Limiting behavior of the stochastic sequential assignment problem

The stochastic sequential assignment problem (SSAP) considers how to allocate available distinct workers to sequentially arriving tasks with stochastic parameters such that the expected total reward obtained from the sequential assignments is maximized. Implementing the optimal assignment policy for the SSAP involves calculating a new set of breakpoints upon the arrival of each task (i.e., for every time period), which is impractical for large‐scale problems. This article studies two problems that are concerned with obtaining stationary policies, which achieve the optimal expected reward per task as the number of tasks approaches infinity. The first problem considers independent and identically distributed (IID) tasks with a known distribution function, whereas in the second problem tasks are derived from r different unobservable distributions governed by an ergodic Markov chain. The convergence rate of the expected reward per task to the optimal value is also obtained for both problems. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

A three‐stage procurement optimization problem under uncertainty

This article examines a problem faced by a firm procuring a material input or good from a set of suppliers. The cost to procure the material from any given supplier is concave in the amount ordered from the supplier, up to a supplier‐specific capacity limit. This NP‐hard problem is further complicated by the observation that capacities are often uncertain in practice, due for instance to production shortages at the suppliers, or competition from other firms. We accommodate this uncertainty in a worst‐case (robust) fashion by modeling an adversarial entity (which we call the “follower”) with a limited procurement budget. The follower reduces supplier capacity to maximize the minimum cost required for our firm to procure its required goods. To guard against uncertainty, the firm can “protect” any supplier at a cost (e.g., by signing a contract with the supplier that guarantees supply availability, or investing in machine upgrades that guarantee the supplier's ability to produce goods at a desired level), ensuring that the anticipated capacity of that supplier will indeed be available. The problem we consider is thus a three‐stage game in which the firm first chooses which suppliers' capacities to protect, the follower acts next to reduce capacity from unprotected suppliers, and the firm then satisfies its demand using the remaining capacity. We formulate a three‐stage mixed‐integer program that is well‐suited to decomposition techniques and develop an effective cutting‐plane algorithm for its solution. The corresponding algorithmic approach solves a sequence of scaled and relaxed problem instances, which enables solving problems having much larger data values when compared to standard techniques. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

不完全信息下军事威逼讨价还价博弈分析

在详细分析威慑与威逼区别的基础上,构建了不完全信息下军事威逼讨价还价博弈模型。按照最大期望效用准则,分析了不完全信息下军事威逼走向讨价还价阶段的条件,研究表明:运用鲁宾斯坦经典讨价还价唯一完美均衡解,得出以下结论:争夺目标自身的效用越大,战争带来的声誉得益效用越大,军事威逼走向讨价还价阶段的可能性越大;一旦进入讨价还价阶段,威逼者会接受挑战者提出的方案,冲突将不再发生。     

基于Multi-Agent的航空集群系统重构机理研究

集群作战是未来空中作战的主要样式,其重构机理的研究对于提升航空集群执行任务的整体性能以及在遭受攻击时的生存能力具有重要作用。从作战任务层面出发,对集群系统重构的定义以及类型、触发机制和基本原则进行了分析阐述;借鉴博弈论理论,将航空集群系统分布式重构问题映射为多Agent之间的合作-竞争问题,建立了基于Multi-Agent的系统重构模型,给出了重构的流程与算法,为航空集群系统自适应重构能力的设计实现提供了理论技术支持。     

双机空战的仿真与分析

用矩阵博弈理论、计算机仿真的方法研究了空战过程,使双机的空中格斗阶段─目标的跟踪、射击、弹道计算及射击效果的评定连续化,并用ＦＯＲＴＲＡＮ─７７语言编程在计算机上进行了Ｆ＿Ａ、Ｆ＿Ｂ两种飞行的空战,仿真结果与实际情况基本一致。本程序具有通用性,可对不同种类的飞机及武器系统的性能作出定性和定量的分析和评估。     

军民融合产业创新集群的形成

在军民融合发展战略与创新驱动发展战略深入推进进程中,军民融合产业创新集群成为军民融合产业发展的重要创新形式,其形成问题研究更是对其发展与演化具有重要影响。以军民融合产业创新集群的内涵着手,通过刺激—反应模型与演化博弈模型,分析其形成过程与促进措施。研究表明,军民融合产业创新集群作为复杂适应系统,创新主体的适应性能力及其内在关系是集群形成的关键所在;为使合作创新行为成为演化博弈的稳定策略,从合作创新能力系数和合作创新成本、拥有的创新资源以及政府资金支持三个方面剖析集群形成的促进作用,对军民融合产业创新集群的发展与演化研究奠定基础。     

序列近似优化方法及其在火箭外形快速设计中的应用

针对序列近似优化方法在代理模型构造与采样策略等方面的不足,基于采样点局部密度,引入与局部密度成反比的样本点影响体积概念,通过优化总影响体积确定径向基函数最优核宽度,满足序列近似优化过程不同规模、非均匀样本条件下的函数近似需要;建立潜在可行域最大距离加点准则,并与潜在最优加点准则结合平衡算法的探索能力与开发能力;建立三步收敛判定准则;构建改进序列近似优化的算法流程。对于Golinski减速器的优化设计问题,算法在目标函数调用42次后便搜索到全局最优解,体现了其良好的全局寻优能力与搜索效率。以"天航二号"火箭为例,建立其外形优化问题数学模型,所提优化方法在调用原始计算模型165次之后便搜索到全局最优解,大大提高了设计效率,同时飞行试验也表明设计结果满足要求。     

攻击主动防御飞行器的微分对策制导律

基于微分对策理论设计了躲避护卫弹的同时攻击飞行器的制导律。根据传统的性能指标推导了该场景的微分对策制导律,并且根据权重系数的取值定义了三种制导律:最优追赶制导律、逃脱-追赶制导律和复合制导律。最优追赶制导律容易被护卫弹拦截,逃脱-追赶制导律容易造成导弹和飞行器的零控脱靶量急剧增大而使得攻击失败,复合制导律很难选择合适的权重系数。针对以上不足,提出了两种改进的制导律,并对该两种制导律的适用情况进行了分析。通过非线性模型仿真,验证了这两种方法的可行性。该两种制导律目的性强,攻击导弹可以躲避护卫弹进而攻击飞行器。     

一种基于博弈论的无线网状网络路由与信道分配联合优化算法

无线网络中的路由与信道分配可极大地影响网络的性能.为了解决无线网状网络中的路由与信道分配问题,提出并研究了一种称为CRAG(基于博弈论的无线网状网络路由与信道分配联合优化)的方法.CRAG采用协同博弈的方式将网络中的每个节点模型化为一个弈者,每个弈者的策略为与其相关的路由与信道分配方案,收益函数为给定流量需求矩阵下的成功传输流量.弈者通过协同博弈来优化收益函数以最大化网络的吞吐量.基于NS3的仿真结果表明,CRAG在收敛性、时延、丢包率和吞吐量方面优于其他当前的算法,从而证明了协同博弈的方法可以用于无线网状网络的路由与信道分配联合优化,并有效地改进网络性能.     

军事攻防中的多属性资源分配对策模型

针对资源受限情形下的两阶段攻防资源分配问题,提出一种基于多属性决策的资源分配对策模型。防守者首先将有限的防护资源分配到不同的目标上,继而进攻者选择一种威胁组合方式对目标实施打击。基于博弈论相关知识,模型的求解结果可以使防守者最小化自身损失,使进攻者最大化进攻收益。同时,针对模型的特点,给出了一些推论和证明。通过一个示例验证了模型的合理性以及相关推论的准确性,能够为攻、防双方规划决策提供辅助支持。