凹资源配置问题的混合动态规划方法

Concave resource allocation problem is an integer programming problem of minimizing a nonincreasing concave function subject to a convex nondecreasing constraint and bounded integer variables. This class of problems are encountered in optimization models involving economies of scale. In this paper, a new hybrid dynamic programming method was proposed for solving concave resource allocation problems. A convex underestimating function was used to approximate the objective function and the resulting convex subproblem was solved with dynamic programming technique after transforming it into a 0-1 linear knapsack problem. To ensure the convergence, monotonicity and domain cut technique was employed to remove certain integer boxes and partition the revised domain into a union of integer boxes. Computational results were given to show the efficiency of the algorithm.     

Discriminative structured dictionary learning for image classification

In this paper, a discriminative structured dictionary learning algorithm is presented. To enhance the dictionary’s discriminative power, the reconstruction error, classification error and inhomogeneous representation error are integrated into the objective function. The proposed approach learns a single structured dictionary and a linear classifier jointly. The learned dictionary encourages the samples from the same class to have similar sparse codes, and the samples from different classes to have dissimilar sparse codes. The solution to the objective function is achieved by employing a feature-sign search algorithm and Lagrange dual method. Experimental results on three public databases demonstrate that the proposed approach outperforms several recently proposed dictionary learning techniques for classification.     

一种基于鲁棒聚类的欠定稀疏源盲分离算法

In underdetermined blind source separation, more sources are to be estimated from less observed mixtures without knowing source signals and the mixing matrix. This paper presents a robust clustering algorithm for underdetermined blind separation of sparse sources with unknown number of sources in the presence of noise. It uses the robust competitive agglomeration (RCA) algorithm to estimate the source number and the mixing matrix, and the source signals then are recovered by using the interior point linear programming. Simulation results show good performance of the proposed algorithm for underdetermined blind sources separation (UBSS).     

0-1规划的填充函数算法

文章首先给出搜索0-1规划局部极小解的邻域搜索算法,在此基础上给出了填充函数算法.该算法的思想是在求得总体优化问题的一个局部极小点后,构造填充函数,通过极小化该填充函数找到比当前局部极小解更好的解 该方法是一种直接算法,我们通过具体的数值实验证实了该算法是有效的.     

Simultaneous perturbation stochastic approximation algorithm combined with neural network and fuzzy simulation

In order to solve three kinds of fuzzy programm model, fuzzy chance-constrained programming mode ng models, i.e. fuzzy expected value and fuzzy dependent-chance programming model, a simultaneous perturbation stochastic approximation algorithm is proposed by integrating neural network with fuzzy simulation. At first, fuzzy simulation is used to generate a set of input-output data. Then a neural network is trained according to the set. Finally, the trained neural network is embedded in simultaneous perturbation stochastic approximation algorithm. Simultaneous perturbation stochastic approximation algorithm is used to search the optimal solution. Two numerical examples are presented to illustrate the effectiveness of the proposed algorithm.     

求一类优化问题全局解的线性化方法

对广泛应用于金融及经济等实际问题中的一类带有多乘积约束的线性规划问题提出一种全局优化算法.利用对数的性质和线性化技术,建立了问题的等价问题的松弛线性规划,并通过对可行域的细分以及一系列求解过程的讨论,从理论上证明了算法收敛到问题的全局最优解,并用数值结果验证了方法的可行性.     

烟花算法在联合补货问题中的应用研究

烟花算法作为一种新型群体智能优化算法,在众多领域得到成功应用。联合采购品种的不断扩大对算法性能提出了巨大挑战。针对联合补货问题设计了基于烟花算法的求解方案,并利用基础算例证明方案有效性。随机生成的大规模算例表明,烟花算法相较于混合差分进化算法,在求解大规模联合补货问题时可获得更优的近似最优解,具有更快的收敛速度和更高的稳定性,验证了烟花算法在混合整数规划方面的应用效果。     

Two-parameters quasi-filled function algorithm for nonlinear integer programming

INTRODUCTION Considering the following nonlinear integer programming problem: (PI) min f(x), s.t. x∈XI, (1) where XI?In is a bounded and closed box set con- taining more than one point, In is the set of integer points in n . If we suppose that f(x) satisfies the following conditions: if x∈XI, then f(x)=f(x), otherwise f(x)= ∞, then Problem PI is equal to the following nonlinear integer programming problem (UPI) min f(x), s.t. x∈In. (2) The formulation in PI allows the set XI t…     

A new heuristic algorithm for general integer linear programming problems

1 Introduction ? Since the cutting plane method [1] and branch-and- bound principle [2] were developed as two types of efficient approaches for integer linear programming problems, how to improve them or to find new algorithms more efficient has become an…     

Two-level Bregman method for MRI reconstruction with graph regularized sparse coding

In this paper, a two-level Bregman method is presented with graph regularized sparse coding for highly undersampled magnetic resonance image reconstruction. The graph regularized sparse coding is incorporated with the two-level Bregman iterative procedure which enforces the sampled data constraints in the outer level and updates dictionary and sparse representation in the inner level. Graph regularized sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge with a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can consistently reconstruct both simulated MR images and real MR data efficiently, and outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.     

