改进的推理型支持向量机

自V apn ik于20世纪90年代末提出推理型支持向量机的概念后,关于推理型支持向量机的研究基本处于停止状态,主要问题是这种支持向量机的优化模型求解有相当的困难.文章试图把它的优化问题变为无约束问题,再构造带有核的光滑无约束最优化问题,由此构建最优化问题易于求解的推理型支持向量机,以突破对它深入研究的瓶颈.     

基于变分不等式的支持向量机优化算法研究

由于标准支持向量机模型是一个二次规划问题,随着数据规模的增大,求解算法过程会越来越复杂.在K-SVCR算法结构的基础上,构造了严格凸的二次规划新模型,该模型的主要特点是可以将其一阶最优化条件转化为变分不等式问题,利用Fischer-Burmeister(FB)函数将互补问题转化为光滑方程组;建立光滑快速牛顿算法求解,并证明了该算法所产生的序列是全局收敛;利用标准数据集测试提出算法的有效性,在训练正确率和运行时间上与K-SVCR算法相比都有较好的表现,实验结果表明该算法可行且有效.     

装备费用预测中的混合核函数支持向量机

在支持向量机预测建模中,核函数用来将低维特征空间中的非线性问题映射为高维特征空间中的线性问题.核函数的特征对于支持向量机的学习和预测都有很重要的影响.考虑到两种典型核函数—全局核(多项式核函数)和局部核(RBF核函数)在拟合与泛化方面的特性,采用了一种基于混合核函数的支持向量机方法用于预测建模.为了评价不同核函数的建模效果、得到更好的预测性能,采用遗传算法自适应进化支持向量机模型的各项参数,并将其应用于装备费用预测的实际问题中.实际计算表明采用混合核函数的支持向量机较单一核函数时有更好的预测性能,可以作为一种有效的预测建模方法在装备管理中推广应用.     

从支持向量机到非平行支持向量机

非平行支持向量机是支持向量机的延伸,受到了广泛的关注.非平行支持向量机构造允许非平行的支撑超平面,可以描述不同类别之间的数据分布差异,从而适用于更广泛的问题.然而,对非平行支持向量机模型与支持向量机模型之间的关系研究较少,且尚未有等价于标准支持向量机模型的非平行支持向量机模型.从支持向量机出发,构造出新的非平行支持向量机模型,该模型不仅可以退化为标准支持向量机,保留了支持向量机的稀疏性和核函数可扩展性.同时,可以描述不同类别之间的数据分布差异,适用于更广泛的非平行结构数据等.最后,通过实验初步验证了所提模型的有效性.     

基于PCA与NSSVR的人口老龄化研究

基于非线性光滑支持向量回归机研究了人口老龄化问题.首先介绍了非线性光滑支持向量回归机(NSSVR);其次,提出了人口老龄化影响体系,利用主成分分析(PCA),在体系基础上提取出对老龄化影响明显的9个指标;再次,通过非线性光滑支持向量回归机模型建立了老龄化率与9个影响指标间的相互关系;最后,用非线性光滑支持向量回归机模型对未来人口老龄率进行预测.实证表明,方法具有很好的预测效果.     

机器学习中的最优化模型与对偶

数学最优化是以数学的方式来刻画和找出问题最优解的一门学科.机器学习利用数据构造预测方法,并对这些方法进行研究.介绍了机器学习中与支持向量机和稀疏重构相关的最优化模型.在此基础上,给出了三个典型最优化模型的对偶问题,并详细地讨论了对偶在求解这些问题中的应用.     

三次样条插值及其在第一类积分方程求解中的应用

从三次样条插值的定义出发,通过研究第一类积分方程中未知函数的三次样条函数逼近,给出了第一类积分方程的三次样条插值离散化.利用该离散化形式,将第一类积分方程转化成线性方程组的形式.由于第一类积分方程的求解通常是不适定的,进而引起线性方程组的病态性.最后,为克服线性方程组的病态性,通过引入未知函数的多重光滑化约束,得到第一...     

函数系数线性自回归模型的样条估计

基于多项式样条全局光滑方法,建立函数系数线性自回归模型中系数函数的样条估计.在适当条件下,证明了系数函数多项式样条估计的相合性,并给出了它们的收敛速度.模拟例子验证了理论结果的正确性.     

