基于B样条的稳健回归算法

利用B样条基构建了拟合函数模型.针对观测数据中存在野值的情形,选取了稳健函数进行稳健回归,并通过迭代再加权法实现了拟合函数模型的求解.试验结果表明:在数据中含有野值的情形下,基于B样条的稳健回归算法比常规的最小二乘回归算法具有更好的表现.     

支持向量顺序回归机的线性规划算法

支持向量顺序回归机是标准支持向量分类机的一个推广，它是一个凸的二次规划问题。本文根据l1范数与l2范数等价关系和优化问题的对偶原理，把凸的二次规划转化成线性规划。由此提了支持向量顺序回归机的线性规划算法，进一步用数值实验验证了此算法的可行性和有效性。并与支持向量顺序回归机相比，它的运行时间缩短了，而且误差i不超过支持向量顺序回归机；     

采用优化加点Kriging模型的助推火箭残骸安全区预示方法

建立火箭及其分离残骸弹道计算动力学模型,并采用四元数方法对姿态角解算进行处理。提出基于优化加点Kriging模型的安全区预示方法,结合Monte Carlo和Kriging代理模型的特点,给出安全区预示流程。以某型助推火箭残骸安全区计算为例,对提出的安全区预示方法进行仿真验证。仿真结果表明,提出的基于优化加点Kriging模型安全区预示方法与Monte Carlo方法相比,在不损失计算精度的前提下,具有更高的计算效率,满足快速迭代的工程需求;相比传统极限偏差叠加方法,可显著降低安全区覆盖面积,具有较强的工程应用价值。     

基于优化加点Kriging模型的助推火箭残骸安全区预示方法

建立火箭及其分离残骸弹道计算动力学模型，并采用四元数方法对姿态角解算进行处理。提出基于优化加点Kriging模型的安全区预示方法，结合Monte Carlo和Kriging代理模型的特点，给出安全区预示流程。以某型助推火箭残骸安全区计算为例，对提出的安全区预示方法进行仿真验证。仿真结果表明：提出的基于优化加点Kriging模型安全区预示方法与Monte Carlo方法相比，在不损失计算精度的前提下，具有更高的计算效率，满足快速迭代的工程需求，相比传统极限偏差叠加方法，可显著降低安全区覆盖面积，具有较强的工程应用价值。     

一类广义延拓四元数矩阵的奇异值分解

从普通四元数矩阵的奇异值分解出发,给出了具有行或列对称结构的一类四元数矩阵(即广义四元数延拓矩阵)的奇异值、奇异向量与其母矩阵的奇异值、奇异向量之间的定量关系,推广了现有文献的结果。理论分析和数值实验的结果表明,就一大类广义四元数延拓矩阵而言,仅用母矩阵进行奇异值分解不但可以节省计算量和存储量,而且不影响任何数值精度。     

军队资产管理效益评价指标体系与模型构建

军队资产管理效益评价过程中,通过构建评价指标体系,选择构建单目标线性规划模型和优属度优化模型,并运用灰色关联分析方法对数学模型进行求解,是一种行之有效的方法。通过灰色关联分析方法求解数学模型,可以得到各个属性的权重值和模型的最优解向量,即各个待评价方案的决策值,据此可知各方案的军队资产管理效益的高低和一段时间内单位资产管理效益变化的趋势。     

邻近支持向量机的阵列波束优化

针对标准支持向量回归波束形成器的计算复杂度高、内存开销大、训练速度慢的缺点,提出了邻近支持向量机(Proximal Support Vector Machine,PSVM)波束优化方法。PSVM打破了通过对偶问题求解原问题的传统思维,将支持向量回归的约束条件等式化,直接对原问题进行分析与求解,给出了基于PSVM波束形成器的优化模型及具体实现过程,并进行了数值仿真实验。研究结果表明,在保持波束形成器性能基本不变的情况下,降低了计算复杂度,减少了内存开销,提高了训练速度。与传统的支持向量回归波束形成相比,具有良好的快速性,为波束形成器的优化设计提供了一种新的有效方法。     

马尔可夫链最优停止的值函数

本文讨论了时间无限的马尔可夫链的最优停止问题。对于无限状态情况,给出了其最优停止变量以及值函数存在的一个充分条件;对于有限状态情况,这个充分条件以及问题的计算等价于解一个线性规划问题。     

