A CLASS OF TRUST REGION METHODS FOR LINEAR INEQUALITY CONSTRAINED OPTIMIZATION AND ITS THEORY ANALYSIS：I．ALGORITHM AND GLOBAL CONVERGENCE

A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.

A CLASS OF TRUST REGION METHODS FOR LINEAR INEQUALITY CONSTRAINED OPTIMIZATION AND ITS THEORY ANALYSIS Ⅱ．LOCAL CONVERGENCE RATE AND NUMERICAL TESTS

In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective.

基于边界法的大型机组组合模型的简化方法

随着电网规模的持续扩大,市场环境下考虑网络安全约束的机组组合(security-constrained unit commitment,SCUC)模型中的变量和约束显著增加,模型的求解性能变差。当模型规模过大时,会出现现有的商用求解器无法求解的状况,造成大规模模型求解困难的问题。为实现大规模机组组合模型的快速求解,从减少模型约束数量的角度出发,提出了一种基于边界法的线性约束简化方法。通过边界法剔除模型中冗余的线性约束,可以有效降低模型规模,实现模型的快速求解。基于IEEE-39、WECC 179和IEEE-118算例,在市场环境下进行日前SCUC测试。通过对比简化前后的求解时间,表明该方法能够显著提高模型的求解速率。

基于改进近似动态规划的安全约束机组组合算法

针对电力系统的安全约束机组组合问题,提出了一种基于改进近似动态规划的求解算法。考虑到安全约束机组组合是一个多时段混合整数非线性规划问题,难以直接求解,所提算法将其建模成马尔可夫决策过程,并利用近似动态规划实现解耦求解。为了处理近似动态规划决策空间过大的问题,所提算法通过决策空间缩减技术提前获得大部分机组的开停机状态,有效提高求解效率。在IEEE 39节点系统和一个实际系统上进行了算例分析,验证了所提算法的有效性。

A New Method for Achieving an Initial Regular Solution of a Linear Programming

A method is provided for finding an initial regular solution of a linear programming in this paper. The key to this method is to solve an auxiliary linear programming instead of to introduce any artificial variable or constraint. Compared with the traditional method of achieving the regular solution by introducing an artificial constraint, it has advantages of saving the memories and little computational efforts.

Energy-constrained ferry route design for sparse wireless sensor networks

In recent years,using message ferries as mechanical carriers of data has been shown to be an effective way to collect information in sparse wireless sensor networks.As the sensors are far away from each other in such highly partitioned scenario,a message ferry needs to travel a long route to access all the sensors and carry the data collected from the sensors to the sink.Typically,practical constraints(e.g.,the energy)preclude a ferry from visiting all sensors in a single tour.In such case,the ferry can only access part of the sensors in each tour and move back to the sink to get the energy refilled.So,the energy-constrained ferry route design(ECFRD)problem is discussed,which leads to the optimization problem of minimizing the total route length of the ferry,while keeping the route length of each tour below a given constraint.The ECFRD problem is proved to be NP-hard problem,and the integer linear programming(ILP)formulation is given.After that,efficient heuristic algorithms are proposed to solve this problem.The experimental results show that the performances of the proposed algorithms are effective in practice compared to the optimal solution.

Design of Perfect Reconstruction Cosine Modulated Filter Bank with Linear Phase

We propose the quadratic constrained formulas for the design of linear phase cosine modulated paraunitary filter banks given in references . Using these formulae, we can, directly, optimize the prototype filter coefficients in a quadratic form. A design example is also given to demonstrate these formulae in this paper.

Eigenstructure Assignment Method and Its Applications to the Constrained Problem

A partial eigenstructure assignment method that keeps the open-loop stable eigenvalues and the corresponding eigenspace unchanged is presented. This method generalizes a large class of systems previous methods and can be applied to solve the constrained control problem for linear invariant continuous-time systems. Besides, it can be also applied to make a total eigenstructure assignment. Indeed, the problem of finding a stabilizing regulator matrix gain taking into account the asymmetrical control constraints is transformed to a Sylvester equation resolution. Examples are given to illustrate the obtained results.

