基于优化最小化的软阈值问题迭代求解方法

软阈值问题是优化理论中非常重要的一种问题。该问题存在显式解,可以通过软阈值算子来求解。软阈值问题的解在信号降噪、深度学习等领域中得到了广泛应用。文章从一种全新的角度来探索软阈值问题的解,在优化最小化框架下给出该问题的一种新的迭代求解方法,并从理论上保证最终得到该问题的局部最优解。在模拟数据上的实验表明,该方法与软阈值算子法求出的解完全一致。

迭代优化最小化唯相位波束形成

为了增强唯相位波束形成(Phase-Only Beamforming,POB)的干扰和噪声抑制性能,提高非凸POB权值求解的实时性,该文设计了迭代优化最小化(Iterative Majorization Minimization,IMM)唯相位最小方差无失真响应波束形成器(Minimum Variance Distortion-less Response Beamformer,MVDRB)。将无失真响应约束转化成最大化期望方向阵列响应,推导了二次型目标函数的上界,得到IMM-POB优化模型,并进一步推导出每次迭代的闭式最优解。仿真分析表明所设计的IMM-POB:在相同输入信噪比下,可获得高于现有迭代算法和最优MVDRB的信干噪比改善;干扰抑制性能几乎完全逼近最优MVDRB,且具有更优的噪声抑制性;受快拍数影响较小;闭式最优权仅包含单次矩阵和向量乘法,使算法具有较强的实时性,可应用于大规模阵列。

基于优化最小化框架的墙体成像算法

在穿墙雷达建筑物布局成像中,针对现有成像算法因没有充分利用墙体本身的物理特性而出现墙体轮廓模糊、边缘不连贯以及成像过程耗时的问题,提出一种基于优化最小化框架的墙体成像算法。该算法首先利用像素块来表征墙体连续块状的物理特性,并将其引入信号模型,然后以LASSO(Least Absolute Shrinkage and Selection Operator)模型为基础,在优化最小化框架下构造稳健的优化目标函数,最后利用墙体回波信号的时移特性并结合卷积得到迭代过程的快速实现。实验结果表明,该算法对墙体成像特征明显,不仅保证了墙体轮廓特性,而且杂波少、分辨率高,并较大幅度减小了成像算法处理时间。

交替迭代最小化稀疏穿墙成像快速算法

针对墙后目标成像分辨率与成像速度不能同时有效满足的问题,提出一种参数交替迭代最小化框架的墙后隐藏目标稀疏成像快速算法。首先,该算法利用稀疏信号贝叶斯模型的最大后验估计准则得到包含参数与成像体散射系数矢量的目标函数,然后在优化最小化框架(MM)下求解出对应的最优化函数,最后利用目标函数对应的优化函数对成像体散射系数、噪声功率和超参数进行交替迭代求解。仿真和实验结果表明,该方法对墙后点目标以及扩展目标进行高质量成像,并且大大提高算法速度。

一种具有多普勒容忍性的通感一体化波形设计

针对现有联合设计的通感一体化波形对运动目标探测性能不足的问题,该文提出了一种具有多普勒容忍性的通感一体化波形联合设计方案。首先,基于脉冲串模糊函数,推导了构造多普勒容忍波形等价于波形在相关区内具有极低的积分旁瓣电平。基于此,构建了以最小化一体化波形的加权积分旁瓣电平为优化准则,以发射波形的能量、峰均功率比以及与通信波形之间的相位差为约束条件的优化问题,从而实现具有多普勒容忍性的通感一体化波形的构造。由于该优化问题的非凸性,该文提出一种基于优化最小化的迭代优化算法对其进行求解。数值仿真实验表明,相比传统一体化波形,该文提出的一体化波形具有更高的多普勒容忍性和更低的误符号率,在保证通信质量的前提下显著提升了通感一体化系统对运动目标的探测性能。