基于再生核三次样条基底的构造及其应用

将三次样条理论与再生核理论相结合,利用再生核函数巧妙地构造了三次样条函数空间的一组基底.基于三次样条插值的高收敛特点,得到了微分方程边值问题近似解的一种新的求解方法.数值算例展现出算法简单、有效.     

可靠性分析中的最小二乘支持向量机分类方法

为了提高支持向量分类机在处理大样本可靠性问题时的计算效率,将最小二乘支持向量分类机引入到可靠性分析中,使得支持向量机中的二次规划问题转化为求解线性方程组问题,减少了计算量.数值算例表明:基于最小二乘支持向量分类机的可靠性方法与基于支持向量分类机的可靠性方法具有一样的计算精度,而且前者的计算效率明显优于后者.     

Reproducing-kernel-based splines for the regularization of the inverse ellipsoidal gravimetric problem

To solve the inverse gravimetric problem, i.e. to reconstruct the Earth's mass density distribution by using the gravitational potential, we introduce a spline interpolation method for the ellipsoidal Earth model, where the ellipsoid has a rotational symmetry. This problem is ill-posed in the sense of Hadamard as the solution may not exist, it is not unique and it is not stable. Since the anharmonic part (orthogonal complement) of the density function produces a zero potential, we restrict our attention only to reconstruct the harmonic part of the density function by using the gravitational potential. This spline interpolation method gives the existence and uniqueness of the unknown solution. Moreover, this method represents a regularization, i.e. every spline continuously depends on the given gravitational potential. These splines are also combined with a multiresolution concept, i.e. we get closer and closer to the unknown solution by increasing the scale and adding more and more data at each step.     

随机优化磨光算法对卫生陶瓷进出口的分析模型

结合磨光法和最优化理论提出一种随机优化磨光算法(SOS算法),算法通过原始值的参数化和调整幅度的修改,利用优化理论优化控制点.实例表明,随机优化磨光算法比样条修正磨光法和灰色马尔可夫链预测模型精度要高得多;而且所得到的误差变化更稳定.     

服务台不可靠的重试排队系统均衡分析

本文研究服务台不可靠的M/M/1常数率重试排队系统中顾客的均衡进队策略, 其中服务台在正常工作和空闲状态下以不同的速率发生故障。在该系统中, 服务台前没有等待空间, 如果到达的顾客发现服务台处于空闲状态, 该顾客可占用服务台开始服务。否则, 如果服务台处于忙碌状态, 顾客可以选择留下信息, 使得服务台在空闲时可以按顺序在重试空间中寻找之前留下信息的顾客进行服务。当服务台发生故障时, 正在被服务的顾客会发生丢失, 且系统拒绝新的顾客进入系统。根据系统提供给顾客的不同程度的信息, 研究队长可见和不可见两种信息情形下系统的稳态指标, 以及顾客基于收入-支出函数的均衡进队策略, 并建立单位时间内服务商的收益和社会福利函数。比较发现, 披露队长信息不一定能提高服务商收益和社会福利。     

Robust univariate spline models for interpolating interval data

We consider spline interpolation problems where information about the approximated function is given by means of interval estimates for the function values over ranges of x-values instead of specific knots. We propose two robust univariate spline models formulated as convex semi-infinite optimization problems. We present simplified equivalent formulations of both models as finite explicit convex optimization problems for splines of degrees up to 3. This makes it possible to use existing convex optimization algorithms and software.     

Effective direct methods for aerodynamic shape optimization

A direct method for aerodynamic shape optimization based on the use of Bézier spline approximation is proposed. The method is tested as applied to the optimization of the supersonic part of an axisymmetric de Laval nozzle. The optimization results are compared with the exact solution obtained by the control contour method (variational nozzle) and with nozzles constructed using another direct method, namely, local linearization. It is shown that both direct optimization methods can be used on rather coarse grids without degrading the accuracy of the solution. The optimization procedure involves the isoperimetric condition that the surface area of the nozzle is given and fixed, which prevents the use of the control contour method. Optimization with allowance for viscosity is performed using the method. For fairly short maximum possible nozzle lengths in the range of Reynolds numbers under consideration, it is shown that allowance for viscosity does not improve the nozzle shape produced by optimization based on the Euler equations. The role of viscosity is reduced to the determination of an optimal length.     