约束聚类算法的多目标QR码定位识别方法

在轮对智能选配系统中,为提高轮对零部件的录入效率,提出多目标环境下对单个QR码的定位识别算法。针对使用聚类算法对其进行具有二维码特征的最优聚类问题,通过预先设定簇个数以及初始聚类点,并在其基础上加入单个QR码的特征作为约束,对聚类算法进行改进。实验表明,相比于现有技术方案,在多目标QR码识别需求下,此方法能够降低QR码识别产品的生产成本,识别率达96%,实现了多目标QR码的同时识别。

Comparison of Economic Dispatch, OPF and Security Constrained-OPF in Power System Studies RN

Electricity network is a very complex entity that comprises several components like generators, transmission lines, loads among others. As technologies continue to evolve, the complexity of the electricity network has also increased as more devices are being connected to the network. To understand the physical laws governing the operation of the network, techniques such as optimal power flow (OPF), Economic dispatch (ED) and Security constrained optimal power flow (SCOPF) were developed. These techniques have been used extensively in network operation, planning and so on. However, an in-depth presentation showcasing the merits and demerits of these techniques is still lacking in the literature. Hence, this paper intends to fill this gap. In this paper, Economic dispatch, optimal power flow and security-constrained optimal power flow are applied to a 3-bus test system using a linear programming approach. The results of the ED, OPF and SC-OPF are compared and presented.

基于BP-LCO的大豆种植密度和施肥量优化

为解决传统回归模型对大豆种植密度及施肥量进行优化时存在的结果不准确的缺陷,本研究提出基于BP神经网络的线性约束优化方法(BP-Linear Constrained Optimization, BP-LCO)。以黑河43为试验材料,进行四因素五水平正交旋转试验,试验因素为大豆种植密度,N、P2O5和K2O施用量,评价指标为大豆产量,采用BP-LCO算法对种植密度、施肥量与产量关系构建拟合模型,并进行全局寻优及验证试验。结果显示:通过模型分析得到最优种植密度36.67×10^(4)株·hm^(-2)、施N量77.98 kg·hm^(-2)、施P2O5量93.79 kg·hm^(-2)、施K2O量24.34 kg·hm^(-2),大豆产量相应为3 679.56 kg·hm^(-2)。验证试验结果表明,最优配比下大豆实际产量为3 702.29 kg·hm^(-2),实际产量与理论产量的相对误差为0.62%。结果说明该方法的优化结果准确,是一种行之有效的大豆种植密度及施肥量优化方法。

New Facts in Regression Estimation under Conditions of Multicollinearity

This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression models are investigated, the first of which corresponds to systems with a negative feedback, while the second class presents systems without the feedback. In the first case the use of shrinkage estimators, especially the Principal Component estimator, is inappropriate but is possible in the second case with the right choice of the regularization parameter or of the number of principal components included in the regression model. This fact is substantiated by the study of the distribution of the random variable , where b is the LS estimate and β is the true coefficient, since the form of this distribution is the basic characteristic of the specified classes. For this study, a regression approximation of the distribution of the event based on the Edgeworth series was developed. Also, alternative approaches are examined to resolve the multicollinearity issue, including an application of the known Inequality Constrained Least Squares method and the Dual estimator method proposed by the author. It is shown that with a priori information the Euclidean distance between the estimates and the true coefficients can be significantly reduced.

碳三加氢装置鲁棒最小协方差约束控制及应用

碳三加氢反应器操作条件多变,并且存在级联反应,传统的手动操作配氢容易过加氢或漏炔,导致出口甲基乙炔(MA)和丙二烯(PD)浓度波动较大,还会影响催化剂的选择性和转化率。由于碳三加氢过程具有非线性、操作区域多变的特点,传统的基于线性模型的模型预测控制器在工业过程控制中存在较大的局限性。Hammerstein模型是一种将非线性稳态环节和线性动态环节串联的非线性模型,非常适合描述非线性工业对象且方便控制器设计。提出了一种基于Hammerstein模型的鲁棒最小协方差约束控制方法,Hammerstein模型的非线性稳态部分采用WaveARX神经网络逼近,并根据多操作点稳态输入输出数据进行辨识,通过机理分析辨识得到的操作点附近线性化模型作为线性动态部分,将非线性鲁棒控制问题转化为线性模型鲁棒约束控制和非线性环节求逆问题,基于Hammerstein模型的建模偏差,对模型输出偏差协方差上限进行约束并最小化,采用线性矩阵不等式求解出次优状态反馈控制律,再根据非线性部分的逆模型得到系统的控制输入,仿真及工业应用结果证实了所提方法的可行性和有效性。

