一种改进灰狼优化算法研究及应用

针对灰狼算法易陷入局部最优、收敛精度不高、收敛速度慢等缺点,提出一种改进的灰狼算法.引入莱维飞行,扩大搜索范围,增强全局搜索能力,避免陷入局部最优;引入贪婪原理,提升种群优良性以提高算法收敛精度;引入自适应收敛因子,加快收敛速度;引入动态权重策略,制约全局搜索与局部搜索的相互影响.将改进算法与其他四种算法作对比,实验表明,改进算法在收敛速度与收敛精度上都有更好的性能.最后,应用于图像多阈值分割中,采用GWO-Otsu法可以克服传统Otsu法在多阈值分割时计算量大,实时性差的特点,不但能够取得最优解,且明显缩减计算时间.     

求解图像分割CV模型的BB算法

给出图像分割的一种新算法——BB算法.该方法的优点在于利用迭代过程中当前点和前一点的信息确定搜索步长,从而更有效地搜索最优解.为此,首先通过变分水平集方法将CV模型转化为最优化问题;其次,将BB算法引入该优化问题进行求解;然后,对BB算法进行收敛性分析,为该算法应用在CV模型中提供了理论依据;最后将该方法与已有的最速下降法、共轭梯度法的分割结果进行比较.结果表明,跟其他两种方法相比,BB算法在保证较好分割效果的前提下,提高了算法的速度和性能.     

一类带线搜索的非单调信赖域新算法

结合非单调信赖域方法,和非单调线搜索技术,提出了一种新的无约束优化算法.信赖域方法的每一步采用线搜索,使得迭代每一步都充分下降加快了迭代速度.在一定条件下,证明了算法具有全局收敛性和局部超线性.收敛速度.数值试验表明算法是十分有效的.     

利用模拟退火遗传算法实现图像阈值分割

本文提出了一种利用模拟退火算法和遗传算法相结合的图像阈值分割算法,试验结果表明该算法增强了算法的全局收敛性,加快了算法的收敛速度,提高了图像阈值分割的效率.     

一个求解无约束优化的ODE型混合方法

基于非单调技术,本文给出一种新的求解无约束优化的ODE型算法.该算法的特点是:每次迭代时只解一次线性方程组系统而获得试验步,然后采用改进的非单调线搜索获得下一个迭代点,从而避免了重复求解线性方程组,减少了算法的计算量.在合理的假设条件下,该算法被证明是全局收敛和局部超线性收敛的.数值试验证实了该算法的有效性.     

一种求解路径优化问题的新型人工鱼群算法

针对人工鱼群算法由于固定视野导致寻优效率低、易陷入局部极值的弊端,引入视野递减反馈策略,提出一种改进人工鱼群算法.视野随着迭代次数和寻优反馈信息适时变化,旨在平衡算法的全局搜索和局部搜索能力.实验测试表明算法在保证收敛速度的基础上提高了计算精度,并且增加了算法陷入局部极值时快速跳出的可能性,最后将改进算法应用于求解国家AAAAA级风景区最短遍历路径问题.     

基于混合单纯形算法的模糊均值图像分割

针对模糊C均值算法用于图像分割时对初始值敏感、容易陷入局部极值的问题,提出基于混合单纯形算法的模糊均值图像分割算法.算法利用Nelder-Mead单纯形算法计算量小、搜索速度快和粒子群算法自适应能力强、具有较好的全局搜索能力的特点,将混合单纯形算法的结果作为模糊C均值算法的输入,并将其用于图像分割.实验结果表明:基于混合单纯形算法的模糊均值图像分割算法在改善图像分割质量的同时,提高了算法的运行速度.     

改进伪并行遗传算法求解作业车间调度问题

针对遗传算法在求解极复杂优化问题中出现的过早收敛、执行效率差的缺点,提出了一种改进的伪并行遗传算法.该算法将并行进化与串行搜索相结合,提高了算法的收敛速度.同时该算法通过种群因子控制伪并行算法中的各子种群的规模,不仅保证了搜索过程中勘探和开采的平衡,克服过早收敛,而且减少了计算的复杂性,特别是在处理复杂优化问题上具有较高的性能.实验结果证明了该算法的有效性.     

