部署情况(数量和位置)。攻方作为主动作战的一方具有主动权,出动多少兵力袭击何种目标,守方事先是不知道的。但是当攻方飞机出动后守方便可知道其用兵的意图。攻方的最终目的是要炸毁守方的要地。为了达到预期的突击效果而又尽量减少损失,采取如下的作战方针:先出动部分兵力去袭击守方的防空体系,如机场、雷达站和高炮地导阵地,我们称之为第一波次;在守方还来不及处理由于轰炸而造成的后果时(即所谓利用第一波次的突击效果),再出动其余兵力去突击要地,我们称之为第二波次。     

Optimization of air vehicles operations using mixed-integer linear programming

A scenario where multiple air vehicles are required to prosecute geographically dispersed targets is considered. Furthermore, multiple tasks are to be successively performed on each target, that is, the targets must be classified, attacked, and verified as destroyed. The optimal, for example, minimum time, performance of these tasks requires cooperation among the vehicles such that critical timing constraints are satisfied, that is, a target must be classified before it can be attacked, and an air vehicle is sent to a target area to verify its destruction only after the target has been attacked. In this paper, the optimal task assignment/scheduling problem is posed as a mixed-integer linear program (MILP). The solution of the MILP assigns all tasks to the vehicles and performs the scheduling in an optimal manner, including staged departure times. Coupled tasks involving timing and task order constraints are automatically addressed. When the air vehicles have sufficient endurance, the existence of a solution is guaranteed.     

Heterogeneous surface-to-air missile defense battery location: a game theoretic approach

In the context of an air defense missile-and-interceptor engagement, a challenge for the defender is that surface-to-air missile batteries often must be located to protect high-value targets dispersed over a vast area, subject to which an attacker may observe the disposition of batteries and subsequently develop and implement an attack plan. To model this scenario, we formulate a two-player, extensive form, three-stage, perfect information, zero-sum game that accounts for, respectively, a defender’s location of batteries, an attacker’s launch of missiles against targets, and a defender’s assignment of interceptor missiles from batteries to incoming attacker missiles. The resulting trilevel math programming formulation cannot be solved via direct optimization, and it is not suitable to solve via full enumeration for realistically-sized instances. We instead adapt the game tree search technique Double Oracle, within which we embed either of two alternative heuristics to solve an important subproblem for the attacker. We test and compare these solution methods to solve a designed set of 52 instances having parametric variations, from which we derive insights regarding the nature of the underlying problem. Enhancing the solution methods with alternative initialization strategies, our superlative methodology attains the optimal solution for over 75% of the instances tested and solutions within 3% of optimal, on average, for the remaining 25% of the instances, and it is promising for realistically-sized instances, scaling well with regard to computational effort.     

Multiple criteria sorting with a set of additive value functions

We present a new multiple criteria sorting method that aims at assigning actions evaluated on multiple criteria to p pre-defined and ordered classes. The preference information supplied by the decision maker (DM) is a set of assignment examples on a subset of actions relatively well known to the DM. These actions are called reference actions. Each assignment example specifies a desired assignment of a corresponding reference action to one or several contiguous classes. The set of assignment examples is used to build a preference model of the DM represented by a set of general additive value functions compatible with the assignment examples. For each action a, the method computes two kinds of assignments to classes, concordant with the DM’s preference model: the necessary assignment and the possible assignment. The necessary assignment specifies the range of classes to which the action can be assigned considering all compatible value functions simultaneously. The possible assignment specifies, in turn, the range of classes to which the action can be assigned considering any compatible value function individually. The compatible value functions and the necessary and possible assignments are computed through the resolution of linear programs.     

On assignment functions

We define a class of functions called assignment functions, one of which is the permanent function. These functions evaluated at matrices of 0's and 1's are shown to be of applied and combinational interest. We define assignment polytopes which generalize the classical assignment polytope and use them to obtain bounds for the assignment function. We propose the determination of the minimum and maximum value of an assignment function on its corresponding assignment polytope and conjecture that the maximum value is 1. A natural conjecture for the minimum value is shown to be false. The minimum and maximum value are determined for special assignment functions.     

快递企业航空货运网络的构建

快递业竞争激烈,构建高效合理的航空货运网络是快递企业提高竞争力的重要手段。“枢纽—辐射”式航空货运网络是整合航空快递资源、提高航空快递资源利用效率、提高快递企业竞争力的有效模式。本文以降低航空快递网络成本、加快航空快递处理时间为目标,从航空快递网络枢纽的选取、指派关系的确定、枢纽个数的选择三个方面研究了航空快递网络模型建立问题,选用遗传算法求解不同枢纽个数下航空快递网络的运输成本,并据此进行枢纽的选取,运用重力模型法进行指派关系的确定,在此基础上运用超效率DEA模型确定枢纽个数。接着,以包含17个节点的顺丰航空快递网络的规划为例,对本文所提出的模型和算法进行了验证,验证结果证实了模型的合理性。本文的研究为快递企业构建航空货运网络提供了科学实用的方法,该方法的使用可以降低航空货运成本,提高效率,从而提高快递企业的竞争力。     

基于Solidarity值的河流水资源分配

河流水资源分配问题可以抽象为图限制下合作对策解的模型.基于图限制下合作对策的Solidarity值对参与者的收益分配进行分析,构造了Solidarity值的结构,给出了该值的分支有效性等四个性质,并利用这四个性质刻画了Solidarity值的唯一性.最后通过一个简单的实例,证明了河流水资源分配问题中,基于Solidarity值的收益分配比Myerson值更优.     

基于仿真的空中进攻战斗效能评估方法研究

通过分析空中进攻战斗的概念定义、兵力编成和过程阶段,构建空中进攻战斗仿真模型,从多次仿真结果中选取战斗效能指标,对效能指标进行简化和标准化处理后,建立空中进攻战斗效能指标体系,在此基础上构建效能指标矢量空间模型和效能优势参数模型,并根据模型对效能指标进行优化分析,最后结合实际算例得出结论.     

Comparative performance of tabu search and simulated annealing heuristics for the quadratic assignment problem

For almost two decades the question of whether tabu search (TS) or simulated annealing (SA) performs better for the quadratic assignment problem has been unresolved. To answer this question satisfactorily, we compare performance at various values of targeted solution quality, running each heuristic at its optimal number of iterations for each target. We find that for a number of varied problem instances, SA performs better for higher quality targets while TS performs better for lower quality targets.     

On the expected optimal value of random assignment problems: Experimental results and open questions

In the paper, we study the expected optimal value of random linear assignment problems, whose data are random variables with the uniform and the exponential distributions. An interior point approach is used to solve large-scale dense assignment problems with size up to 10,000 nodes and 100 million edges. Our computational results indicate the validity of a long-standing conjecture about the limiting value of the expected optimal assignment. Some interesting open problems and extensions are discussed.