考虑输入受限的高超声速飞行器预设性能控制

针对考虑输入幅值与速率受限的高超声速飞行器跟踪性能问题,提出基于受限指令滤波器的预设性能控制方案。为了提高系统瞬态和稳态性能,设计预设性能反演控制器,并通过设计新的性能函数使得跟踪误差超调量更小。引入指令滤波器来处理反演控制器设计中难以求导的问题。针对输入受限问题,构造一种受限指令滤波器来约束系统控制律,保证控制输入满足幅值和速率的限制要求,并进行相应的理论证明。另外,考虑系统参数不确定性与外界干扰,采用线性扩张状态观测器进行观测并补偿。基于Lyapunov稳定理论证明系统的所有跟踪误差最终一致有界。通过仿真验证该方法的有效性。

考虑风电出力不确定性的风电-抽水蓄能互补系统短期优化调度

风电和抽水蓄能电站联合运行可以平抑风电随机波动、提升风电消纳率。文章针对多个风电场的出力不确定性,采用概率性序列方法进行处理,提出了一种基于厂网协商机制的风电-抽水蓄能联合调度模式,并建立了基于机会约束规划的风电-抽水蓄能互补系统短期优化调度模型。模型以风电-抽水蓄能互补系统总发电收益最大为目标,综合考虑了抽水蓄能电站的水力约束、机组运行约束和系统功率平衡约束。为提高模型求解效率并获得全局最优解,文章将原模型转换为混合整数线性规划(Mixed Integer Linear Programming,MILP)模型,最后使用商业化求解器LINGO进行求解。优化调度结果表明,抽水蓄能电站能够很好的补偿风电出力的波动性,并显著提升互补系统的总发电收益。

基于LSD聚类拟合与KF的轨道检测算法

针对传统无人机巡检中视觉轨道识别的识别效率低、精度差的问题,提出了一种基于LSD的约束聚类拟合与卡尔曼滤波相结合的轨道线检测算法。首先针对由于镜头视角造成的视角畸变,采用IPM算法矫正,并通过LSD算法检测出轨道轮廓,在轨道间距约束将LSD检测结果进行聚类并进行最小二乘拟合得到轨道直线。然后根据轨道几何特征和无人机动力学特性建立数学模型,并结合卡尔曼滤波器对轨道坐标信息进行跟踪估计,以保证算法的稳定性和鲁棒性。采用无人机采集多个场景的轨道图像作为测试样本,对检测算法与其他算法进行对比实验。实验结果表明,本文轨道识别算法优于其他算法,其轨道准确识别率达到92.49%,识别速率达到23frame/s,满足轨道检测的稳定性和实时性要求。

基于MILP的应用服务器集群能耗与性能实时优化

在节能减排和激烈同行竞争的环境下,应用服务器集群的能耗与性能优化十分迫切.针对已有研究在性能指标和实时性方面的不足,提出一种集群能耗与性能实时优化方案.该方案结合采用线性加权法和主目标法优化集群功率与请求丢弃率这两个目标,将双目标优化转换成一个单目标约束优化.首先基于CPU频率等效连续调整模式下的服务器负载-功率模型,定义很少的变量将集群优化描述成混合整数二次规划问题,然后采用变量拆分和变量转换将其转化成混合整数线性规划(mixed integer linear programming,MILP)问题并引入特殊顺序集约束,最后采用Gurobi优化器求解该MILP.通过对CPU频率调整的进一步优化,大幅度减少了CPU频率的切换.多种场景下的测试表明,该方案的求解时间约在10 ms左右,特殊顺序集约束的引入使求解时间更为稳定,从而能够保证优化的实时进行.

一种求解度约束最小生成树问题的混合整数线性规划方法

针对含有度约束的最小生成树问题,区别于传统启发式算法和智能算法,提出了一种将度约束最小生成树问题线性化的方法。通过邻接矩阵和关联矩阵处理各节点的出线度约束,以电力系统中直流潮流节点功率平衡思想处理网络的辐射性约束,并基于CPLEX平台调用yalmip求解MILP模型。以8节点系统,9节点系统,旅行商问题的eil51系统进行算例测试,证明线性模型能够有效求解含有度约束生成树规划问题。

地震道的非线性约束反演

对于复杂波场储层研究,非线性反演在解空间的性质、状态方面比线性反演更具有优势。基于非线性最优化理论,本文提出了构造—测井约束下的地震资料非线性反演方法,该方法综合了测井约束反演和宽带约束反演等线性反演方法的优点。实际地震资料的处理结果表明,该方法运算速度快、稳定、精度高,在油气储层研究中具有良好的应用前景。

一种非线性约束优化的微粒群新算法

通过对标准微粒群算法(PSO)改进,采用动态罚函数的方法,提出了一种求解非线性约束优化问题的新算法.由于使用了一种新的适应度函数,该算法具有很强的全局寻优能力.