一阶多智能体受扰系统的自抗扰分布式优化算法

研究一类具有未知外部干扰的一阶多智能体系统的分布式优化问题.在分布式优化任务中,每个智能体只被容许利用自己的局部目标函数和邻居的状态信息,设计一个分布式优化算法,使全局目标函数取得最小值,其中全局目标函数是所有局部目标函数之和.针对该问题,首先提出由扩张状态观测器和优化算法组成的自抗扰分布式优化算法.其次,在Lyapunov稳定性的基础上发展新的方法,对闭环系统的收敛性和稳定性进行严格的证明;当外部干扰为常值时,所设计的优化算法能使所有智能体的状态指数收敛到全局目标函数的最小值;当外部干扰为有界干扰时,通过调整扩张状态观测器的增益参数,所设计的优化算法能使所有智能体的状态收敛到全局目标函数最小值的任意小的邻域内.最后,仿真结果表明了该优化算法的有效性.     

基于平滑技术和一维搜索的全局优化进化算法及其收敛性

为了解决全局优化算法中的一个难点--算法易于陷入局部极小点,设计了一个平滑函数,该函数可以消除一些局部极小点,而在包含最优点的部分,函数保持不变.这样,通过对此平滑函数的优化,局部极小点的数目就会在迭代过程中大量地减少,使算法更易找出全局极小点;根据平滑函数的性质,设计了一个新的杂交算子,此算子能自适应地产生优质的后代;利用平滑函数的性质,巧妙地将一维搜索技术用于算法的设计之中,从而使算法的速度大大提高;在此基础上,设计了一个解全局优化问题的新的高效进化算法,并且证明了其全局收敛性.最后的数值实验也表明新算法十分有效.     

基于一种改进的Powell算法和互信息的医学图像配准方法

Powell是一种直接法,不用计算目标函数的梯度,仅通过比较目标函数的数值大小来移动迭代点就可求出极值。但Powell算法对参数的初始值有很大的依赖性,在图像配准的优化过程中易陷入局部最优,使得优化结果很大程度上依赖于初始值,会得到错误的配准参数,从而影响配准效果。为解决这一问题,使用粒子群优化算法(PSO)求取Powell算法的初始值。经检验,此方法克服了Powell算法的缺点,大大提高了配准精度。     

二阶智能体的分布式非光滑资源分配算法

分布式资源分配问题旨在满足局部约束下完成一定量资源分配的同时使全局成本函数最小.首先,针对无向连通网络下二阶积分器型线性智能体系统,结合Karush-Kuhn-Tucker条件,提出一种初始值任意的分布式优化算法,其中,全局等式约束对偶变量实现比例积分控制,局部凸函数不等式约束对偶变量实现自动获取.当全局成本函数为非光滑凸函数时,借助集值LaSalle不变性原理理论证明所提出算法渐近收敛到全局最优解.其次,将所提出算法推广至无向连通网络下参数未知的Euler-Lagrange多智能体系统.当全局成本函数为非光滑凸函数时,借助Barbalat引理理论证明所提出算法渐近收敛到全局最优解.最后,通过数值仿真验证了所提算法的有效性.     

基于预设时间收敛的分布式优化算法

考虑一类分布式优化问题,其目标是通过局部信息交互,使得局部成本函数之和构成的全局成本函数最小.针对该类问题,通过引入时基发生器(TBG),提出两种基于预设时间收敛的分布式比例积分(PI)优化算法.与现有的基于有限/固定时间收敛的分布式优化算法相比,所提出算法的收敛时间不依赖于系统的初值和参数,且可以任意预先设计.此外,在全局成本函数关于最优值点有限强凸,局部成本函数为可微的凸函数,且具有局部Lipschitz梯度的条件下,通过Lyapunov理论证明了所提算法都能实现预设时间收敛.最后,通过数值仿真验证了所提出算法的有效性.     

基于事件触发的分布式优化算法

本文研究了一类分布式优化问题,其目标是通过局部信息交换使由局部成本函数之和构成的全局成本函数最小.针对无向连通图,我们提出了两种基于比例积分策略的分布式优化算法.在局部成本函数可微且凸的条件下,证明了所提算法渐近收敛到全局最小值点.更进一步,在局部成本函数具有局部Lipschitz梯度和全局成本函数关于全局最小值点是有...     

基于樽海鞘群体优化非负矩阵分解的高光谱图像解混算法

针对鲁棒非负矩阵分解应用于高光谱图像处理时,存在对初始值的敏感性,求解目标函数时易陷入局部最优的缺点,提出基于樽海鞘群体优化鲁棒非负矩阵分解的高光谱图像解混算法.该算法基于鲁棒线性混合模型,在RNMF框架下,采用樽海鞘群体算法取代乘法迭代策略,以增强算法全局搜索能力,在约束空间内随机搜索满足目标函数的全局最优解,可有效地完成非线性高光谱图像解混.仿真数据与真实遥感数据实验结果表明,本文算法在处理高光谱图像时,能够有效地避免RNMF算法易陷入局部最优解的局限性,具有更好的解混性能.     

