A multi‐stage stochastic programming approach for network capacity expansion with multiple sources of capacity

In networks, there are often more than one sources of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spot market capacity, and contract capacity. We use a scenario tree to model the uncertainty, and build a multi‐stage stochastic integer program that can incorporate multiple sources and multiple types of capacities in a general network. We propose two solution methodologies for the problem. Firstly, we design an asymptotically convergent approximation algorithm. Secondly, we design a cutting plane algorithm based on Benders decomposition to find tight bounds for the problem. The numerical experiments show superb performance of the proposed algorithms compared with commercial software. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 600–614, 2017     

基于双层规划的通信干扰兵力部署优化

投掷式通信干扰机是未来通信对抗装备发展的一种趋势,针对其压制无线战术通信的兵力部署优化问题,引入"通信干扰压制概率"和"通信干扰效益"两个指标,建立了基于双层规划的兵力部署优化模型,上层规划以整体通信干扰效益最大化为目标,下层为随机机会约束规划,以通信干扰压制概率满足一定置信水平为约束,以干扰机需求量最小化为目标。采用随机模拟、遗传算法和动态规划相结合的混合智能算法求解双层规划模型,并通过算例分析验证了模型的有效性。     

基于贝叶斯混合博弈的空袭火力资源分配决策模型

从博弈论的角度出发研究空袭火力资源的分配问题,针对空袭编队和防空火力单元攻防对抗过程中存在的不确定性、静态性以及动态性,建立基于贝叶斯混合博弈的空袭对抗火力分配模型。通过构造贝叶斯混合博弈树,采用逆向回溯法分别建立不同的博弈分析模型,利用混合粒子群算法求解那什均衡。仿真结果表明:以博弈论为背景研究空袭作战火力分配问题,符合真实的作战坏境,有效性好,有较高的理论应用价值。     

带优先级的单类型航空弹药转运多目标规划模型

针对航母航空弹药转运过程非常复杂、涉及设备多、要求高的特点,在对其流程进行细致分析的基础上,将其抽象为一个两阶段多目标规划问题。同时,深入分析了转运过程中的各种约束条件、构建了该问题的两阶段优化模型。建模时,不仅考虑了武器升降机的有效利用、弹药量的合理分配等因素,还考虑了转运时对于不同类型弹药转运优先级与停机区弹药需求优先级的要求。通过模型优化,在满足转运优先级要求的基础上,能有效提高航空弹药的转运效率。     

基于多Agent无人机协同侦察任务规划模型

建立了多无人机协同侦察任务规划模型,在考虑侦察时间间隔约束和目标载荷需求基础上,给出了位于不同基地的无人机优化部署和调度策略,并提出了基于多Agent的优化搜索仿真算法,利用Matlab实现了无人机优化配置和任务规划模型,得出了无人机优化配置和任务规划方案,最后分析了模型算法存在的某些不足,提出了模型改进的方向。     

合成分队双层主从决策模型研究

针对合成分队不同指挥层级之间的决策交互优化问题,提出了基于主从决策的双层武器目标分配模型。该模型能够体现上下指挥层级之间交互式决策协调优化的特点:上层目标为主攻方向我方遭受威胁最小,下层目标为对敌打击最大。结合合成分队作战决策的特点和要求,提出了一种求解该模型的改进型粒子群优化算法。仿真结果表明,该模型合理有效,改进的求解算法能够获得满意解。     

适用于认知无线传感器网络的高效频谱分配方法

广泛工作在ISM(Industrial,Scientific and Medical)频段的无线传感器网络面临严重的频谱稀缺问题。在无线通信中,动态频谱分配被认为是提高频谱效能的重要途径。针对典型集中式管理的认知无线传感器网络设计了基于图着色结合负载强度的高效频谱分配算法。首先在协议干扰模型下确保频谱资源在空间上充分利用,随后综合考虑节点负载强度与公平性建立优化模型并按照乘子法加拟牛顿法框架求解最优值。仿真实验表明算法与固定频谱分配方式和传统自适应频谱分配算法相比,在系统吞吐量和节点缓冲区队列长度两个关键性能指标上具有显著优势。     

Analytic solution for the nucleolus of a three‐player cooperative game

The nucleolus solution for cooperative games in characteristic function form is usually computed numerically by solving a sequence of linear programing (LP) problems, or by solving a single, but very large‐scale, LP problem. This article proposes an algebraic method to compute the nucleolus solution analytically (i.e., in closed‐form) for a three‐player cooperative game in characteristic function form. We first consider cooperative games with empty core and derive a formula to compute the nucleolus solution. Next, we examine cooperative games with nonempty core and calculate the nucleolus solution analytically for five possible cases arising from the relationship among the value functions of different coalitions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

An integer decomposition algorithm for solving a two‐stage facility location problem with second‐stage activation costs

We study a stochastic scenario‐based facility location problem arising in situations when facilities must first be located, then activated in a particular scenario before they can be used to satisfy scenario demands. Unlike typical facility location problems, fixed charges arise in the initial location of the facilities, and then in the activation of located facilities. The first‐stage variables in our problem are the traditional binary facility‐location variables, whereas the second‐stage variables involve a mix of binary facility‐activation variables and continuous flow variables. Benders decomposition is not applicable for these problems due to the presence of the second‐stage integer activation variables. Instead, we derive cutting planes tailored to the problem under investigation from recourse solution data. These cutting planes are derived by solving a series of specialized shortest path problems based on a modified residual graph from the recourse solution, and are tighter than the general cuts established by Laporte and Louveaux for two‐stage binary programming problems. We demonstrate the computational efficacy of our approach on a variety of randomly generated test problems. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

A partial characterization of the optimal ordering/rationing policy for a periodic review system with two demand classes and backordering

We consider a finite horizon periodic review, single product inventory system with a fixed setup cost and two stochastic demand classes that differ in their backordering costs. In each period, one must decide whether and how much to order, and how much demand of the lower class should be satisfied. We show that the optimal ordering policy can be characterized as a state dependent (s,S) policy, and the rationing structure is partially obtained based on the subconvexity of the cost function. We then propose a simple heuristic rationing policy, which is easy to implement and close to optimal for intensive numerical examples. We further study the case when the first demand class is deterministic and must be satisfied immediately. We show the optimality of the state dependent (s,S) ordering policy, and obtain additional rationing structural properties. Based on these properties, the optimal ordering and rationing policy for any state can be generated by finding the optimal policy of only a finite set of states, and for each state in this set, the optimal policy is obtained simply by choosing a policy from at most two alternatives. An efficient algorithm is then proposed. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010