一种改进的FastICA算法

FastICA算法是一种快速独立分量分析(Independent Component Analysis:ICA)算法,但它是基于牛顿迭代方法和合理近似的一种算法,所以具有改进空间.近年来提出了许多改进的具有更高阶收敛性质的牛顿迭代方法.将一种3阶收敛的牛顿迭代方法引入ICA算法的推导中,在合理近似的基础上,提出了一种改进的两步迭代FastICA算法.与传统FastICA算法相比,提出的改进的FastICA算法一次迭代的计算量有所增加.但是,实验结果表明,新提出的改进的FastICA算法更稳健、具有更快的收敛速度.     

一个新的连分式算法及其收敛性

本文利用连分式插值,得到了一个新的一维搜索方法——连分式算法.用此算法,每迭代一次,只需计算三个点的函数值;在计算连分式插值式的每个系数时,只需一次除法.因此,数值稳定性较好.本文还证明了此算法的收敛性,收敛速度较快,收敛阶近似1.8393.按效能指标E=P~(1/μ)评价,此算法是一个较好的局部一维搜索方法.如果用此法于不精确的一维搜索,因只需计算三个点的函数值,故它是一个较好的、不精确的一维搜索方法,同时也是解超越方程的一个新算法.数值例子表明,它确实有效.     

Fast Nonparametric Density-Based Clustering of Large Datasets Using a Stochastic Approximation Mean-Shift Algorithm

Mean-shift is an iterative procedure often used as a nonparametric clustering algorithm that defines clusters based on the modal regions of a density function. The algorithm is conceptually appealing and makes assumptions neither about the shape of the clusters nor about their number. However, with a complexity of O(n²) per iteration, it does not scale well to large datasets. We propose a novel algorithm which performs density-based clustering much quicker than mean shift, yet delivering virtually identical results. This algorithm combines subsampling and a stochastic approximation procedure to achieve a potential complexity of O(n) at each step. Its convergence is established. Its performances are evaluated using simulations and applications to image segmentation, where the algorithm was tens or hundreds of times faster than mean shift, yet causing negligible amounts of clustering errors. The algorithm can be combined with existing approaches to further accelerate clustering.     

A fast algorithm for image segmentation based on fuzzy region competition

Variational models for image segmentation are usually solved by the level set method, which is not only slow to compute but also dependent on initialization strongly. Recently, fuzzy region competition models or globally convex segmentation models have been introduced. They are insensitive to initialization, but contain TV-regularizers, making them difficult to compute. Goldstein, Bresson and Osher have applied the split Bregman iteration to globally convex segmentation models which avoided the regularization of TV norm and speeded up the computation. However, the split Bregman method needs to solve a partial differential equation (PDE) in each iteration. In this paper, we present a simple algorithm without solving the PDEs proposed originally by Jia et al. (2009) with application to image segmentation problems. The algorithm also avoids the regularization of TV norm and has a simpler form, which is in favor of implementing. Numerical experiments show that our algorithm works faster and more efficiently than other fast schemes, such as duality based methods and the split Bregman scheme.     

Combining a hybrid preconditioner and a optimal adjustment algorithm to accelerate the convergence of interior point methods

In this work, the optimal adjustment algorithm for p coordinates, which arose from a generalization of the optimal pair adjustment algorithm is used to accelerate the convergence of interior point methods using a hybrid iterative approach for solving the linear systems of the interior point method. Its main advantages are simplicity and fast initial convergence. At each interior point iteration, the preconditioned conjugate gradient method is used in order to solve the normal equation system. The controlled Cholesky factorization is adopted as the preconditioner in the first outer iterations and the splitting preconditioner is adopted in the final outer iterations. The optimal adjustment algorithm is applied in the preconditioner transition in order to improve both speed and robustness. Numerical experiments on a set of linear programming problems showed that this approach reduces the total number of interior point iterations and running time for some classes of problems. Furthermore, some problems were solved only when the optimal adjustment algorithm for p coordinates was used in the change of preconditioners.     

Fast Multilevel CVT-Based Adaptive Data Visualization Algorithm

<正>Efficient data visualization techniques are critical for many scientific applications. Centroidal Voronoi tessellation(CVT) based algorithms offer a convenient vehicle for performing image analysis,segmentation and compression while allowing to optimize retained image quality with respect to a given metric.In experimental science with data counts following Poisson distributions,several CVT-based data tessellation algorithms have been recently developed.Although they surpass their predecessors in robustness and quality of reconstructed data,time consumption remains to be an issue due to heavy utilization of the slowly converging Lloyd iteration.This paper discusses one possible approach to accelerating data visualization algorithms.It relies on a multidimensional generalization of the optimization based multilevel algorithm for the numerical computation of the CVTs introduced in[1],where a rigorous proof of its uniform convergence has been presented in 1-dimensional setting.The multidimensional implementation employs barycentric coordinate based interpolation and maximal independent set coarsening procedures.It is shown that when coupled with bin accretion algorithm accounting for the discrete nature of the data,the algorithm outperforms Lloyd-based schemes and preserves uniform convergence with respect to the problem size.Although numerical demonstrations provided are limited to spectroscopy data analysis,the method has a context-independent setup and can potentially deliver significant speedup to other scientific and engineering applications.     

