Linear Neural Network Training Algorithms For Real-World Benchmark Problems

This paper describes the Adaptive Steepest Descent (ASD) and Optimal Fletcher-Reeves (OFR) algorithms for linear neural network training. The algorithms are applied to well-known pattern classification and function approximation problems, belonging to benchmark collection Proben1. The paper discusses the convergence behavior and performance of the ASD and OFR training algorithms by computer simulations and compares the results with those produced by linear-RPROP method.     

Linear Time Algorithms for Generalized Edge Dominating Set Problems

We prove that a generalization of the edge dominating set problem, in which each edge e needs to be covered b _e times for all e∈E, admits a linear time 2-approximation for general unweighted graphs and that it can be solved optimally for weighted trees. We show how to solve it optimally in linear time for unweighted trees and for weighted trees in which b _e ∈{0,1} for all e∈E. Moreover, we show that it solves generalizations of weighted matching, vertex cover, and edge cover in trees.     

线性约束优化问题演化算法求解的初始解集确定

演化算法求解线性约束问题时需要确定初始解集，文章提出了一个通用高效的确定完备初始解集的算法，并作出了评价。     

多播路由中的问题及算法

根据多点广播服务的最优化函数和限制条件对多播路由中的问题进行了分类,对每类问题提出了基本的路由算法,并讨论了它们的优缺点。     

Evolutionary Algorithms and Matroid Optimization Problems

We analyze the performance of evolutionary algorithms on various matroid optimization problems that encompass a vast number of efficiently solvable as well as NP-hard combinatorial optimization problems (including many well-known examples such as minimum spanning tree and maximum bipartite matching). We obtain very promising bounds on the expected running time and quality of the computed solution. Our results establish a better theoretical understanding of why randomized search heuristics yield empirically good results for many real-world optimization problems.     

一种基于线性代数的图像处理算法研究

将线性代数中的马尔可夫链蒙特卡洛算法与贝叶斯网络引入图像处理中,提出一种基于线性代数的图像处 理算法,并对图像进行处理。仿真结果表明,所提算法只需要Gibbs抽样法10%的迭代次数以及比较简单的跳转核。 实验结果表明该方法有较好的效率和较低的实现复杂度。     

Parallel Approximation Algorithms by Positive Linear Programming

Several sequential approximation algorithms for combinatorial optimization problems are based on the following paradigm: solve a linear or semidefinite programming relaxation, then use randomized rounding to convert fractional solutions of the relaxation into integer solutions for the original combinatorial problem. We demonstrate that such a paradigm can also yield parallel approximation algorithms by showing how to convert certain linear programming relaxations into essentially equivalent positive linear programming [LN] relaxations that can be near-optimally solved in NC. Building on this technique, and finding some new linear programming relaxations, we develop improved parallel approximation algorithms for Max Sat, Max Directed Cut, and Max k CSP. The Max Sat algorithm essentially matches the best approximation obtainable with sequential algorithms and has a fast sequential version. The Max k CSP algorithm improves even over previous sequential algorithms. We also show a connection between probabilistic proof checking and a restricted version of Max k CSP. This implies that our approximation algorithm for Max k CSP can be used to prove inclusion in P for certain PCP classes. Received November 1996; revised March 1997.     

经典线性算法的非线性核形式

经典线性算法的非线性核形式是近10年发展起来的一类非线性机器学习技术．它们最显著的特点是利用满足Mercer条件的核函数巧妙地推导出线性算法的非线性形式。并表述为与样本数目有关、与维数无关的优化问题．为了提高数值计算的稳定性、控制算法的推广能力以及改善迭代过程的收敛性。部分算法还采用了正则化技术．在概述核思想与核函数、正则化技术的基础上,系统地介绍了经典线性算法的非线性核形式,同时分析它们的优缺点,井讨论了进一步发展的方向．     

Asynchronous Iterative Algorithms for Nonexpansive Linear Systems

In this paper we give a convergence result for parallel synchronous or asynchronous algorithms with bounded delays, associated with nonexpansive linear systems which are not necessarily contractive. This result allows us to apply these algorithms to consistent singular linear systems and to finite homogenous Markov chains.     

Linear Time Algorithms for Exact Distance Transform

In 2003, Maurer et al. (IEEE Trans. Pattern Anal. Mach. Intell. 25:265–270, 2003) published a paper describing an algorithm that computes the exact distance transform in linear time (with respect to image size) for the rectangular binary images in the k-dimensional space ℝ ^k and distance measured with respect to L _p -metric for 1≤p≤∞, which includes Euclidean distance L ₂. In this paper we discuss this algorithm from theoretical and practical points of view. On the practical side, we concentrate on its Euclidean distance version, discuss the possible ways of implementing it as signed distance transform, and experimentally compare implemented algorithms. We also describe the parallelization of these algorithms and discuss the computational time savings associated with them. All these implementations will be made available as a part of the CAVASS software system developed and maintained in our group (Grevera et al. in J. Digit. Imaging 20:101–118, 2007). On the theoretical side, we prove that our version of the signed distance transform algorithm, GBDT, returns the exact value of the distance from the geometrically defined object boundary. We provide a complete proof (which was not given of Maurer et al. (IEEE Trans. Pattern Anal. Mach. Intell. 25:265–270, 2003) that all these algorithms work correctly for L _p -metric with 1<p<∞. We also point out that the precise form of the algorithm from Maurer et al. (IEEE Trans. Pattern Anal. Mach. Intell. 25:265–270, 2003) is not well defined for L ₁ and L _∞ metrics. In addition, we show that the algorithm can be used to find, in linear time, the exact value of the diameter of an object, that is, the largest possible distance between any two of its elements.     

