Affine-scaling for linear programs with free variables

The affine-scaling modification of Karmarkar's algorithm is extended to solve problems with free variables. This extended primal algorithm is used to prove two important results. First the geometrically elegant feasibility algorithm proposed by Chandru and Kochar is the same algorithm as the one obtained by appending a single column of residuals to the constraint matrix. Second the dual algorithm as first described by Adler et al., is the same as the extended primal algorithm applied to the dual.     

基于蝙蝠退火算法的无等待流水线调度问题研究

无等待流水线调度问题(no-wait flow shop scheduling problem,NWFSP)是一类比较重要的复杂生产调度问题,并已经被证明是典型的NP问题.蝙蝠算法(Bat algorithm,BA)是一种较新颖的群体智能算法.本文针对蝙蝠算法在求解无等待流水线调度问题上的不足,提出一种蝙蝠退火算法,它通过采用ROV的编码方式以实现离散问题的连续编码,同时为了避免算法早熟现象引入了模拟退火算法.算法采用基于NEH的局部搜索规则,在很大程度上提高了算法的性能.利用标准Car问题和Rec问题算例进行仿真实验,结果表明了改进算法的可行性和有效性.     

Solving the split equality problem without prior knowledge of operator norms

The split equality problem has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Moudafi proposed an alternating CQ algorithm and its relaxed variant to solve it. However, to employ Moudafi’s algorithms, one needs to know a priori norm (or at least an estimate of the norm) of the bounded linear operators (matrices in the finite-dimensional framework). To estimate the norm of an operator is very difficult, but not an impossible task. It is the purpose of this paper to introduce a projection algorithm with a way of selecting the stepsizes such that the implementation of the algorithm does not need any priori information about the operator norms. We also practise this way of selecting stepsizes for variants of the projection algorithm, including a relaxed projection algorithm where the two closed convex sets are both level sets of convex functions, and a viscosity algorithm. Both weak and strong convergence are investigated.     

Estimating Hidden Semi-Markov Chains From Discrete Sequences

This article addresses the estimation of hidden semi-Markov chains from nonstationary discrete sequences. Hidden semi-Markov chains are particularly useful to model the succession of homogeneous zones or segments along sequences. A discrete hidden semi-Markov chain is composed of a nonobservable state process, which is a semi-Markov chain, and a discrete output process. Hidden semi-Markov chains generalize hidden Markov chains and enable the modeling of various durational structures. From an algorithmic point of view, a new forward-backward algorithm is proposed whose complexity is similar to that of the Viterbi algorithm in terms of sequence length (quadratic in the worst case in time and linear in space). This opens the way to the maximum likelihood estimation of hidden semi-Markov chains from long sequences. This statistical modeling approach is illustrated by the analysis of branching and flowering patterns in plants.     

有关单机两代理排序问题的两个结果

研究了两个单机两代理排序问题. 在第一个两代理排序问题中, 代理A的目标函数为极小化所有工件的加权完工时间总和, 代理B的目标函数为极小化最大工件费用. 在第二个两代理排序问题中, 代理A的目标函数为极小化所有工件的加权完工时间总和, 代理B的目标函数为极小化所有工件的最大完工时间. 证明了第一个问题是强NP-难的, 改进了已有的一般意义NP-难的结果; 对第二个问题给出了一个与现有的动态规划算法不同的动态规划算法.     

二阶数乘问题的一个最优算法

研究一个有趣的组合优化问题——二阶数乘问题.问题描述如下：给定n≥2个正整数a_1,a_2,…,a_n,设π为{1,2,…,n}的一个置换,表示该问题的一个解,试图找到一个置换π以至∑_（i=1）~n a_（π_i）a_（π_（i＋1））最小,在这里π_（n＋1）=π_1.给出了一个算法复杂度为O（n log n）的最优算法.     

