递进优化技术在汽油机工作过程优化计算中的应用

采用数学规化的方法优化汽油机的工作过程,可以在限制发动机热负荷、机械负荷、氧化氮排放和不爆震的条件下,使发动机在运行过程中经济性最好.但是要求得比较精确的优化解,一般要进行大量计算,花费较多机时.本文提出了一种分段、分层、分级的递进优化方法,应用于汽油机工作过程的优化计算中,取得了较好的效果.     

Minimizing sums and products of linear fractional functions over a polytope

In this paper, we develop efficient deterministic algorithms for globally minimizing the sum and the product of several linear fractional functions over a polytope. We will show that an elaborate implementation of an outer approximation algorithm applied to the master problem generated by a parametric transformation of the objective function serves as an efficient method for calculating global minima of these nonconvex minimization problems if the number of linear fractional terms in the objective function is less than four or five. It will be shown that the Charnes–Cooper transformation plays an essential role in solving these problems. Also a simple bounding technique using linear multiplicative programming techniques has remarkable effects on structured problems. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 583–596, 1999     

Coordinated replenishments from multiple suppliers with price discounts

In this study we present an integer programming model for determining an optimal inbound consolidation strategy for a purchasing manager who receives items from several suppliers. The model considers multiple suppliers with limited capacity, transportation economies, and quantity discounts. We propose an integrated branch and bound procedure for solving the model. This procedure, applied to a Lagrangean dual at every node of the search tree, combines the subgradient method with a primal heuristic that interact to change the Lagrangean multipliers and tighten the upper and lower bounds. An enhancement to the branch and bound procedure is developed using surrogate constraints, which is found to be beneficial for solving large problems. We report computational results for a variety of problems, with as many as 70,200 variables and 3665 constraints. Computational testing indicates that our procedure is significantly faster than the general purpose integer programming code OSL. A regression analysis is performed to determine the most significant parameters of our model. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 579–598, 1998     

Probabilistic analysis of an asymptotically optimal solution for the completion time variance problem

Scheduling a set of n jobs on a single machine so as to minimize the completion time variance is a well‐known NP‐hard problem. In this paper, we propose a sequence, which can be constructed in O(n log n) time, as a solution for the problem. Our primary concern is to establish the asymptotical optimality of the sequence within the framework of probabilistic analysis. Our main result is that, when the processing times are randomly and independently drawn from the same uniform distribution, the sequence is asymptotically optimal in the sense that its relative error converges to zero in probability as n increases. Other theoretical results are also derived, including: (i) When the processing times follow a symmetric structure, the problem has 2^{⌊(n−1)/2⌋} optimal sequences, which include our proposed sequence and other heuristic sequences suggested in the literature; and (ii) when these 2^{⌊(n−1)/2⌋} sequences are used as approximate solutions for a general problem, our proposed sequence yields the best approximation (in an average sense) while another sequence, which is commonly believed to be a good approximation in the literature, is interestingly the worst. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 373–398, 1999     

On gamma estimation via matrix kriging

In financial engineering, sensitivities of derivative prices (also known as the Greeks) are important quantities in risk management, and stochastic gradient estimation methods are used to estimate them given the market parameters. In practice, the surface (function) of the Greeks with respect to the underlying parameters is much more desired, because it can be used in real‐time risk management. In this paper, we consider derivatives with multiple underlying assets, and propose three stochastic kriging‐based methods, the element‐by‐element, the importance mapping, and the Cholesky decomposition, to fit the surface of the gamma matrix that can fulfill the time constraint and the precision requirement in real‐time risk management. Numerical experiments are provided to illustrate the effectiveness of the proposed methods.     

针对不同视场辅助信标的无人机目标定位方法

针对无人机在单站测角测距的目标定位过程中受无人机姿态角误差影响较大的问题,提出一种对辅助信标进行探测并与惯性传感器相结合的无人机姿态求解方法。建立基于容积卡尔曼滤波的惯性传感器姿态求解模型,采用梯度下降法对基于辅助信标的无人机位姿参数进行求解,并综合它们的结果对无人机的姿态偏差进行估计和校正,最后完成了不同视场条件下的目标定位和仿真计算。结果表明,所提方法对无人机目标定位精度有明显提高。     

面向多星观测调度的分层迭代算法

提出一种基于分治策略的多星观测分层调度框架,在该框架下,用蚁群优化算法把任务分配至各轨道圈次上,并利用自适应模拟退火算法求解各轨道圈次的调度问题。根据各轨道圈次调度结果的反馈情况,再调整任务分配方案,重复上述过程直到达到算法终止条件。为了提高算法的性能,在设计蚁群算法的启发式信息模型时,应充分考虑卫星调度问题的领域知识;在模拟退火算法中设计两个邻域结构,采用动态选择策略在优化过程中确定最佳邻域搜索结构。仿真实验表明,该方法有效地降低了问题求解的复杂度,尤其在求解大规模多星观测调度问题时表现出优异的性能。     

磁梯度张量的旋转计算方法

为了获得磁梯度张量数据,提出旋转计算磁梯度张量的方法。使倾斜放置的磁梯度计绕竖直轴线转动,利用测得的空间磁梯度数据计算得到磁梯度张量。以磁梯度张量的理论值作为参考,选取一组较优的转动角、倾角和基线长度等模型参数,分析磁力仪三轴指向误差对磁梯度张量计算结果的影响。数值仿真结果表明:该旋转合成方法能够有效获取磁张量信息,合成计算值与理论值之间的差别较小。     

多输入多输出雷达恒模稳健波形联合优化算法

针对目标冲激响应及杂波冲激响应分布特性先验知识不准确导致的多输入多输出雷达检测性能下降的问题,提出恒模稳健波形与接收机滤波器联合优化算法。将目标冲激响应及杂波冲激响应分布特性先验知识不准确时的优化问题建模为一个极大极小化问题。运用迭代优化算法将联合优化问题分解为两个子优化步骤:将波形固定时的接收机滤波器权值优化问题建模为广义瑞利商模型,求解得到相应的接收机滤波器权值矢量;利用半正定松弛技术对权值固定时的波形优化问题进行求解,获得对应的波形矩阵,并根据得到的波形矩阵,通过高斯随机化的方法获得所需的恒模波形。对所提算法的收敛性进行了证明,仿真结果表明所提算法有效。     

火箭-双燃烧室冲压组合循环发动机概念研究

临近空间高超声速飞行器近年来获得了广泛关注,本文提出一种以基于火箭发动机和双燃烧室冲压发动机的多模态火箭-双燃烧室冲压组合循环发动机作为飞行器的动力系统,并进行了性能分析研究。该飞行器在海拔10 km左右高度以0.8马赫的速度投放,在重力和发动机推力的联合作用下,能够在海拔5～8 km处加速到2马赫;然后加速爬升进入临近空间,发动机工作在引射亚燃或者双燃烧室亚燃模态下。可以根据实际选择高推重比、较低推进剂比冲效率的引射亚燃模态,或是较低推重比、高推进剂比冲效率的双燃烧室亚燃模态。最终飞行器加速到6马赫(26 km),进入双燃室超燃模态。针对空中发射模式和地面发射模式进行了轨道优化,仿真结果表明:在加速爬升到6马赫(26 km)的过程中,空中发射模式相比较地面发射模式可以节省37%的推进剂;空中发射模式存在一个负的最优初始飞行角度使得剩余质量与初始质量的比值达到最大。