线性规划优化分析的元模型方法及其比较

线性规划优化分析在经济管理等领域有着广泛的应用。当线性规划约束条件的右端向量在一定范围内变化时,目标函数的最优值是右端向量的一个复杂的分片线性函数,但通常难以给出分析表达式。应用多项式回归、径向基函数、Kriging法及多项式回归 Kriging法这四种元模型方法,能快速预测最优值函数。通过仿真实验,对这四种形式的元模型作较全面的比较分析。数值实验的结果表明,用次数较少的实验设计,后三种方法都具有较高的拟合精度;特别地,多项式回归 Kriging法不仅拟合精度高,而且还能用一个二阶多项式给出最优值函数的一个简明的近似描述。结果表明,元模型方法是研究线性规划优化分析问题的有效途径。     

一类复变函数问题的统一解法

本文通过具体例子阐述了一类复变函数问题的统一解法,而且简单易行。     

A stochastic assignment problem

There are n boxes with box i having a quota value Balls arrive sequentially, with each ball having a binary vector attached to it, with the interpretation being that if X_i = 1 then that ball is eligible to be put in box i. A ball's vector is revealed when it arrives and the ball can be put in any alive box for which it is eligible, where a box is said to be alive if it has not yet met its quota. Assuming that the components of a vector are independent, we are interested in the policy that minimizes, either stochastically or in expectation, the number of balls that need arrive until all boxes have met their quotas. © 2014 Wiley Periodicals, Inc. 62:23–31, 2015     

Optimal pricing and scheduling control of product shipping

In this article, we seek to understand how a capacity‐constrained seller optimally prices and schedules product shipping to customers who are heterogeneous on willingness to pay (WTP) and willingness to wait (WTW). The capacity‐constrained seller does not observe each customer's WTP and WTW and knows only the aggregate distributions of WTP and WTW. The seller's problem is modeled as an M/M/N_s queueing model with multiclass customers and multidimensional information screening. We contribute to the literature by providing an optimal and efficient algorithm. Furthermore, we numerically find that customers with a larger waiting cost enjoys a higher scheduling priority, but customers with higher valuation do not necessarily get a higher scheduling priority. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 215–227, 2015     

Generation and storage dispatch in electricity networks with generator disruptions

We present methods for optimizing generation and storage decisions in an electricity network with multiple unreliable generators, each colocated with one energy storage unit (e.g., battery), and multiple loads under power flow constraints. Our model chooses the amount of energy produced by each generator and the amount of energy stored in each battery in every time period in order to minimize power generation and storage costs when each generator faces stochastic Markovian supply disruptions. This problem cannot be optimized easily using stochastic programming and/or dynamic programming approaches. Therefore, in this study, we present several heuristic methods to find an approximate optimal solution for this system. Each heuristic involves decomposing the network into several single‐generator, single‐battery, multiload systems and solving them optimally using dynamic programming, then obtaining a solution for the original problem by recombining. We discuss the computational performance of the proposed heuristics as well as insights gained from the models. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 493–511, 2015     

基于改进PLOW算法的干涉相位滤波

针对合成孔径雷达干涉相位滤波问题,提出了一种改进的分块局部最佳维纳滤波算法（Patch-based Locally Optimal Wiener, PLOW）。该算法是加性高斯白噪声下的线性最小均方误差估计（Linear Minimum Mean Square Estimation, LMMSE）,利用目前图像滤波最前沿的技术——非局部技术,来联合估计图像的一、二阶矩。针对干涉相位中噪声的空变性,在应用中提出了两点改进：首先,估计噪声的标准差时,用均值代替中值;其次,根据噪声标准差的最大值和均值的比值,自适应的确定类的数量。经过仿真和实测数据验证,改进后的PLOW算法是有效的,并优于其他三种算法。     

应用改进的线性预测算法构建虚拟阵的精确定向方法

为了克服传统线性预测(Linear Prediction,LP)算法在构建虚拟阵过程中存在预测误差容易累积的弊端,提出了一种能够更充分利用实阵信息量的改进LP算法来构建虚拟阵。采用实际基阵方法、传统LP虚拟阵方法和改进LP虚拟阵方法分别对假定基阵的波束性能进行计算机仿真及对湖试数据进行处理成像,研究结果表明,与传统LP方法相比,改进的LP方法能够有效地抑制波束旁瓣,进一步提高了基阵的角度分辨力和阵增益,将其运用于特定试验背景下的实际湖底目标声探测,方向分辨精度可提高75%。     

银河机向量线性代数库的并行算法研究及优化

文中对YH-1标量线性代数库进行并行算法研究:改造串行算法,挖掘其中的向量成份,实行并行计算。根据并行机的特点采取有效的程序优化措施,设计出银河机向量线性代数库。该库采用各种直接解法的并行算法求解各类线性代数问题,精度好,运行速度快(当n=300时,向量库运行速度平均为标量库的13倍)。     

双层随机机会约束规划的通信干扰任务分配优化仿真

研究不确定条件下的通信干扰任务分配优化问题具有重要的军事意义。基于干扰效益因子的概念,剖析了影响通信干扰任务分配的不确定性因素,建立了基于双层随机机会约束规划的通信干扰任务分配优化模型,设计了遗传蚁群智能算法,实例计算得到了通信干扰任务分配的最佳策略。     

Optimal control of noncollaborative servers in two‐stage tandem queueing systems

We consider two‐stage tandem queueing systems with dedicated servers in each station and a flexible server that is trained to serve both stations. We assume no arrivals, exponential service times, and linear holding costs for jobs present in the system. We study the optimal dynamic assignment of servers to jobs assuming a noncollaborative work discipline with idling and preemptions allowed. For larger holding costs in the first station, we show that (i) nonidling policies are optimal and (ii) if the flexible server is not faster than the dedicated servers, the optimal server allocation strategy has a threshold‐type structure. For all other cases, we provide numerical results that support the optimality of threshold‐type policies. Our numerical experiments also indicate that when the flexible server is faster than the dedicated server of the second station, the optimal policy may have counterintuitive properties, which is not the case when a collaborative service discipline is assumed. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 435–446, 2014