3GPP最小化路测技术及最新进展

本文介绍了3GPP的R10版本以来引入的最小化路测技术(MDT),概要描述了R10 MDT的架构、模式分类、激活过程、测量配置及上报机制等内容,总结了最新的R11 MDT协议扩展情况。

闭式泵控液压-机械直线执行器的离散PID控制

液压驱动因其功率密度高、直线输出力大,广泛应用于装备制造领域。但非对称液压缸受两腔面积差的制约,在阀控系统中需要用非对称阀控制,在闭式泵控系统中需要增加额外的补油回路。而电动缸具有对称的输出力和较高的能效,解决了非对称液压缸面积差的影响,但功率密度低使电动缸难以满足低转速大扭矩的高负载工况。针对上述问题,提出了液压回转与机械直线转换相结合的新型驱动方式,采用闭式泵控马达驱动滚珠丝杠带动活塞杆动作。由于在闭环控制中单一的PID难以满足全负载工况,系统采用局部最小化优化方法自动寻找最优PID参数,生成离散PID图表并根据负载自动选择对应的PID参数控制以减小负载干扰。结果表明:离散PID自动调定的系统能避免负载变化产生较大干扰,在变负载和目标位移情况下,离散PID参数自动调整的响应曲线阶跃下降和上升的稳态误差最大分别为4.5 mm、3.0 mm。

基于MI-RRT^(*)算法的路径规划研究

针对Informed-RRT(rapidly-exploring random tree)^(*)算法收敛速度慢、优化效率低和生成路径无法满足实际需求等问题,开展了基于MI-RRT^(*)(Modified Informed-RRT^(*))算法的路径规划研究,通过引入贪心采样和自适应步长的方法提高算法的收敛率,减少路径生成时间、降低内存占用;利用最小化Snap曲线优化的方法使路径平滑的同时动力也变化平缓,达到节省能量的效果,并提供实际可执行的路径。最后通过多组不同复杂度的实验环境表明,较Informed-RRT^(*)算法MI-RRT^(*)算法稳定性更高、所得规划路径平滑可执行,并且能够减少20%的迭代次数和25%的搜索时间,得出在开阔以及密集环境中MI-RRT^(*)算法较Informed-RRT^(*)和RRT^(*)算法有明显的优势。

基于非最小化优化的手眼标定方法

在分析手眼标定问题数值特征的基础上,提出一种新的基于非最小化优化的手眼标定方法。采用张量的形式描述手眼标定方程,提出了非最小化优化条件下的代价函数,通过特征计算求解相应估计方程。扰动分析证明了该方法求解的精确性。分别采用仿真数据和真实数据进行试验。试验结果显示,该方法能够通过无初值的计算实现手眼方程的求解,避免了优化迭代产生的复杂计算,具有较高的鲁棒性、有效性和天然的运动选择特性。与其他方法相比较,新方法大大节省了运算时间,并降低了计算误差,为机器人系统的实际标定提供一个很好的选择。

基于图像局部方向特性的自适应全变分去噪模型

针对全变分模型(total variation,TV)以图像的梯度信息作为去噪的尺度参数,未考虑图像局部纹理的方向性的缺点,提出了一种基于图像局部方向特性的自适应全变分去噪模型(Adaptive directional total variation,ADTV),并推导出该模型的迭代数值求解过程。在该模型中,首先,计算出图像局部方向的角度矩阵。然后,构造与图像纹理方向一致的椭圆区域代替TV模型的圆形区域。最后,通过优化最小化算法迭代求解以获得去噪后图像。通过对比实验证明,本文提出的模型取得了更高的峰值信噪比,去噪过程中更好地增强了图像的细节信息。

带总观测误差约束的模糊图像恢复

模糊图像恢复是数字图像处理领域的研究热点之一,总变差(Total Variation,TV)规整化可以很好的保持图像的细节,然而,传统的TV图像恢复模型需要考虑最优的正则化参数,由此,提出了一族包含不同规整化因子,带总观测误差约束的模糊图像恢复模型,并分为去模糊和去噪两步求解此模型。在去模糊过程中,利用共轭梯度法求出一个满足总观测误差约束的初始恢复图像;在去噪过程中,首先,以去模糊的结果作为初始估计;其次,针对lp范数最小化问题,利用优化—最小化(Majoriziation-Minimization,MM)算法的思想,将原问题转化为一系列容易求解的优化子问题;最后,极小化优化子问题,得到最终的恢复图像。实验结果表明,该算法对模糊图像的恢复效果是显著地。