Linear Least-Squares Algorithms for Temporal Difference Learning

We introduce two new temporal difference (TD) algorithms based on the theory of linear least-squares function approximation. We define an algorithm we call Least-Squares TD (LS TD) for which we prove probability-one convergence when it is used with a function approximator linear in the adjustable parameters. We then define a recursive version of this algorithm, Recursive Least-Square TD (RLS TD). Although these new TD algorithms require more computation per time-step than do Suttons TD() algorithms, they are more efficient in a statistical sense because they extract more information from training experiences. We describe a simulation experiment showing the substantial improvement in learning rate achieved by RLS TD in an example Markov prediction problem. To quantify this improvement, we introduce the TD error variance of a Markov chain, TD, and experimentally conclude that the convergence rate of a TD algorithm depends linearly on TD. In addition to converging more rapidly, LS TD and RLS TD do not have control parameters, such as a learning rate parameter, thus eliminating the possibility of achieving poor performance by an unlucky choice of parameters.     

求解背包问题的演化算法

背包问题(Knapsack Problem, KP)是一类著名的组合优化问题,也是一类NP难问题,它包括0-1背包问题、有界背包问题、多维背包问题、多背包问题、多选择背包问题、二次背包问题、动态背包问题和折扣背包问题等多种形式,在众多领域有着广泛的应用.演化算法(EAs)是一类有效的快速近似求解KP的算法.本文对近十余年来利用EAs求解KP的研究情况进行一个较为详细的总结,它一方面讨论了利用EAs求解各种KP问题时个体的编码方法与处理不可行解的有效方法,另一方面为今后进一步利用最新提出的EAs求解KP问题提供一个可借鉴的思路.     

Quantum Algorithms for Matching Problems

We present quantum algorithms for the following matching problems in unweighted and weighted graphs with n vertices and m edges:

贪心算法求解k-median问题

文章讨论了用贪心算法解k-m edian问题以及其试验结果。首先提出了一个解k-m edian问题的简单贪心算法,然后对求解质量和求解的近似性能比进行了探讨。主要讨论了公制空间和非公制空间初始解的产生,用贪心算法解k-m edian问题以及全局最优解的计算。试验结果表明:贪心算法解公制空间的k-m edian问题效果要好于解非公制空间的k-m edian问题;用贪心算法解公制空间和非公制空间k-m edian问题都能得到较好的结果。     

求解线性丢番图方程（组）的串,并行算法

本文给出了求解线性丢番图方程(组)的串行算法和在CREW-SM-SIMD并行计算模型上的并行算法,并对上述算法进行了分析。     

Exact Algorithms for Linear Programming over Algebraic Extensions

Abstract. We study the computational complexity of linear programs with coefficients that are real algebraic numbers under a Turing machine model of computation. After reviewing a method for exact representation of algebraic numbers under the Turing model, we show that the fundamental tasks of comparison and arithmetic can be performed in polynomial time. Our technique for establishing polynomial-time algorithms for comparison and arithmetic is distinct from the usual resultant-based approaches, and has the advantage that it provides a natural framework for analysis of the complexity of computational tasks, such as Gaussian elimination, that involve a sequence of arithmetic operations. Our main contribution is to show that a variant of the ellipsoid method can be used to solve linear programming in time polynomial in the encoding size of the problem coefficients and the degree of any algebraic extension that contains those coefficients.     

用GA寻优线性系统模糊控制器规则

控制精度和自适应能力一直是模糊控制应用中较难解决的问题,解决这一问题的关键在于选取适当的控制规则,而遗传算法可以较好地解决常规的数学优化技术所不能有效解决的问题。该文给出了对于具有修正因子的控制规则,采用遗传算法对其参数进行自调整的方法,它可提高模糊控制器的性能。通过仿真实验表明了该方法对于线性系统的控制是有效的。     

求解半线性椭圆型方程组的并行算法

本文结合区域分裂技术、多重网格方法、加速Ｓｃｈｗａｒｚ收敛方法、高低解方法、非线性Ｊａｃｏｂｉ迭代方法和Ｎｅｗｔｏｎ线性化迭代方法,设计了三种求解半线性椭圆型方程（组）的并行算法：并行Ｎｅｗｔｏｎ多重网格算法、并行非线性多重网格算法和并行加速Ｓｃｈｗａｒｚ收敛算法。数值试验说明这三种算法的并行计算是可行的。