一种无需基础矩阵的鲁棒性极线校正算法

立体视觉校正也称为极线校正,它的目的是使得立体图像的对应极线平行于水平方向,消除垂直方向上的视差,从而使得在立体匹配过程中可以更为快速准确地寻找对应点.在传统的投影校正算法的基础上提出了一种鲁棒性校正算法,直接通过原始匹配点计算投影变换矩阵,利用遗传算法良好的全局搜索能力和Levenberg-Marquardt算法稳定快速的局部搜索功能进行分步优化计算,同时本算法采用了随机抽样一致算法（RANSAC）鲁棒估计思想,避免了由于对应点噪声引起的误差.此外,还针对两个平行放置的摄像机之间具有较小运动的情况,提出了一种鲁棒的优化函数.实验结果说明,该算法是一种有效的极线校正方法.     

基于本质矩阵的摄像机自标定方法

本质矩阵描述了在摄像机内参数矩阵已知的条件下的对极几何关系,是归一化图像坐标下的基础矩阵。鉴于本质矩阵具有两相等的非零奇异值,提出了一种基于本质矩阵的自标定方法,该方法首先利用本质矩阵这个特性来构造目标函数,考虑到传统非线性优化算法的诸多不足,最后用粒子群优化算法来求解。实验结果表明,该方法精度较高、鲁棒性较强,是一种简单而有效的自标定方法。     

泰勒级数准则函数鲁棒性点云配准算法

为减小离群点对点云配准精确度的影响,避免点云配准迭代计算过程中陷入局部最小值,基于鲁棒性准则函数点云配准框架提出泰勒级数准则函数鲁棒性点云配准算法.该方法分为泰勒级数准则函数的提出和配准初始值的确定2个方面.泰勒级数准则函数中,考虑各准则函数限制离群点影响来提高配准精确度的内因,对权值递减速率较合理的Cauchy准则函数进行泰勒级数展开,构造泰勒级数准则函数解决离群值问题;配准初始值的确定中,通过计算待匹配点云数据集的重心,根据重心信息确定平移向量,解决局部最小值问题.数值实验结果表明,泰勒级数准则函数配准误差较最小二乘法、Huber、Tukey和Cauchy准则函数更小,在配准精度上有了较大的提高,并且误差值稳定收敛;引入插值算法对点云数据进行处理,对后续的配准精度有一定的改善.     

Fibonacci multi-modal optimization algorithm in noisy environment

Noises are very common in practical optimization problems. It will cause interference on optimization algorithms and thus makes the algorithms difficult to find a true global extreme point and multiple local extreme points. For the problem, this paper proposes a Fibonacci multi-modal optimization (FMO) algorithm. Firstly, the proposed algorithm alternates between global search and local optimization in order not to fall into local optimum points and to retain multiple optimum points. And then, a Fibonacci regional scaling criterion is proposed in the FMO algorithm to alleviate the effects of noise, and the position of optimum point is determined according to its probability distribution under noise interference. In experiments, we evaluate the performance of the proposed FMO algorithm through 35 benchmark functions. The experimental results show that compared with Particle Swarm Optimization (PSO) algorithm, three improved versions of PSO, and Genetic algorithm (GA), the proposed FMO algorithm can gain more accurate location of optimum point and more global and local extreme points under noisy environment. Finally, an example of practical optimization in radio spectrum monitoring is used to show the performance of the FMO algorithm.     

Developments in structural-acoustic optimization for passive noise control

Summary  Low noise constructions receive more and more attention in highly industrialized countries. Consequently, decrease of noise radiation challenges a growing community of engineers. One of the most efficient techniques for finding quiet structures consists in numerical optimization. Herein, we consider structural-acoustic optimization understood as an (iterative) minimum search of a specified objective (or cost) function by modifying certain design variables. Obviously, a coupled problem must be solved to evaluate the objective function. In this paper, we will start with a review of structural and acoustic analysis techniques using numerical methods like the finite- and/or the boundary-element method. This is followed by a survey of techniques for structural-acoustic coupling. We will then discuss objective functions. Often, the average sound pressure at one or a few points in a frequency interval accounts for the objective function for interior problems, wheareas the average sound power is mostly used for external problems. The analysis part will be completed by review of sensitivity analysis and special techniques. We will then discuss applications of structural-acoustic optimization. Starting with a review of related work in pure structural optimization and in pure acoustic optimization, we will categorize the problems of optimization in structural acoustics. A suitable distinction consists in academic and more applied examples. Academic examples iclude simple structures like beams, rectangular or circular plates and boxes; real industrial applications consider problems like that of a fuselage, bells, loudspeaker diaphragms and components of vehicle structures. Various different types of variables are used as design parameters. Quite often, locally defined plate or shell thickness or discrete point masses are chosen. Furthermore, all kinds of structural material parameters, beam cross sections, spring characteristics and shell geometry account for suitable design modifications. This is followed by a listing of constraints that have been applied. After that, we will discuss strategies of optimization. Starting with a formulation of the optimization problem we review aspects of multiobjective optimization, approximation concepts and optimization methods in general. In a final chapter, results are categorized and discussed. Very often, quite large decreases of noise radiation have been reported. However, even small gains should be highly appreciated in some cases of certain support conditions, complexity of simulation, model and large frequency ranges. Optimization outcomes are categorized with respect to objective functions, optimization methods, variables and groups of problems, the latter with particular focus on industrial applications. More specifically, a close-up look at vehicle panel shell geometry optimization is presented. Review of results is completed with a section on experimental validation of optimization gains. The conclusions bring together a number of open problems in the field.     