A min-max optimization approach for weight determination in analytic hierarchy process

A min-max optimization method is proposed as a new approach to deal with the weight determination problem in the context of the analytic hierarchy process. The priority is obtained through minimizing the maximal absolute difference between the weight vector obtained from each column and the ideal weight vector. By transformation, the. constrained min- max optimization problem is converted to a linear programming problem, which can be solved using either the simplex method or the interior method. The Karush-Kuhn- Tucker condition is also analytically provided. These control thresholds provide a straightforward indication of inconsistency of the pairwise comparison matrix. Numerical computations for several case studies are conducted to compare the performance of the proposed method with three existing methods. This observation illustrates that the min-max method controls maximum deviation and gives more weight to non- dominate factors.

Optimal Structural Design of the Midship of a VLCC Based on the Strategy Integrating SVM and GA

In this paper a hybrid process of modeling and optimization, which integrates a support vector machine （SVM） and genetic algorithm （GA）, was introduced to reduce the high time cost in structural optimization of ships. SVM, which is rooted in statistical learning theory and an approximate implementation of the method of structural risk minimization, can provide a good generalization performance in metamodeling the input-output relationship of real problems and consequently cuts down on high time cost in the analysis of real problems, such as FEM analysis. The GA, as a powerful optimization technique, possesses remarkable advantages for the problems that can hardly be optimized with common gradient-based optimization methods, which makes it suitable for optimizing models built by SVM. Based on the SVM-GA strategy, optimization of structural scantlings in the midship of a very large crude carrier （VLCC） ship was carried out according to the direct strength assessment method in common structural rules （CSR）, which eventually demonstrates the high efficiency of SVM-GA in optimizing the ship structural scantlings under heavy computational complexity. The time cost of this optimization with SVM-GA has been sharply reduced, many more loops have been processed within a small amount of time and the design has been improved remarkably.

Multiple objectives application approach to waste minimization

Besides economics and controllability, waste minimization has now become an objective in designing chemical processes, and usually leads to high costs of investment and operation. An attempt was made to minimize waste discharged from chemical reaction processes during the design and modification process while the operation conditions were also optimized to meet the requirements of technology and economics. Multiobjectives decision nonlinear programming (NLP) was employed to optimize the operation conditions of a chemical reaction process and reduce waste. A modeling language package-SPEEDUP was used to simulate the process. This paper presents a case study of the benzene production process. The flowsheet factors affecting the economics and waste generation were examined. Constraints were imposed to reduce the number of objectives and carry out optimal calculations easily. After comparisons of all possible solutions, best-compromise approach was applied to meet technological requirements and minimize waste.

Optimization Framework for Conceptual Powertrain Design

With an increasing number of vehicles with alternative powertrains, the choice of the most appropriate powertrain system for a vehicle class or a load cycle is challenging. This paper introduces a method to design an optimal alternative powertrain based on a longitudinal dynamic simulation. The objective function of the minimization problem describes the characteristic map of the traction system. The goal of the optimization is to minimize fuel consumption respectively energy demand. Different types of propulsion systems are investigated. The results show that the proposed method delivers useful alternative powertrains by applying an optimization with reasonable restrictions.

Enhancements of Genetic Algorithm for Minimum Cost Design of Steel Frames Considering Fabrication Cost

A discrete optimization problem for minimizing the sum of fabrication cost and steel material cost of sf^el frames under constraints based on Japanese seismic code is set up. Enhancements of the genetic algorithm for the above-mentioned problem are proposed, which are combined with a 1D （one-dimensional） search or a 2D （two-dimensional） search. After the proposed methods are described, they are applied to a five-story frame. A comparison with an exact solution obtained by a revised enumeration algorithm demonstrates the effectiveness of the proposed methods.

