一种适用于多机器人搜索动态目标的改进粒子群算法

粒子群算法引导机器人搜索跟踪动态目标时,在迭代后期易出现收敛停滞现象。为了改善上述情况,本文提出了结合牛顿法的改进粒子群算法。为了结合粒子群算法与牛顿法,我们在算法中引入了马尔科夫链,这使得机器人在每一次迭代时以一定的概率随机选择牛顿法或粒子群算法搜索跟踪目标。为了模拟机器人搜索动态目标的真实环境,本文还利用了通信项使机器人以一定的方式努力与基站保持通信,用来实时更新目标信息。仿真结果表明,改进的粒子群算法能有效的寻找并跟踪动态目标。     

A Fast 2D Shape Recovery Approach by Fusing Features and Appearance

In this paper, we present a fusion approach to solve the nonrigid shape recovery problem, which takes advantage of both the appearance information and the local features. We have two major contributions. First, we propose a novel progressive finite Newton optimization scheme for the feature-based nonrigid surface detection problem, which is reduced to only solving a set of linear equations. The key is to formulate the nonrigid surface detection as an unconstrained quadratic optimization problem that has a closed-form solution for a given set of observations. Second, we propose a deformable Lucas-Kanade algorithm that triangulates the template image into small patches and constrains the deformation through the second-order derivatives of the mesh vertices. We formulate it into a sparse regularized least squares problem, which is able to reduce the computational cost and the memory requirement. The inverse compositional algorithm is applied to efficiently solve the optimization problem. We have conducted extensive experiments for performance evaluation on various environments, whose promising results show that the proposed algorithm is both efficient and effective.     

一种求解图着色问题的优化组合遗传算法①

图着色算法是一种典型的NP-完全问题。在逆序算子、对偶算子和矩阵遗传算子的性能研究基础上,采用自然数与二进制相互转换的编码方案,应用图着色问题的约束条件建立适应度评价函数,将具有良好局部搜索性能的矩阵遗传算子与具有良好局部搜索性能的逆序与对偶组合算子优化组合应用,构造了一种用于求解图着色问题的优化组合遗传算法,保证了算法的全局收敛性。与基本遗传算法相比较,实验结果表明,该算法对图着色问题有较好的求解性能。     

基于光滑l0范数和修正牛顿法的压缩感知重建算法

基于光滑l0范数最小的压缩感知重建算法——SL0算法,通过引入光滑函数序列去逼近l0范数,从而将l0范数最小的问题转化为光滑函数的最优化问题.针对光滑函数的选取以及求解该函数的最优化问题,提出一种基于光滑l0范数和修正牛顿法的重建算法——NSL0算法.首先采用双曲正切函数序列来逼近l0范数,得到一个新的最优化问题;为了提高该优化问题的计算效率,推导出针对双曲正切函数的修正牛顿方向,并采用修正牛顿法进行求解.实验结果表明,在相同的测试条件下,NSL0算法无论在重建效果还是在计算时间方面都明显优于其他同类算法.     

信赖域共轭梯度法求解二次规划逆问题

为了有效地求解二次规划逆问题,提出了一种求解其对偶问题的子问题的光滑化信赖域共轭梯度法。该方法采用增广拉格朗日法求解其对偶问题,引入光滑函数将对偶问题的子问题转换成连续的无约束优化问题,将信赖域法与共轭梯度法结合,设计出求解二次规划逆问题的算法流程。数值实验结果表明,该方法可行且有效,与牛顿法相比,更适合求解大规模问题。     

Regularized level-set-based inverse lithography algorithm for IC mask synthesis

Inverse lithography technology(ILT)is one of the promising resolution enhancement techniques,as the advanced IC technology nodes still use the 193 nm light source.In ILT,optical proximity correction(OPC)is treated as an inverse imaging problem to find the optimal solution using a set of mathematical approaches.Among all the algorithms for ILT,the level-set-based ILT(LSB-ILT)is a feasible choice with good production in practice.However,the manufacturability of the optimized mask is one of the critical issues in ILT;that is,the topology of its result is usually too complicated to manufacture.We put forward a new algorithm with high pattern fidelity called regularized LSB-ILT implemented in partially coherent illumination(PCI),which has the advantage of reducing mask complexity by suppressing the isolated irregular holes and protrusions in the edges generated in the optimization process.A new regularization term named the Laplacian term is also proposed in the regularized LSB-ILT optimization process to further reduce mask complexity in contrast with the total variation(TV)term.Experimental results show that the new algorithm with the Laplacian term can reduce the complexity of mask by over 40%compared with the ordinary LSB-ILT.     