基于ELM算法的羊肉水分含量的快速无损检测

在近红外光谱900-1700nm的波长范围内采集南疆羊肉的光谱数据,来研究水分含量的快速无损检测.为减弱非目标因素对光谱的影响,采用SNV和去趋势法对光谱数据进行预处理.为降低建模的复杂度,去除共线性的影响,采用连续投影算法和相关系数法相结合选取8个特征波长变量,最后使用PLS和ELM算法分别进行建模.实验表明,与采用全光谱波段建模相比,采用特征波长变量建模,PLS和ELM算法的运行时间都大大缩短,并且在运行时间和预测精度上,ELM算法均优于PLS算法.ELM算法采用8个特征波段变量建模,预测精度达到0.9768,均方误差为4.4291e-04,相关系数为0.7603,运行时间可控制在1e-04s之下,这可为研发羊肉水分含量的便携式检测装置提供理论参考.     

Approximating the fixed linear crossing number

We present a randomized polynomial-time approximation algorithm for the fixed linear crossing number problem (FLCNP). In this problem, the vertices of a graph are placed in a fixed order along a horizontal “node line” in the plane, each edge is drawn as an arc in one of the two half-planes (pages), and the objective is to minimize the number of edge crossings. FLCNP is NP-hard, and no previous polynomial-time approximation algorithms are known. We show that the problem can be generalized to k pages and transformed to the maximum k-cut problem which admits a randomized polynomial-time approximation. For the 2-page case, our approach leads to a randomized polynomial time 0.878+0.122ρ approximation algorithm for FLCNP, where ρ is the ratio of the number of conflicting pairs (pairs of edges that cross if drawn in the same page) to the crossing number. We further investigate this performance ratio on the random graph family G_n,1/2, where each edge of the complete graph K_n occurs with probability . We show that a longstanding conjecture for the crossing number of K_n implies that with probability at least 1-4e^-λ2, the expected performance bound of the algorithm on a random graph from G_n,1/2 is 1.366+O(λ/n). A series of experiments is performed to compare the algorithm against two other leading heuristics on a set of test graphs. The results indicate that the randomized algorithm yields near-optimal solutions and outperforms the other heuristics overall.     

一种改进的遗传k-means聚类算法

在经典的k-means聚类算法中,聚类数k必须事先给定,然而在现实中k很难被精确的确定.本文提出了一种改进的遗传k-means聚类算法,并构造了一个用来评价分类程度好坏的适应度函数,该适应度函数考虑的是在提高紧凑度(类内距)和分离度(类间距)的同时使得分类个数尽可能少.最后采用两个人工数据集和三个UCI数据集对k-means聚类算法(KM),遗传聚类算法(GA),遗传k-means聚类算法(GKM)和改进的遗传k-means聚类算法(IGKM)进行比较研究,比较的指标有类间距、类内距和分类正确率.研究证明改进的遗传k-means算法能够自动获取最佳聚类数k并且保持较高的正确率.     

基于资源受限广义指派问题的分解启发式算法

资源受限广义指派问题(RGAP)是NP-难的,对RGAP问题给出一个分解启发式算法.通过分解目标函数及约束条件,把原问题分解成子问题的集合,并设计分解启发式算法找到该问题的满意解.最后,通过算例说明算法的有效性.     

构建最小k 重控制集的概率算法

点集D ⊆ V (G) 称为图G 的k 重控制集, 如果D 满足V (G) - D 中任意结点在D 中至少有k 个邻居. 在无线网络中, 最小k 重控制集(MkDS) 用以构建健壮的虚拟骨干网. 构建虚拟骨干网是无线网络中最基本也是最重要的问题. 在本文中, 我们提出一种快速的分布式概率算法来构建k重控制集. 我们构建的k 重控制集的期望大小不超过最优解的O(k²) 倍. 算法的运行时间复杂度为O((Δ logΔ+log log n)n),其中Δ = max{|D(p)|}, D(p) 是以p 为中心半径为1 的圆盘中的结点, 最大值的比较范围是给定集合中所有的p 点.     

蚂蚁算法和小生境遗传算法的融合

蚂蚁算法是一种新型的模拟进化算法,也是一种随机型智能搜索算法.较为系统的总结了算法的基本理论,分析了其基本算法解决TSP问题的模型,针对蚂蚁算法易出现停滞的缺点,把小生境遗传算法和蚂蚁算法融合,仿真比较实验结果表明优于基本蚂蚁算法.     

