Efficiency of equilibria in restricted uniform machine scheduling with total weighted completion time as social cost

In the last decade, there has been much progress in understanding scheduling problems in which selfish jobs aim to minimize their individual completion time. Most of this work has focused on makespan minimization as social objective. In contrast, we consider as social cost the total weighted completion time, that is, the sum of the agent costs, a standard definition of welfare in economics. In our setting, jobs are processed on restricted uniform parallel machines, where each machine has a speed and is only capable of processing a subset of jobs; a job's cost is its weighted completion time; and each machine sequences its jobs in weighted shortest processing time (WSPT) order. Whereas for the makespan social cost the price of anarchy is not bounded by a constant in most environments, we show that for our minsum social objective the price of anarchy is bounded above by a small constant, independent of the instance. Specifically, we show that the price of anarchy is exactly 2 for the class of unit jobs, unit speed instances where the finite processing time values define the edge set of a forest with the machines as nodes. For the general case of mixed job strategies and restricted uniform machines, we prove that the price of anarchy equals 4. From a classical machine scheduling perspective, our results establish the same constant performance guarantees for WSPT list scheduling. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

基于Gauss伪谱法和直接打靶法结合的月球定点着陆轨道优化

将一种求解最优控制问题的新方法—高斯伪谱法( Gauss Pseudospectral Method-GPM)和传统的直接打靶法有效结合,对月球着陆器定点软着陆轨道快速优化问题做出了研究.推导了高精度模型下着陆动力学方程.针对优化方法各自的特点和多约束条件下最优月球软着陆轨道设计的难点,提出了问题求解的串行优化策略:将控制变量和终端时间一同作为优化变量,同时离散控制变量与状态变量,取较少的Gauss节点,利用GPM求解初值,初值的求解采用从可行解到最优解的串行优化策略;在Gauss节点上离散控制变量,利用直接打靶法求解精确最优解.仿真结果表明,本文提出的轨道优化方法具有较强的鲁棒性和快速收敛性.     

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。     

基于ISIGHT的微型飞行器布局优化设计研究

微型飞行器具有飞行雷诺数低、易受外界环境干扰等特点,并存在多目标优化问题,因此其气动布局优化设计难度较大。针对微型飞行器的特点及优化设计要求,采用N-S方程与遗传算法相结合的方法对微型飞行器的多目标优化设计,基于ISIGHT软件来实现该方法的具体流程,克服了计算量大、无法实现自主迭代的缺点。并对微型飞行器的展弦比、尾翼安装角、尾翼的高度和根弦长进行优化,优化目标为飞行器的静稳定性和升阻特性,优化后的构型具有良好的气动性能,结果表明该方法明显提高了计算的精度和优化设计的水平,在工程上有一定的应用价值。     

战时弹药输送路径PSO决策分析

介绍了粒子群优化算法的基本思想和理论,阐述了基于粒子群优化算法的战时弹药输送路径决策分析的实现过程。通过实例应用,证实了粒子群优化算法对弹药输送路经决策问题是可行和有效的。     

不同磁浮列车外形的气动性能比较

上海磁浮列车由于流线型车头较短,气动性能并不理想,根据国内厂家给定的列车横断面尺寸和对气动性能的要求,对国产磁浮列车气动外形进行多方案设计,通过求解三维可压N-S方程和k-ε双方程湍流模型,对提出的磁浮列车各种外形方案的气动性能进行数值模拟计算,并根据计算结果进一步改进气动外形,如此反复,直至得出气动性能和外观最优的磁浮列车外形。在最终选定的三种设计方案中,方案3由于水平投影轮廓线较窄、最大纵剖面轮廓线曲率较小,其整车空气阻力和列车交会压力波都较其它两种方案要小,因此为最佳的气动外形方案。通过比较分析,此次选用的国产磁浮列车外形,列车以430km/h运行时三节车总的空气阻力为33.84kN,而上海磁浮列车为54.07kN;国产磁浮列车最大列车交会压力波幅值为2913Pa,而在同等条件下上海磁浮列车为3827Pa,其气动性能明显优于上海磁浮列车。     

Maximizing the ratio of two convex functions over a convex set

The purpose of this article is to present an algorithm for globally maximizing the ratio of two convex functions f and g over a convex set X. To our knowledge, this is the first algorithm to be proposed for globally solving this problem. The algorithm uses a branch and bound search to guarantee that a global optimal solution is found. While it does not require the functions f and g to be differentiable, it does require that subgradients of g can be calculated efficiently. The main computational effort of the algorithm involves solving a sequence of subproblems that can be solved by convex programming methods. When X is polyhedral, these subproblems can be solved by linear programming procedures. Because of these properties, the algorithm offers a potentially attractive means for globally maximizing ratios of convex functions over convex sets. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

任务规划系统研究综述

任务规划系统作为举世瞩目的高科技技术,已经引起了广泛的关注和应用.目前世界上一些主要国家都在研制任务规划系统,且进展很快.为了更好地推进我国学者对于任务规划系统的研究,对任务规划系统的研究进行了全面综述.主要内容包括任务规划系统的发展、应用、主要实现方法及未来发展方向.在应用中,综述了任务规划系统在战场态势评估、无人飞行器、机器人领域的应用.在主要实现方法中,主要描述了数学规划、D*优化算法、Agent方法和遗传算法四种方法.最后给出了任务规划系统未来发展方向:现代技术的融合、发展战略级任务规划系统及未来社会任务规划系统预研.     

雷达网优化部署仿真系统研究

雷达网优化部署仿真系统可以模拟雷达网的部署,自动地计算出雷达网各项战术指标,并能对雷达网的部署方案进行评估、调整、选优.主要描述了雷达网优化部署仿真系统的组成、其核心部分优化部署模块数学模型的建立及其理论依据、该数学模型优化算法的实现及其与其它优化方法的性能比较.     

基于模糊多目标决策的舰艇导弹优化配置

运用模糊理论和多目标优化理论探索舰艇编队所携带导弹的合理配置。采用灰色系统理论的关联度分析方法,得出各型导弹对理想导弹的关联度,构建进攻能力和防御能力的隶属度函数;通过多目标优化模型的求解,实现各型号导弹的最优配置。使用该优化算法,当舰艇编队面对不同的攻防任务时,能有效地辅助军事指挥员做出最优决策。