混合均衡问题和不动点问题的公共元的迭代算法

在Hilbert空间中,利用超梯度算法,用以逼近混合均衡问题的解集与半压缩映像不动点集的公共元,并且证明了该算法的收敛性。使用新的分析技巧证明了一个强收敛定理。     

上、下半连续性关系及其在经济上的应用

上、下半连续性在数学中的重要性不言而喻,在微观经济分析中也有着广泛应用,特别是静态优化问题。分别在单值映射、集值映射中探讨了上半连续性和下半连续性的关系。先证明了单值映射上、下半连续性等价的结论(定理1),并利用引理1对常见函数的上、下半连续性进行了探讨以进一步说明定理1;然后通过举反例进行论证,得出了集值映射中上、下半连续性不等价的结论(定理2);最后例举了上、下半连续性在数理经济上的应用,具有创新价值。通过对数理经济学中参数约束最优化问题的最大值定理(引理2)条件和结论所做的两点注记,并附以具体实例予以解释,说明了单、集值映射中上、下半连续性的关系,以及在数理经济上的重要应用。     

模糊优选动态规划在稀缺军事资源配置中的应用

在对稀缺军事资源配置问题进行数学描述的基础上,建立起评价指标相对优属度计算模型,实现了局部优选。在此基础上,通过分配目标综合评价模型实现了对局部优选数据的综合处理,最后建立资源分配的动态规划模型实现了对方案的优选。最后通过实例演示了解决该类问题的具体方法和步骤,对部队建设具有一定的参考和应用价值。     

有人机—无人机群协同空战目标分配算法

针对有人机—无人机群协同空战目标分配问题,运用离散粒子群算法,分为1架UCAV分配1个目标,1架UCAV分配2个目标时不考虑攻击先后影响和考虑攻击先后影响3种情况进行了仿真研究,提出了一种新的粒子构造方法。综合考虑空战能力指数和优势函数,构造了收益风险矩阵和多目标分配的代价函数。仿真结果具有良好收敛性,对有人机—无人机群协同空战目标分配具有参考价值。     

A generalized assignment model for dynamic supply chain capacity planning

We consider a generalization of the well‐known generalized assignment problem (GAP) over discrete time periods encompassed within a finite planning horizon. The resulting model, MultiGAP, addresses the assignment of tasks to agents within each time period, with the attendant single‐period assignment costs and agent‐capacity constraint requirements, in conjunction with transition costs arising between any two consecutive periods in which a task is reassigned to a different agent. As is the case for its single‐period antecedent, MultiGAP offers a robust tool for modeling a wide range of capacity planning problems occurring within supply chain management. We provide two formulations for MultiGAP and establish that the second (alternative) formulation provides a tighter bound. We define a Lagrangian relaxation‐based heuristic as well as a branch‐and‐bound algorithm for MultiGAP. Computational experience with the heuristic and branch‐and‐bound algorithm on over 2500 test problems is reported. The Lagrangian heuristic consistently generates high‐quality and in many cases near‐optimal solutions. The branch‐and‐bound algorithm is also seen to constitute an effective means for solving to optimality MultiGAP problems of reasonable size. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

基于不完全信息空战的火力分配建模与应用

为了解决不完全信息空战中的火力分配问题,分析了常规空战火力分配模型,指出了其中的不足,建立了一种改进的火力分配模型。针对不完全信息空战特点,给出了其中关键参数的确定方法。该改进模型可有效利用战机在不完全信息条件下容易获取的有限参数进行火力分配,具有很强的实用性。最后通过典型应用实例验证了模型的有效性。     

A mathematical programming approach for improving the robustness of least sum of absolute deviations regression

This paper discusses a novel application of mathematical programming techniques to a regression problem. While least squares regression techniques have been used for a long time, it is known that their robustness properties are not desirable. Specifically, the estimators are known to be too sensitive to data contamination. In this paper we examine regressions based on Least‐sum of Absolute Deviations (LAD) and show that the robustness of the estimator can be improved significantly through a judicious choice of weights. The problem of finding optimum weights is formulated as a nonlinear mixed integer program, which is too difficult to solve exactly in general. We demonstrate that our problem is equivalent to a mathematical program with a single functional constraint resembling the knapsack problem and then solve it for a special case. We then generalize this solution to general regression designs. Furthermore, we provide an efficient algorithm to solve the general nonlinear, mixed integer programming problem when the number of predictors is small. We show the efficacy of the weighted LAD estimator using numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

结构振动系统的模态解耦控制

基于特征结构配置的参数化结果,给出了实现结构振动系统模态解耦的充要条件,导出了期望的反馈增益阵及闭环特征向量矩阵的全体参数化表示。该方法在实现模态解耦的同时,还提供了全部自由度,可用来实现系统设计中某些性能要求。该方法直接基于原系统的参数矩阵,便于工程应用。三级质量弹簧系统的实例表明该方法有效。     

货郎担问题新算法

将指派问题的匈牙利解法用于货郎担问题,通过恰当地添加大正数构造效率矩阵,得到了计算货郎担问题较快的算法。文中给出的2个例子具体地说明了算法实施过程,该算法具有一定的实用性。     

作战指挥工作流程建模方法

针对作战指挥工作流程的建模与仿真研究较少的现状,采用了基于高级Petri网的建模方法。首先在企业相关概念定义基础上,对建模对象———作战指挥工作流程进行了定义,简要介绍了Petri网建模方法的特点以及对基本Petri网的扩展,举例说明了4种过程机制映射到Petri网上的方法,提出结合树状组织结构图和资源管理表的方法扩展Petri网库所容量的含义及管理机制。