Global optimization: an auxiliary cost function approach

An efficient and practical solution to a class of global function optimization is proposed. The algorithm consists of a stochastic search of initial guesses and a gradient-based solution-finding algorithm. The key idea is to introduce an auxiliary cost function that can indicate whether the gradient-based solution-finding process goes toward a global minimum of the cost function and that helps us to prevent the process from going to local minima. Simulation examples are used to show the mechanism, power, and restrictions of the approach     

Hybridization of gradient descent algorithms with dynamic tunnelingmethods for global optimization

An algorithm based on gradient descent techniques with dynamic tunneling methods fur global optimization is proposed. The proposed algorithm consists of gradient descent for local search and a direct search scheme, based on dynamic tunneling technique, for repelling away from local minimum to find the point of next local descent. This search process applied repeatedly finds the global minimum of an objective function. The convergence properties of the proposed algorithm is validated experimentally on benchmark problems. A comparative computational results confirm the importance of dynamic tunneling in gradient descent techniques     

Nonlinear model predictive control using deterministic global optimization

This paper presents a Nonlinear Model Predictive Control (NMPC) algorithm utilizing a deterministic global optimization method. Utilizing local techniques on nonlinear nonconvex problems leaves one susceptible to suboptimal solutions at each iteration. In complex problems, local solver reliability is difficult to predict and dependent upon the choice of initial guess. This paper demonstrates the application of a deterministic global solution technique to an example NMPC problem. A terminal state constraint is used in the example case study. In some cases the local solution method becomes infeasible, while the global solution correctly finds the feasible global solution. Increased computational burden is the most significant limitation for global optimization based online control techniques. This paper provides methods for improving the global optimization rates of convergence. This paper also shows that globally optimal NMPC methods can provide benefits over local techniques and can successfully be used for online control.     

凸松弛全局优化机器人手眼标定

针对机器人运动学正解及相机的外参数标定存在偏差时,基于非线性最优化的手眼标定算法无法确保目标函数收敛到全局极小值的问题,提出基于四元数理论的凸松弛全局最优化手眼标定算法。考虑到机械手末端相对运动旋转轴之间的夹角对标定方程求解精度的影响,首先利用随机抽样一致性（RANSAC）算法对标定数据中旋转轴之间的夹角进行预筛选,再利用四元数参数化旋转矩阵,建立多项式几何误差目标函数和约束,采用基于线性矩阵不等式（LMI）凸松弛全局优化算法求解全局最优手眼变换矩阵。实测结果表明,该算法可以求得全局最优解,手眼变换矩阵几何误差平均值不大于1.4 mm,标准差小于0.16 mm,结果稍优于四元数非线性最优化算法。     

On Parameter Estimation Using Nonparametric Noise Models

Fitting multidimensional parametric models in frequency domain using nonparametric noise models is considered in this paper. A nonparametric estimate of the noise statistics is obtained from a finite number of independent data sets. The estimated noise model is then substituted for the the true noise covariance matrix in the maximum likelihood loss function to obtain suboptimal parameter estimates. The goal here is to present an analysis of the resulting estimates. Sufficient conditions for consistency are derived, and an asymptotic accuracy analysis is carried out. The first- and second-order statistics of the cost function at the global minimum point are also explored, which can be used for model validation. The analytical findings are validated using numerical simulation results.     

A direct search variant of the simulated annealing algorithm for optimization involving continuous variables

A memory-based simulated annealing algorithm is proposed which fundamentally differs from the previously developed simulated annealing algorithms for continuous variables by the fact that a set of points rather than a single working point is used. The implementation of the new method does not need differentiability properties of the function being optimized. The method is well tested on a range of problems classified as easy, moderately difficult and difficult. The new algorithm is compared with other simulated annealing methods on both test problems and practical problems. Results showing an improved performance in finding the global minimum are given.Scope and purposeThe inherent difficulty of global optimization problems lies in finding the very best optimum (maximum or minimum) from a multitude of local optima. Many practical global optimization problems of continuous variables are non-differentiable and noisy and even the function evaluation may involve simulation of some process. For such optimization problems direct search approaches are the methods of choice. Simulated annealing is a stochastic global optimization algorithm, initially designed for combinatorial (discrete) optimization problems. The algorithm that we propose here is a simulated annealing algorithm for optimization problems involving continuous variables. It is a direct search method. The strengths of the new algorithm are: it does not require differentiability or any other properties of the function being optimized and it is memory-based. Therefore, the algorithm can be applied to noisy and/or not exactly known functions. Although the algorithm is stochastic in nature, it can memorise the best solution. The new simulated annealing algorithm has been shown to be reliable, fast, general purpose and efficient for solving some difficult global optimization problems.