A duality‐based relaxation and decomposition approach for inventory distribution systems

We propose a new method for making the inventory replenishment decisions in distribution systems. In particular, we consider distribution systems consisting of multiple retailers that face random demand and a warehouse that supplies the retailers. The method that we propose is based on formulating the distribution problem as a dynamic program, and relaxing the constraints that ensure the nonnegativity of the shipments to the retailers, by associating Lagrange multipliers with them. We show that our method provides lower bounds on the value functions, and a good set of values for the Lagrange multipliers can be obtained by maximizing a concave function in a relatively straightforward manner. Computational experiments indicate that our method can provide significant improvements over the traditional approaches for making the inventory replenishment decisions, in terms of both the tightness of the lower bounds on the value functions and the performance of the policies. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

电化学极化状态对潜艇螺旋桨扰动电场模型的影响

潜艇服役期间涂层性能退变影响潜艇电场分布,以材料电化学极化状态为边界条件,应用边界元法建立潜艇涂层性能下降、涂层渗透腐蚀、涂层局部破损极化三种潜艇腐蚀静电场模型,从时域和频域特征对螺旋桨扰动电场模型进行分析。研究结果表明：电化学极化状态对螺旋桨扰动电场的电位信号特征及电场谐波频段影响显著。恒电位、线性极化、非线性极化三种边界条件下,螺旋桨以相同频率旋转扰动静电场时,各模型的频率成分占比差异明显。非线性边界条件下的扰动频率和2倍扰动频占比相差最大,线性边界条件下的扰动频率和2倍扰动频占比相差最小。三种边界条件下电场模型的3倍扰动频以上的谐波范围会发生改变,恒电位边界下模型谐波范围最小,非线性边界条件下谐波范围最大。     

Radar pulse interleaving for multi‐target tracking

In a multifunction radar, the maximum number of targets that can be managed or tracked is an important performance measure. Interleaving algorithms developed to operate radars exploit the dead‐times between the transmitted and the received pulses to allocate new tracking tasks that might involve transmitting or receiving pulses, thus increasing the capacity of the system. The problem of interleaving N targets involves a search among N! possibilities, and suboptimal solutions are usually employed to satisfy the real‐time constraints of the radar system. In this paper, we present new tight 0–1 integer programming models for the radar pulse interleaving problem and develop effective solution methods based on Lagrangian relaxation techniques. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

光滑物体表面反射光偏振特征分析及反射光分离技术

物体表面反射光由镜面反射光和漫反射光组成,针对光滑物体表面镜面反射光和漫反射光的分离问题,建立了一个结合镜面反射和漫反射共同作用的偏振态表征模型,并使用该模型对混合反射区域偏振特征进行分析。基于镜面反射光和漫反射光的偏振特征,根据镜面反射光和漫反射光在光滑物体表面垂直方向及平行方向上的分布关系,采用偏振正交分解的方法实现了镜面反射成分和漫反射成分的求解。利用镜面反射光图像和漫反射光图像之间的相关性,通过梯度下降算法得到镜面反射成分和漫反射成分归一化互相关最小值及其对应的镜面反射偏振度和漫反射偏振度,从而实现反射光的分离。通过对不同场景中获取的反射光图像进行测试,实验结果表明,该算法具有较好的反射光分离效果。     

舰船航渡过程中的松弛时间与航渡策略问题

针对舰船特点和任务要求,提出了舰船航渡中的松弛时间问题。在对问题分析的基础上,给出了松弛时间的定义并对其进行了建模,讨论了航渡失败的判断准则,给出了松弛时间的上下限以及航渡中实际的松弛时间的计算方法,并采用仿真的方法进行了典型航渡过程的松弛时间和成功概率的计算。在大量计算的基础上,初步探讨了航渡成功概率与各类航渡参数之间的关系,并对舰船最优航渡策略问题进行了初步分析,最后对于优化目标、计算初值、结果的表达方式等提出了一个可行的解决方案。     

航天测控调度问题的拉格朗日启发式算法

通过分析航天测控调度问题的测控需求,建立了航天测控调度0-1整数规划模型,运用拉格朗日松弛方法对模型中的任务约束和设备约束进行了松弛,运用次梯度优化算法求得了航天测控调度问题上界,同时得到了决策变量对应的拉格朗日权重,可以作为决策变量在最优解中是否被调度的启发式信息,对拉格朗日权重进行分析,提出了求解问题可行解的拉格朗日启发式算法。最后,通过对两个场景的试验分析验证了拉格朗日启发式算法所求可行解的优越性。     

基于拉格朗日松弛的航天测控调度上界求解算法

通过分析航天测控调度问题的测控需求,建立了航天测控调度0-1整数规划模型,运用拉格朗日松弛方法对模型中的设备约束和卫星约束进行了松弛,运用次梯度优化算法求得了拉格朗日对偶问题的上界.最后,通过对两个场景的试验分析,证明了运用次梯度优化算法求得的上界的有效性.     

军队人力资源培训问题的整数线性规划模型

文章研究了军队人力资源培训问题,并基于时间和费用两个指标,建立了一个满足培训时间约束且费用最省的0-1整数线性规划模型,给出了基于Lagrange松驰分解的模型求解算法。在算法中,采用一种简单可行的Lagrange乘子更新方法代替传统的次梯度法。另外,文章证明了算法获得最优解的两个充分条件,计算实例初步表明给出的算法是行之有效的。     

Interdiction models for delaying adversarial attacks against critical information technology infrastructure

Information technology (IT) infrastructure relies on a globalized supply chain that is vulnerable to numerous risks from adversarial attacks. It is important to protect IT infrastructure from these dynamic, persistent risks by delaying adversarial exploits. In this paper, we propose max‐min interdiction models for critical infrastructure protection that prioritizes cost‐effective security mitigations to maximally delay adversarial attacks. We consider attacks originating from multiple adversaries, each of which aims to find a “critical path” through the attack surface to complete the corresponding attack as soon as possible. Decision‐makers can deploy mitigations to delay attack exploits, however, mitigation effectiveness is sometimes uncertain. We propose a stochastic model variant to address this uncertainty by incorporating random delay times. The proposed models can be reformulated as a nested max‐max problem using dualization. We propose a Lagrangian heuristic approach that decomposes the max‐max problem into a number of smaller subproblems, and updates upper and lower bounds to the original problem via subgradient optimization. We evaluate the perfect information solution value as an alternative method for updating the upper bound. Computational results demonstrate that the Lagrangian heuristic identifies near‐optimal solutions efficiently, which outperforms a general purpose mixed‐integer programming solver on medium and large instances.     

顾及地磁影响的GNSS电离层层析不等像素间距算法

突破传统全球导航卫星系统(Global Navigation Satellite System, GNSS)层析反演研究忽略地球磁场对电离层变化活动的影响,同时顾及不同电离层高度电子密度变化较大的影响,提出在地磁坐标系下建立电离层高度方向上不等像素间距的GNSS层析反演方法。在此基础上,通过建立新的电离层层析迭代松弛因子,提高GNSS电离层电子密度层析反演结果精度。利用IRI—2007电离层模型、GNSS实测数据与电离层测高仪数据,从模拟验证和实测数据对比两方面,反演统计了不同层析算法估算的峰值电离层电子密度误差、电子密度剖面结果平均绝对百分比误差及均方根误差,验证了顾及地磁影响的GNSS电离层层析不等像素间距算法的有效性。