SVM在空中目标威胁值评估中的应用

构建了基于回归型支持向量机的空中目标威胁值评估模型,确定了基于粗糙集理论的空中目标威胁因素,并建立了数据离散化、归一化的标准。将常用的4种核函数应用于对空中目标威胁值的估计,并通过基于网格法和遗传算法的搜索方法找到模型的最优参数。最后通过Matlab对算例进行了仿真验证。     

导弹飞行轨迹运动参数的稳健回归

对导弹飞行轨迹分析中的运动学方程参数求解拟合问题进行了研究,给出了运动学参数的数值计算方法,对参数拟合误差进行了分析.采用了基于B样条函数基的参数稳健回归拟合方法,有效降低了测量异常值对计算结果的影响,提高了拟合精度.试验结果表明:该方法能很好地解决导弹运动参数的曲线拟合与误差分析问题.     

A bicriterion approach to common flow allowances due window assignment and scheduling with controllable processing times

We investigate a single‐machine scheduling problem for which both the job processing times and due windows are decision variables to be determined by the decision maker. The job processing times are controllable as a linear or convex function of the amount of a common continuously divisible resource allocated to the jobs, where the resource allocated to the jobs can be used in discrete or continuous quantities. We use the common flow allowances due window assignment method to assign due windows to the jobs. We consider two performance criteria: (i) the total weighted number of early and tardy jobs plus the weighted due window assignment cost, and (ii) the resource consumption cost. For each resource consumption function, the objective is to minimize the first criterion, while keeping the value of the second criterion no greater than a given limit. We analyze the computational complexity, devise pseudo‐polynomial dynamic programming solution algorithms, and provide fully polynomial‐time approximation schemes and an enhanced volume algorithm to find high‐quality solutions quickly for the considered problems. We conduct extensive numerical studies to assess the performance of the algorithms. The computational results show that the proposed algorithms are very efficient in finding optimal or near‐optimal solutions. © 2017 Wiley Periodicals, Inc. Naval Research Logistics, 64: 41–63, 2017     

两种改进Lagrange插值格式的对比分析

本文基于Lagrange插值多项式,给出了两种改进的Lagrange插值格式：Aitken插值和重心Lagrange插值。从算法的复杂性及数值稳定性两个方面进行了比较分析,结果表明重心形式的Lagrange插值是最优的。文末给出数值试验表明算法的有效性。     

CPU-GPU协同加速Kriging插值的负载均衡方法

Kriging插值算法被广泛应用于地学各领域,有着极其重要的现实意义,但在面对大规模输出网格及大量输入采样点时,不可避免地遇到了性能瓶颈。利用Open CL和Open MP在异构平台上实现了CPU与GPU协同加速普通Kriging插值。针对Kriging插值中采样点的不规则分布及CPU和GPU由于体系结构差异对其的不同适应性,提出一种基于不同设备间计算性能的差异和数据分布特点的负载均衡方法。试验结果表明,该方法能有效提高普通Kriging插值速度,同时还能节约存储空间和提高访存效率。     

A refined deterministic linear program for the network revenue management problem with customer choice behavior

We present a new deterministic linear program for the network revenue management problem with customer choice behavior. The novel aspect of our linear program is that it naturally generates bid prices that depend on how much time is left until the time of departure. Similar to the earlier linear program used by van Ryzin and Liu (2004), the optimal objective value of our linear program provides an upper bound on the optimal total expected revenue over the planning horizon. In addition, the percent gap between the optimal objective value of our linear program and the optimal total expected revenue diminishes in an asymptotic regime where the leg capacities and the number of time periods in the planning horizon increase linearly with the same rate. Computational experiments indicate that when compared with the linear program that appears in the existing literature, our linear program can provide tighter upper bounds, and the control policies that are based on our linear program can obtain higher total expected revenues. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Interval uncertain optimization for damping fluctuation of asegmented electromagnetic buffer under intensive impact load

Aiming at the problems of demagnetization effect of electromagnetic buffer (EMB) caused by high ve-locity under intensive impact load and the difficulty and error of machining composite thin-walled long tube, a segmented EMB is proposed. The inner tube and air-gap are divided into initial segments and the traversing segments. Through theoretical analysis, impact test and simulation, it can be found that the RRF curve has two peaks. Firstly, in order to reduce the resultant resistance force (RRF) peaks, the sensitivity analysis based on optimal Latin hypercube design (OLHD) and polynomial regression was performed. The results show that the smallest contribution ratio to the dynamic response is the seventh and ninth segments of the inner tube, which are less than 1％. Then, fully considering the uncertain factors, important parameters are selected for uncertain optimization after sensitivity analysis. The in-terval order and interval probability degree methods are used to establish interval uncertain optimiza-tion model of the RRF considering robustness. The model was solved using an interval nested optimization method based on radial basis function (RBF) neural network. Finally, the Pareto front is obtained and numerical simulation is performed to verify the optimal value. It indicates that the two kinds of RRF peak is obviously reduced, and the optimization object and strategy are effective.     