改进的正则化模型在图像恢复中的应用

目的 由拟合项与正则项组成的海森矩阵,如果不具有特殊结构,其逆矩阵计算比较困难,为克服此缺点,提出一种海森矩阵可分块对角化的牛顿投影迭代算法。方法 首先,用L₂范数描述拟合项,用自变量是有界变差函数的复合函数刻画正则项,建立能量泛函正则化模型。其次,引入势函数,将正则化模型转化为增广能量泛函。再次,构造预条件矩阵,使得海森矩阵可分块对角化。最后,为防止牛顿投影迭代算法收敛到局部最优解,采用回溯线性搜索算法和改进的Barzilai-Borwein步长更新准则使得算法全局收敛。结果 针对图像去模糊正则化模型容易使边缘平滑和产生阶梯效应“两难”问题,提出一种新的正则化模型和牛顿投影迭代算法。仿真结果表明,“两难”问题通过本文算法得到了很好的解决。结论 与其他正则化图像去模糊模型相比,本文算法明显改善图像的质量,如有效地保护图像的边缘,抑制阶梯效应,相对偏差和误差较小,较高的峰值信噪比和结构相似测度。     

Numerical inversions of a source term in the FADE with a Dirichlet boundary condition using final observations

This paper deals with an inverse problem of determining a source term in the one-dimensional fractional advection-dispersion equation (FADE) with a Dirichlet boundary condition on a finite domain, using final observations. On the basis of the shifted Grünwald formula, a finite difference scheme for the forward problem of the FADE is given, by means of which the source magnitude depending upon the space variable is reconstructed numerically by applying an optimal perturbation regularization algorithm. Numerical inversions with noisy data are carried out for the unknowns taking three functional forms: polynomials, trigonometric functions and index functions. The reconstruction results show that the inversion algorithm is efficient for the inverse problem of determining source terms in a FADE, and the algorithm is also stable for additional data having random noises.     

Finite‐Time Average Consensus Based Approach for Distributed Convex Optimization

In this paper, we consider a distributed convex optimization problem where the objective function is an average combination of individual objective function in multi‐agent systems. We propose a novel Newton Consensus method as a distributed algorithm to address the problem. This method utilises the efficient finite‐time average consensus method as an information fusion tool to construct the exact Newtonian global gradient direction. Under suitable assumptions, this strategy can be regarded as a distributed implementation of the classical standard Newton method and eventually has a quadratic convergence rate. The numerical simulation and comparison experiment show the superiority of the algorithm in convergence speed and performance.     

Source term identification for an axisymmetric inverse heat conduction problem

We consider an inverse heat source problem of determining the heat source term from the final temperature history of a cylinder. This problem is ill-posed. A simplified Tikhonov regularization method is applied to formulate regularized solution, which is stably convergent to the exact one with a logarithmic type error estimate.     

基于小波变换的工业内窥镜图像融合算法

针对工业内窥镜使用场所特殊而存在采集的图像效果不佳的问题,提出了一种基于多尺度小波变换和不同融合算子的图像融合算法。首先对源图像进行小波变换,然后对代表近似信息的低频系数采用简单的平均算法融合,对代表细节信息的高频系数采用基于区域方差的动态加权平均算法融合,最后对处理的低频和高频系数进行小波逆变换得到融合图像。实验结果表明,与其它几种算法比较,该算法得到的图像参数较好,提高了图像处理效果。     

基于Moreau-包络的近似平滑迭代磁共振图像重建算法

针对基于压缩感知（CS）的磁共振成像（MRI）稀疏重建中存在的两个非平滑正则项问题,提出了一种基于Moreau包络的近似平滑迭代算法（PSIA）。基于CS的经典MRI稀疏重建是求解一个由最小二乘保真项、小波变换稀疏正则项和总变分（TV）正则项线性组合成的目标函数最小化问题。首先,对目标函数中的小波变换正则项作平滑近似;然后,将数据保真项与平滑近似后的小波正则项的线性组合看成一个新的可以连续求导的凸函数;最后,采用PSIA对新的优化问题进行求解。该算法不仅可以同时处理优化问题中的两个正则约束项,还避免了固定权重带来的算法鲁棒性问题。仿真得到的体模图像及真实磁共振图像的实验结果表明,所提算法与四种经典的稀疏重建算法：共轭梯度（CG）下降算法、TV1范数压缩MRI（TVCMRI）算法、部分k空间重建算法（RecPF）和快速复合分离算法（FCSA）相比,在图像信噪比、相对误差和结构相似性指数上具有更好的重建结果,且在算法复杂度上与现有最快重建算法即FCSA相当。     