一类广义非线性比式和问题的全局优化算法

对广义非线性比式和问题的等价问题使用指数变换及线性下界估计。建立等价问题的松弛线性规划，通过对松弛线性规划可行域的细分及一系列线性规划的求解达到提出的一种确定型全局优化算法。理论上证明收敛到问题的全局最优解．实验表明，该算法具有可行性、有效性．     

基于变换域的压缩感知快速重构算法

压缩感知是信号处理领域热门研究课题,其应用前提为原信号是稀疏或可压缩的。时域非稀疏信号可以变换为频域稀疏信号,但变换后的信号和传感矩阵表示形式为复数,增加了重构复杂度。为了降低复杂度,提高信号重构效率,提出一种基于实变换的重构算法,该算法将复数形式的稀疏信号和传感矩阵的实部和虚部分离后再参与重构。与传统重构算法相比,该算法改善了重构信号的均方误差,明显缩短了重构时间,极大提高了信号重构效率。     

SOLVING CONVEX QUADRATIC PROGRAMMING BY POTENTIAL-REDUCTION INTERIOR-POINT ALGORITHM

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A Multi-Objective Genetic Algorithm for Optimal Portfolio Problems

This paper concerns with modeling and design of an algorithm for the portfolio selection problems with fixed transaction costs and minimum transaction lots. A mean-variance model for the portfolio selection problem is proposed, and the model is formulated as a non-smooth and nonlinear integer programming problem with multiple objective functions. As it has been proven that finding a feasible solution to the problem only is already NP-hard, based on NSGA-II and genetic algorithm for numerical optimization of constrained problems (Genocop), a multi-objective genetic algorithm (MOGA) is designed to solve the model. Its features comprise integer encoding and corresponding operators, and special treatment of constraints conditions. It is illustrated via a numerical example that the genetic algorithm can efficiently solve portfolio selection models proposed in this paper.This approach offers promise for the portfolio problems in practice.     

基于图结构正则化稀疏表示的双层伯格曼图像插值算法

为了提高图像插值的恢复效果,提出了一种基于图结构正则化稀疏表示的双层伯格曼迭代算法．该迭代算法的外层用于约束图像观测数据,内层用于更新图像块的学习字典和稀疏表示系数．引入的图结构正则化稀疏表示约束可以有效地自适应图像块的局部结构,对于严重受损的情形也能得到精确的恢复结果．此外,在内层迭代中改进的稀疏表示和简洁的字典更新策略使算法能快速地趋于收敛．数值实验结果表明,所提出的算法可以有效地恢复图像,在主观视觉效果和客观量化标准上要优于目前已有的算法．     

稀疏长时延水声信道的压缩感知估计(英文)

提出一种基于压缩感知框架下的长时延水声信道估计算法.用传统的自适应算法如最小二乘(LS)算法处理典型的长时延水声信道的估计问题时,会导致其收敛速率下降,即跟踪能力有限,而使用时延多普勒函数则加大了计算量和复杂度.通过训练序列构建一个Toeplitz矩阵作为测量矩阵,将长时延信道估计问题转为压缩感知问题,并利用信道的稀疏结构特性进行稀疏估计.与传统的l1范数或基于指数形式的近似l0范数稀疏恢复策略不同,所提出的是一种新的似l0范数稀算法(简称AL0),该算法通过融合最陡梯度和迭代投影寻优进行求解.仿真与海试数据结果验证了所提算法的优越性.     

基于组稀疏残差去噪的磁共振图像重构

为了克服磁共振图像重构精度低的问题,方便医生诊断与治疗,提出一种将组稀疏残差去噪和近似消息传递相结合的磁共振图像重构算法.在基于迭代软阈值的去噪近似消息传递(D-AMP)重构算法中,滤波的去噪算法将使用基于组稀疏残差约束(GSRC)的图像去噪实现.实验结果表明,基于组稀疏残差去噪的磁共振图像重建算法可有效缓解重建图像局...     

Solving convex quadratic programming by potential-reduction interior-point algorithm

The solution of quadratic programming problems is an important issue in the field of mathematical programming and industrial applications. In this paper, we solve convex quadratic programming by a potential-reduction interior—point algorithm. It is proved that the potential—reduction interior-point algorithm is globally convergent. Some numerical experiments were made.     

一种求非线性整数规划全局最小解的算法

设计了一种求非线性整数规划全局最小解的算法.首先,利用改进的遗传算法快速找到初始的离散局部极小解;其次,把该离散局部极小解作为初始点,用所设计的局部搜索算法极小化填充函数去寻找一个更好的局部极小解,并且通过有限次迭代,最后得到全局最小解.数值实验表明该算法是有效的.     

SA法在求解非线性约束优化问题中的应用

传统数学规划方法如梯度法等在解决非线性规划问题时,往往会由于问题本身的多峰性而落入局部最优解中,得不到全局最优解,这使得传统方法在解决非线性规划问题中受到很大的限制.80年代初,S.Kirkpatrick提出了模拟退火算法(Simutaneous Annealing),该方法在解决复杂的组合优化问题中可以得出很好的结果.它是一种仿金属退火物理过程的随机算法,在理想状态下可得出全局最优解,并能以一定的概率跳出局部最优解所在的区域.本文我们将探讨SA法在求解非线性约束优化问题中的应用.