The fractional fixed-charge problem

Fractional fixed-charge problems arise in numerous applications, where the measure of economic performance is the time rate of earnings or profit (equivalent to an interest rate on capital investment). This paper treats the fractional objective function, after suitable transformation, as a linear parametric fixed-charge problem. It is proved, with wider generality than in the case of Hirsch and Dantzig, that some optimal solution to the generalized linear fixed-charge problem is an extreme point of the polyhedral set defined by the constraints. Furthermore, it is shown that the optimum of the generalized fractional fixed-charge problem is also a vertex of this set. The proof utilizes a suitable penalty function yielding an upper bound on the optimal value of the objective function; this is particularly useful when considering combinations of independent transportation-type networks. Finally, it is shown that the solution of a fractional fixed-charge problem is obtainable through that of a certain linear fixed-charge one.     

涡轮盘疲劳寿命可靠性设计仿真及优化策略

涡轮盘是航空发动机主要部件之一,一旦发生破坏性故障将导致严重的后果。在充分考虑影响涡轮盘高低周复合疲劳寿命因素不确定性基础上,以MATLAB为平台,设计了涡轮盘高低周复合疲劳寿命可靠性优化设计的联合仿真平台。利用寿命函数和寿命可靠性分析极限状态函数中的共性需求,提出了在优化迭代的过程中自适应构建寿命函数Kriging模型和寿命可靠性极限状态面Kriging模型时共用训练样本点的策略。同时,提出了一种构建寿命函数Kriging模型的学习函数。使用所搭建的疲劳寿命可靠性优化设计平台,完成了某型涡轮盘盘心、榫槽以及涡轮盘系统高低周复合疲劳寿命的可靠性优化设计。结果表明,最优设计方案的局部最大应力显著降低,均值寿命大幅提高,并满足可靠性约束。     

时延数字控制系统最优控制问题的离散正交多项式解法

本文利用一般的离散正交多项式研究了具有2s个时延项离散系统的最优控制问题。文中导出了系统状态和控制向量离散正交级数展开式中系数向量间的关系,然后,将离散动态系统的最优控制问题转化为直接对二次型性能指标中一组系数向量的参数优化问题,并由一组线性代数方程给出了这组最优系数向量的解。最后,还介绍了一个数值例子。     

Two‐agent scheduling on a single sequential and compatible batching machine

We study two‐agent scheduling on a single sequential and compatible batching machine in which jobs in each batch are processed sequentially and compatibility means that jobs of distinct agents can be processed in a common batch. A fixed setup time is required before each batch is started. Each agent seeks to optimize some scheduling criterion that depends on the completion times of its own jobs only. We consider several scheduling problems arising from different combinations of some regular scheduling criteria, including the maximum cost (embracing lateness and makespan as its special cases), the total completion time, and the (weighted) number of tardy jobs. Our goal is to find an optimal schedule that minimizes the objective value of one agent, subject to an upper bound on the objective value of the other agent. For each problem under consideration, we provide either a polynomial‐time or a pseudo‐polynomial‐time algorithm to solve it. We also devise a fully polynomial‐time approximation scheme when both agents’ scheduling criteria are the weighted number of tardy jobs.     

A note on the single-machine scheduling problem with minimum weighted completion time and maximum allowable tardiness

This paper analyzes the Smith-heuristic for the single-machine scheduling problem where the objective is to minimize the total weighted completion time subject to the constraint that the tradiness for any job does not exceed a prespecified maximum allowable tardiness. We identify several cases of this problem for which the Smith-heuristic is guaranteed to lead to optimal solutions. We also provide a worst-case analysis of the Smith-heuristic; the analysis shows that the fractional increase in the objective function value for the Smith-heuristic from the optimal solution is unbounded in the worst case.