Adaptive Surface Reconstruction Based on Tensor Product Algebraic Splines

Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis (Adv. Comput. Math., 17 (2002), pp. 135-152) based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Jiittler's method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.AMS subject classifications: 65D17     

Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions

We present a new strategy for the constrained global optimization of expensive black box functions using response surface models. A response surface model is simply a multivariate approximation of a continuous black box function which is used as a surrogate model for optimization in situations where function evaluations are computationally expensive. Prior global optimization methods that utilize response surface models were limited to box-constrained problems, but the new method can easily incorporate general nonlinear constraints. In the proposed method, which we refer to as the Constrained Optimization using Response Surfaces (CORS) Method, the next point for costly function evaluation is chosen to be the one that minimizes the current response surface model subject to the given constraints and to additional constraints that the point be of some distance from previously evaluated points. The distance requirement is allowed to cycle, starting from a high value (global search) and ending with a low value (local search). The purpose of the constraint is to drive the method towards unexplored regions of the domain and to prevent the premature convergence of the method to some point which may not even be a local minimizer of the black box function. The new method can be shown to converge to the global minimizer of any continuous function on a compact set regardless of the response surface model that is used. Finally, we considered two particular implementations of the CORS method which utilize a radial basis function model (CORS-RBF) and applied it on the box-constrained Dixon–Szegö test functions and on a simple nonlinearly constrained test function. The results indicate that the CORS-RBF algorithms are competitive with existing global optimization algorithms for costly functions on the box-constrained test problems. The results also show that the CORS-RBF algorithms are better than other algorithms for constrained global optimization on the nonlinearly constrained test problem.     

A new kernel function for SPH with applications to free surface flows

Smoothed particle hydrodynamics (SPH) is a popular meshfree Lagrangian particle method, which uses a kernel function for numerical approximations. The kernel function is closely related to the computational accuracy and stability of the SPH method. In this paper, a new kernel function is proposed, which consists of two cosine functions and is referred to as double cosine kernel function. The newly proposed double cosine kernel function is sufficiently smooth, and is associated with an adjustable support domain. It also has smaller second order momentum, and therefore it can have better accuracy in terms of kernel approximation. SPH method with this double cosine kernel function is applied to simulate a dam-break flow and water entry of a horizontal circular cylinder. The obtained SPH results agree very well with the experimental results. The double cosine kernel function is also comparatively studied with two frequently used SPH kernel functions, Gaussian and cubic spline kernel functions.     

基于正弦型光滑打磨函数对0-1规划问题的连续化求解方法

传统的求解0-1规划问题方法大多属于直接离散的解法.现提出一个包含严格转换和近似逼近三个步骤的连续化解法:(1)借助阶跃函数把0-1离散变量转化为[0,1]区间上的连续变量;(2)对目标函数采用逼近折中阶跃函数近光滑打磨函数,约束条件采用线性打磨函数逼近折中阶跃函数,把0-1规划问题由离散问题转化为连续优化模型;(3)利用高阶光滑的解法求解优化模型.该方法打破了特定求解方法仅适用于特定类型0-1规划问题惯例,使求解0-1规划问题的方法更加一般化.在具体求解时,采用正弦型光滑打磨函数来逼近折中阶跃函数,计算效果很好.     

基于径向基函数网络的区域物流能力投资结构优化

针对如何有效地提高区域物流能力,以推动区域经济增长的问题,构建了区域物流能力的投资结构优化模型.首先详细分析了优化区域产业投资结构能增强区域物流能力的原因,从产业结构的角度揭示了区域物流能力与产业投资分配之间复杂的非线性关系;然后采用径向基函数神经网络实现了它们之间的非线性映射,进而建立了有约束条件限制的非线性规划投资结构优化模型;最后以四川省2005年的产业投资实际数据为基础,采用改进遗传算法对该模型进行求解,获得了优化问题的近似最优解以及投资结构的优化方向.优化结果表明:建立的模型对产业投资结构的优化是合理、有效的,从而提供了一个能提高区域物流能力的实用且切实可行的新方法.