Reformulating linear programs with transportation constraints—With applications to workforce scheduling

We study linear programming models that contain transportation constraints in their formulation. Typically, these models have a multistage nature and the transportation constraints together with the associated flow variables are used to achieve consistency between consecutive stages. We describe how to reformulate these models by projecting out the flow variables. The reformulation can be more desirable since it has fewer variables and can be solved faster. We apply these ideas to reformulate two well‐known workforce staffing and scheduling problems: the shift scheduling problem and the tour scheduling problem. We also present computational results. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

多层弹道导弹防御体系火力分配优化研究

对多层弹道导弹防御体系火力分配问题进行了研究。首先对多层弹道导弹防御体系火力分配问题进行了描述,在此基础上建立了基于最大化资源剩余价值目标函数的多层弹道导弹防御体系火力分配模型,分析了求解该模型的难点,提出了基于文化基因的多层弹道导弹防御体系火力分配问题文化基因求解算法,最后应用实例验证了模型的有效性,并对算法进行了对比分析。试验结果证明,合理制定多层弹道导弹防御体系火力分配方案,对于提升防御效能具有重要意义。     

数学解题教学中寻求隐含条件的规律探索

中学数学教学中,解数学难题的过程就是从题设中不断地挖掘并利用隐含条件进行推理和变形的过程。数学题中的隐含条件形形色色,花样繁多,但从对解题过程的影响看,又可以分为制约解题方向的隐含条件、制约解题思路的隐含条件、制约解题准确性的隐含条件等三类隐含条件。只要我们把握了难题中隐含条件的规律特征,运用我们获得的数学知识,结合适当的数学思想和数学方法,就可以轻松解决难题了。     

基于混合智能算法的小型通信干扰装备分配优化

如何充分发挥小型通信干扰装备的作战效能是指挥员面临的棘手问题。本文将战术指标——干扰后的通信畅通区覆盖程度作为评估通信干扰装备分配优劣的指标,分别建立了单机和多部干扰时的通信干扰有效压制区和通信畅通区边界的计算模型,并给出了通信干扰有效压制区和通信畅通区面积的计算方法。构建了基于机会约束规划的空域频域通信干扰任务分配模型,并设计了混合蚁群算法和遗传算法的模型求解算法。最后进行了仿真实验,验证分析了模型和算法的合理性。研究成果为通信对抗战术计算和作战运用研究拓展了思路。     

弹道导弹防御中拦截弹最优分层配置

多层弹道导弹防御系统在助推段、飞行中段或再入段不同阶段实施拦截,可有效提高系统拦截概率,不同拦截阶段存在拦截弹最优配比问题。为了解决拦截弹道导弹过程中的最优分层配置的问题,本文分别以单层、双层、三层这三种拦截系统为例,通过公式演算和计算机仿真,得出了分段拦截弹道导弹时、不同拦截阶段的拦截弹之间的数量比与整体拦截成功率之间的关系;并提出了整体拦截成功率的概念。经仿真表明,在整体拦截成功率给定的情况下,使用本文所得出的不同拦截段之间所需拦截弹数目之间的最优比,可以最大限度地降低弹道导弹的拦截成本。     

UCAV空面多目标攻击三维轨迹规划技术

研究了单架无人作战飞机(UCAV)攻击多个地面目标的三维轨迹规划问题。首先,将问题形式化为一类特殊的旅行商问题(TSP),即带动力学约束的邻域访问TSP问题(DCTSPN)。其次,针对规划空间维度过高、搜索代价过大的问题,提出了一种基于概率路标图(PRM)的方法。该方法借鉴了基于采样的运动规划方法的思想,并结合多种组合优化技术,将原本连续状态空间中的轨迹规划问题转化为离散拓扑图上的路由问题。求解过程分为离线预处理和在线查询两个阶段。离线阶段采用Halton拟随机采样算法及Noon-Bean转换方法,将原问题转化为经典的非对称旅行商问题(ATSP);在线阶段根据战场态势的实时变化,快速更新路标图,然后采用LKH算法在线求解问题的近似最优解。为了保证生成的飞行轨迹满足平台的运动学/动力学约束,算法基于Gauss伪谱法构建了局部轨迹规划器。最后,以攻击时间最短为优化指标对算法进行了仿真实验。结果表明,本文提出的方法能够以较高的精度和在线收敛速度生成真实可行的、较优的多目标攻击轨迹。     

A dynamic allocation heuristic for centralized safety stock

An inventory system that consists of a depot (central warehouse) and retailers (regional warehouses) is considered. The system is replenished regularly on a fixed cycle by an outside supplier. Most of the stock is direct shipped to the retailer locations but some stock is sent to the central warehouse. At the beginning of any one of the periods during the cycle, the central stock can then be completely allocated out to the retailers. In this paper we propose a heuristic method to dynamically (as retailer inventory levels change with time) determine the appropriate period in which to do the allocation. As the optimal method is not tractable, the heuristic's performance is compared against two other approaches. One presets the allocation period, while the other provides a lower bound on the expected shortages of the optimal solution, obtained by assuming that we know ahead of time all of the demands, period by period, in the cycle. The results from extensive simulation experiments show that the dynamic heuristic significantly outperforms the “preset” approach and its performance is reasonably close to the lower bound. Moreover, the logic of the heuristic is appealing and the calculations, associated with using it, are easy to carry out. Sensitivities to various system parameters (such as the safety factor, coefficient of variation of demand, number of regional warehouses, external lead time, and the cycle length) are presented. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Optimal control of a capacitated inventory system with multiple demand classes

This article studies the optimal control of a periodic‐review make‐to‐stock system with limited production capacity and multiple demand classes. In this system, a single product is produced to fulfill several classes of demands. The manager has to make the production and inventory allocation decisions. His objective is to minimize the expected total discounted cost. The production decision is made at the beginning of each period and determines the amount of products to be produced. The inventory allocation decision is made after receiving the random demands and determines the amount of demands to be satisfied. A modified base stock policy is shown to be optimal for production, and a multi‐level rationing policy is shown to be optimal for inventory allocation. Then a heuristic algorithm is proposed to approximate the optimal policy. The numerical studies show that the heuristic algorithm is very effective. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 43–58, 2011     

机械系统可靠性设计若干问题探讨

机械系统的可靠性设计是当前可靠性工程界面临的热点和难点问题之一,从分析机械系统可靠性设计的特点和难点入手,探讨了机械系统可靠性建模、分配、预计等机械系统可靠性设计中急需解决的关键问题。     

边界元角点问题的重节点法分析

应用重节点法处理三维弹性力学角节点问题,采用等参变换插值逼近的方法离散边界积分方程,解决了由于角节点表面力不连续带来的方程求解困难问题。算例分析结果表明,该方法具有操作简单,计算方便,求解结果满足计算精度的要求等优点,尤其在角点存在应力集中场合更具优越性。