一种自适应的四阶Newton-Cotes求积方法

本文给出了一种基于四阶Newton-Cotes公式的自适应求积算法，该算法能根据给定的容许误差，由计算机自动选取积分步长，克服了由于被积函数的性态不好而导致积分较复杂的缺陷．     

混沌遗传算法对BP神经网络的改进研究

BP神经网络算法是目前应用最广泛的一种神经网络算法,但有收敛速度慢和易陷入局部极小值等缺陷.本文利用混沌遗传算法(CGA)具有混沌运动遍历性、遗传算法反演性的特性来改进BP神经网络算法.该算法的基本思想是用混沌遗传算法对BP神经网络算法的初始权值和初始阈值进行优化.把混沌变量加入遗传算法中,提高遗传算法的全局搜索能力和收敛速度;用混沌遗传算法优化后得到的最优解作为BP神经网络算法的初始权值和阈值.通过实验观察,改进后的结果与普通的BP神经网络算法的结果相比,具有更高的准确率.     

艾拉姆咖分布参数变点的Bayes估计

研究了艾拉姆咖分布变点估计的非迭代抽样算法(IBF)和MCMC算法.在贝叶斯框架下,选取无信息先验分布,得到关于变点位置的后验分布和各参数的满条件分布,并且详细介绍了IBF算法和MCMC方法的实施步骤.最后进行随机模拟试验,结果表明两种算法都能够有效的估计变点位置,并且IBF算法的计算速度优于MCMC方法.     

Phase Condition for the Grover Algorithm

For the Grover algorithm, we derive the exact formula of the norm of the amplitude in the marked state in a sine-function form and use this formula to derive the necessary and sufficient phase condition sin Δ ≤ |β| for this algorithm with arbitrary phase rotations. We show that the condition of identical rotation angles θ = φ, which is a special case of our condition, is a sufficient but not necessary phase condition.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 3, pp. 472–483, September, 2005.     

Convergence of the (GOP) algorithm for a large class of smooth optimization problems

In this paper it is shown that the (GOP) algorithm is guaranteed to be convergent for a large class of smooth mathematical programming problems.     

Two algorithms for weighted matroid intersection

Consider a finite setE, a weight functionw:E→R, and two matroidsM ₁ andM ₂ defined onE. The weighted matroid intersection problem consists of finding a setI⊆E, independent in both matroids, that maximizes Σ{w(e):e inI}. We present an algorithm of complexity O(nr(r+c+logn)) for this problem, wheren=|E|,r=min(rank(M ₁), rank (M ₂)),c=max (c ₁,c ₂) and, fori=1,2,c _i is the complexity of finding the circuit ofI∪{e} inM _i (or show that none exists) wheree is inE andI⊆E is independent inM ₁ andM ₂. A related problem is to find a maximum weight set, independent in both matroids, and of given cardinalityk (if one exists). Our algorithm also solves this problem. In addition, we present a second algorithm that, given a feasible solution of cardinalityk, finds an optimal one of the same cardinality. A sensitivity analysis on the weights is easy to perform using this approach. Our two algorithms are related to existing algorithms. In fact, our framework provides new simple proofs of their validity. Other contributions of this paper are the existence of nonnegative reduced weights (Theorem 6), allowing the improved complexity bound, and the introduction of artificial elements, allowing an improved start and flexibility in the implementation of the algorithms. This research was supported in part by NSF grant ECS 8503192 to Carnegie-Mellon University.     

一类约束优化问题的非单调信赖域算法

本文就一类等式约束优化问题,结合当前比较流行的非单调技术,提出了一类新的求解等式约束优化的非单调信赖域算法.其非单调程度由算法自适应控制,计算预测下降量和实际下降量的比值时,采用前m(k)个点的信息,这不同于以前在计算预测下降量和实际下降量的比值时,仅仅采用当前-个点的信息.在没有正则性条件的假设下我们证明了算法是有定义的.并且通过对不同情况的讨论证明了算法的全局收敛性.基本的数值试验表明算法是有效的,且说明提出的非单调信赖域算法比单调信赖域算法有效.     

对一类overlay层组播路由问题的模型的改进

根据overlay层虚拟网图的特点，本给出了一类overlay层组播路由问题的数学模型的改进，及相应的一种启发式算法，即MMD算法，并分析了该算法的性质，证明了它是一个多项式时间算法。