Optimization of volume to point conduction problem based on a novel thermal conductivity discretization algorithm

A conduction heat transfer process is enhanced by filling prescribed quantity and optimized-shaped high thermal conductivity materials to the substrate. Numerical simulations and analyses are performed on a volume to point conduction problem based on the principle of minimum entropy generation. In the optimization, the arrangement of high thermal conductivity materials is variable, the quantity of high thermal-conductivity material is constrained, and the objective is to obtain the maximum heat conduction rate as the entropy is the minimum.A novel algorithm of thermal conductivity discretization is proposed based on large quantity of calculations.Compared with other algorithms in literature, the average temperature in the substrate by the new algorithm is lower, while the highest temperature in the substrate is in a reasonable range. Thus the new algorithm is feasible. The optimization of volume to point heat conduction is carried out in a rectangular model with radiation boundary condition and constant surface temperature boundary condition. The results demonstrate that the algorithm of thermal conductivity discretization is applicable for volume to point heat conduction problems.

一种遥感影像超分辨率重建的稀疏表示建模及算法

为了对单幅低分辨率遥感影像的空间分辨率进行增强,提出一种基于稀疏表示的超分辨率重建方法。该方法首先采用优化最小化方法学习高-低分辨率联合字典对,通过构造一个参数互相解耦的易于优化的代理函数,替代原来的参数互相耦合难以优化的目标函数,保证每一次迭代求解的值在局部范围内最优。然后,将学习的字典对用以指导其他低分辨率遥感影像的超分辨率重建。试验表明,与传统的插值方法相比,本研究算法在客观的评价指标上具有一定的提高,在主观的视觉效果上也取得一些改善,可为其他单幅低分辨率遥感影像的超分辨率重建提供有用的高频细节信息,具有一定的普适性。

Constructal optimization of cylindrical heat sources with forced convection based on entransy dissipation rate minimization

Based on constructal theory and entransy theory,the optimal designs of constant-and variable-cross-sectional cylindrical heat sources are carried out by taking dimensionless equivalent resistance minimization as optimization objective.The effects of the cylindrical height,the cylindrical shape and the ratio of thermal conductivity of the fin to that of the heat source are analyzed.The results show that when the volume of the heat source is fixed,there exists an optimal ratio of the center-to-centre distance of the fin and the heat source to the cylinder radius which leads to the minimum dimensionless equivalent thermal resistance.With the increase in the height of the cylindrical heat source and the ratio of thermal conductivity,the minimum dimensionless equivalent thermal resistance decreases gradually.For the heat source model with inverted variable-cross-sectional cylinder,there exist an optimal ratio of the center-to-centre distance of the fin and the heat source to the cylinder radius and an optimal radius ratio of the smaller and bigger circles of the cylindrical fin which lead to a double minimum dimensionless equivalent thermal resistance.Therefore,the heat transfer performance of the cylindrical heat source is improved by adopting the cylindrical model with variable-cross-section.The optimal constructs of the cylindrical heat source based on the minimizations of dimensionless maximum thermal resistance and dimensionless equivalent thermal resistance are different.When the thermal security is ensured,the optimal construct of the cylindrical heat source based on minimum equivalent thermal resistance can provide a new alternative scheme for the practical design of heat source.The results obtained herein enrich the work of constructal theory and entransy theory in the optimal design field of the heat sources,and they can provide some guidelines for the designs of practical heat source systems.

An Optimal Online Algorithm for Fractional Scheduling on Uniform Machines with Three Hierarchies

This paper is concerned with the fractional version of online hierarchical scheduling problem on uniform machines.In the problem,the jobs and machines have several different hierarchies and each job can be arbitrarily split between the machines with hierarchies not above the hierarchy of the job.The objective is to minimize the makespan.The authors present an optimal algorithm for the problem with three hierarchies.