Multi-Label Markov Random Fields as an Efficient and Effective Tool for Image Segmentation,Total Variations and Regularization

One of the classical optimization models for image segmentation is the well known Markov Random Fields (MRF) model. This model is a discrete optimization problem, which is shown here to formulate many continuous models used in image segmentation. In spite of the presence of MRF in the literature, the dominant perception has been that the model is not effective for image segmentation. We show here that the reason for the non-effectiveness is due to the lack of access to the optimal solution. Instead of solving optimally, heuristics have been engaged. Those heuristic methods cannot guarantee the quality of the solution nor the running time of the algorithm. Worse still, heuristics do not link directly the input functions and parameters to the output thus obscuring what would be ideal choices of parameters and functions which are to be selected by users in each particular application context.We describe here how MRF can model and solve efficiently several known continuous models for image segmentation and describe briefly a very efficient polynomial time algorithm, which is provably fastest possible, to solve optimally the MRF problem. The MRF algorithm is enhanced here compared to the algorithm in Hochbaum (2001) by allowing the set of assigned labels to be any discrete set. Other enhancements include dynamic features that permit adjustments to the input parameters and solves optimally for these changes with minimal computation time. Several new theoretical results on the properties of the algorithm are proved here and are demonstrated for images in the context of medical and biological imaging. An interactive implementation tool for MRF is described, and its performance and flexibility in practice are demonstrated via computational experiments.We conclude that many continuous models common in image segmentation have discrete analogs to various special cases of MRF and as such are solved optimally and efficiently, rather than with the use of continuous techniques, such as PDE methods, which restrict the type of functions used and furthermore, can only guarantee convergence to a local minimum.     

多集分裂等式问题的逐次松弛投影算法

多集分裂等式问题是分裂可行性问题的拓展问题,在图像重建、语言处理、地震探测等实际问题中具有广泛的应用。为了解决这个问题,提出了逐次松弛投影算法,设计了变化的步长,使其充分利用当前迭代点的信息且不需要算子范数的计算,证明了算法的弱收敛性。数值算例验证了算法在迭代次数与运行时间等方面的优越性。     

A ROBUST SUPERLINEARLY CONVERGENT ALGORITHM FOR LINEARLY CONSTRAINED OPTIMIZATION PROBLEMS UNDER DEGENERACY

1.IntroductionTheproblemconsideredinthispaperiswhereX={xER"laTx5hi,jEI={l,.'.,m}},ajeR"(jEI)areallcolumn*ThisresearchissupportedbytheNationalNaturalSciencesFoundationofChinaandNaturalSciencesFoundationofHunanProvince.vectors,hiERI(j6I)areallscalars,andf:R"-- Risacontinuouslydifferentiablefunction.Weonlyconsiderinequalityconstraintsheresinceanyequalitycanbeexpressedastwoinequalities.Withoutassumingregularityofthelinearconstraints,thereisnotanydifficultyinextendingtheresultstothegenera…     

求解分段常数图象分割模型的一个快速算法

针对Xue-ChengTai等提出的分段常数图象分割模型,我们提出了一个新的快速求解算法。通过引进一个函数来选择模型中的正则化参数β的值,并判断在迭代过程中何时求解不含惩罚项的泛函F。此函数的引入有效地加速了算法的收敛速度。结合原始-对偶Newton方法来求解总变差最小化问题。数值试验表明新算法具有很快的收敛速度与良好的分割效果,且算法对初始值的要求不高。     

Lasso变量选择的分布式算法

Lasso是机器学习中比较常用的一种变量选择方法,适用于具有稀疏性的回归问题.当样本量巨大或者海量的数据存储在不同的机器上时,分布式计算是减少计算时间提高效率的重要方式之一.本文在给出Lasso模型等价优化模型的基础上,将ADMM算法应用到此优化变量可分离的模型中,构造了一种适用于Lasso变量选择的分布式算法,证明了...