一种改进牛顿法的盲源分离算法

针对盲信号分离中超高斯信号亚高斯信号混叠难以分离的问题,提出一种基于改进牛顿法的盲源分离算法.该方法引入开关准则,利用随机变量的峭度来区分信号的类型,不同的信号选择不同的非线性函数,通过牛顿迭代方法求出分离矩阵,实现同时含有超高斯信号和亚高斯信号的杂系混合信号的盲源分离.仿真实验表明了该方法计算量小,易于实现,对于杂系...     

A meshless method to the numerical solution of an inverse reaction–diffusion–convection problem

In this paper, the determination of the source term in a reaction–diffusion convection problem is investigated. First with suitable transformations, the problem is reduced, then a new meshless method based on the use of the heat polynomials as basis functions is proposed to solve the inverse problem. Due to the ill-posed inverse problem, the Tikhonov regularization method with a generalized cross-validation criterion is employed to obtain a numerical stable solution. Finally, some numerical examples are presented to show the accuracy and effectiveness of the algorithm.     

A monotone Newton multisplitting method for the nonlinear complementarity problem with a nonlinear source term

In this paper, we develop a Newton multisplitting method for the nonlinear complementarity problem with a nonlinear source term in which the multisplitting method is used as secondary iterations to approximate the solutions for the resulting linearized subproblems. We prove the monotone convergence theorem for the proposed method under proper conditions.     

A Newton method for Bernoulli’s free boundary problem in three dimensions

Summary The present paper is dedicated to the numerical solution of Bernoulli’s free boundary problem in three dimensions. We reformulate the given free boundary problem as a shape optimization problem and compute the shape gradient and Hessian of the given shape functional. To approximate the shape problem we apply a Ritz–Galerkin discretization. The necessary optimality condition is resolved by Newton’s method. All information of the state equation, required for the optimization algorithm, are derived by boundary integral equations which we solve numerically by a fast wavelet Galerkin scheme. Numerical results confirm that the proposed Newton method yields an efficient algorithm to treat the considered class of problems.      

Application of particle swarm optimization in epileptic spike EEG source localization

Surgical therapy has become an important therapeutic alternative for patients with medically intractable epilepsy. Correct and anatomically precise localization of an epileptic focus is essential to decide if resection of brain tissue is possible. The inverse problem in EEG-based source localization is to determine the location of the brain sources that are responsible for the measured potentials at the scalp electrodes. We propose a new global optimization method based on particle swarm optimization (PSO) to solve the epileptic spike EEG source localization inverse problem. In a forward problem a modified subtraction method is proposed to reduce the computational time. The good accuracy and fast convergence are demonstrated for 2D and 3D cases with realistic head models. The results from the new method are promising for use in the pre-surgical clinic in the future.     

基于负熵最大化改进的语音音乐信号分离

负熵是一种重要的非高斯性度量方法,最大化负熵使随机变量的非高斯性达到最大,从而使输出的各分量之间相互独立。负熵最大化算法以负熵作为目标函数,牛顿迭代法作为优化算法,针对牛顿迭代法中对初始值选择敏感的问题,用牛顿下山法代替牛顿迭代法,通过改变下山因子,使目标函数呈下降趋势,降低算法对初始值的依赖性。实验结果表明,改进后的算法在不同初始值下均能较好地分离语音音乐混合信号,改善了初值敏感问题。     

鲁棒最小二乘支持向量回归机

针对最小二乘支持向量回归机(LS-SVR)对异常值较敏感的问题,通过设置异常值所造成的损失上界,提出一种非凸的Ramp损失函数。该损失函数导致相应的优化问题的非凸性,利用凹凸过程(CCCP)将非凸优化问题转化为凸优化问题。给出Newton算法进行求解并分析了算法的计算复杂度。数据集测试的结果表明,与最小二乘支持向量回归机相比,该算法对异常值具有较强的鲁棒性,获得了更优的泛化能力,同时在运行时间上也具有明显优势。