单背包问题的半定松弛算法

首先给出了单背包问题的秩1半定松驰规划，然后在此基础上提出了求解该问题的半定松驰随机算法KSSD。分析结果表明：（1）当σ＞0.19时，算法KSSD的近似比就会超过0.27。（2）算法KSSD中的参数θ对某种大规模情形将不起作用。     

一种解无约束优化问题的新的非单调自适应信赖域方法

本文提出了一种解无约束优化问题的新的非单调自适应信赖域方法.这种方法借助于目标函数的海赛矩阵的近似数量矩阵来确定信赖域半径.在通常的条件下,给出了新算法的全局收敛性以及局部超线性收敛的结果,数值试验验证了新的非单调方法的有效性.     

路段容量约束弹性需求交通均衡分配近似算法

本文研究了带路段容量约束弹性需求用户均衡交通分配问题及其近似解法.采用超需求模型将弹性需求转化为固定需求,提出了一种带路段容量约束弹性需求用户均衡交通分配近似算法.该算法在迭代过程中,通过不断自适应调节排队延误因子、误差因子来近似真实路段行驶时间,使路段流量逐步满足约束条件,最终达到广义用户均衡.这种方法克服了容量约束弹性需求用户均衡分配计算量大及随机分配法要求枚举所有路径的困难.随后证明了算法的收敛性,并对一个小型路网进行了数值试验.     

Schwarz交替方向法的代数处理

本文利用代数方法获得二子区域情形带松驰因子的加法型Ｓｃｈｗａｒｚ交替方向法的最优松驰因子，结果表明代数平均是最优的．接着通过反例说明该结果不可推广至多子区域情形．最后，本文将该代数技巧用于证明一些现有的重要结果,和原有证明相比，现证简单、直观     

具非线性控制变量的非自治松驰系统时间最优追踪控制问题中的若干结果

本文讨论了一类广义非自治离散松驰系统的时间最优控制问题，将R^n中点曲线的目标约束推广为凸集值函数的超曲线约束．在证明了松驰系统与原系统可达集相等的基础上，得到了最优控制的存在性．由凸集分离定理及终端时间闺值函数方程，我们获得了最大值原理及最优控制时间的确定方法．较之Hamilton方法，本文的条件更一般．离散松驰系统的相关结论可以用于分散控制．     

矩形区域上非线性变分不等式的并行SOR格式及其全局收敛性

数值方法的并行化是近些年随计算机并行性能的开发而兴起的研究方向之一。众所周知,逐次超松弛迭代(简记为SOR)是解方程组及其它数学问题简单而又实用的数值算法。八十年代末及九十年代初,Mangasarian及De.Leone等人将此算法的并行格式用于求解线     

几何规划问题的一种分枝定界方法

本文通过指数函数变换，把解几何规划GP（Ω）等价地转化为另外一个非线优化问题NLP（－↑Ω），根据问题（－↑Ω）的结构特征，构造它的一个线性规划松驰上确定它的最优值的一个下界，由此给出问题GP（Ω）的一个新的分枝定界算法。最后证明了这个算法是收敛的。     

广义鞍点问题的改进的类SOR算法

针对广义鞍点问题,本文提出了一个改进的类逐次超松弛迭代算法,在较弱的条件下,分析了算法的收敛性及线性收敛率.新算法的每步计算量与已有的算法类似,都是需要（近似）求解线性方程组,但新算法有更好的灵活度通过合适地选取参数矩阵,每一步子问题可以容易地求解,甚至可以有闭式解（closed-form solution）.数值实验结果显示了新算法的有效性.     

区间自适应遗传算法优化无约束非线性规划问题

针对无约束非线性规划传统优化方法存在的问题,将区间自适应遗传算法引入无约束非线性规划优化中,算法可以利用当前进化信息,自适应移动搜索区间,找到全局最优解,故可缩短搜索区间长度,提高编码精度,降低算法计算量,解决了传统遗传算法处理优化问题时,给定区间必须包含最优解这一问题,这也是本算法有别于其他优化算法的独特优势,为某些最优解所在区间难以估计的无约束非线性规划问题的优化提供了一条有效可行的途径.系统阐述了区间自适应遗传算法的原理,给出了算法优化无约束非线性规划问题的步骤,以MatlabR2016b仿真方式对算法进行了实例测试,结果表明,方法是一种计算稳定、正确、有效、可靠实用的无约束非线性规划优化方法.     

恒应力寿命试验截尾模型参数的最佳估计

对恒定应力加速寿命试验建立了定时截尾与定数截尾参数模型.在诂计模型参数时,考虑定时截尾产品失效数的随机性,引入近似因子、修偏乘子和修偏项,建立起参数估计通用式并逐次进行跟随修偏估计.对定数截尾考虑数据信息随机性短缺,通过变量变换分别建立最优线性无偏估计和简单线性无偏估计在指数分布条件下的式子,并按统计分析考虑随机因数的影响引入综合修偏因子,按抽样数目的多少分别采用修偏后的式子.最后应用实际数据对模型参数逐次修偏估计和不同估计方法对比的最佳估计.     

Adaptive Splines and Genetic Algorithms

Most existing algorithms for fitting adaptive splines are based on nonlinear optimization and/or stepwise selection. Stepwise knot selection, although computationally fast, is necessarily suboptimal while determining the best model over the space of adaptive knot splines is a very poorly behaved nonlinear optimization problem. A possible alternative is to use a genetic algorithm to perform knot selection. An adaptive modeling technique referred to as adaptive genetic splines (AGS) is introduced which combines the optimization power of a genetic algorithm with the flexibility of polynomial splines. Preliminary simulation results comparing the performance of AGS to those of existing methods such as HAS, SUREshrink and automatic Bayesian curve fitting are discussed. A real data example involving the application of these methods to a fMRI dataset is presented.     

A new exact method for the two-dimensional orthogonal packing problem

The two-dimensional orthogonal packing problem (2OPP) consists in determining if a set of rectangles (items) can be packed into one rectangle of fixed size (bin). In this paper we propose two exact algorithms for solving this problem. The first algorithm is an improvement on a classical branch&bound method, whereas the second algorithm is based on a new relaxation of the problem. We also describe reduction procedures and lower bounds which can be used within enumerative methods. We report computational experiments for randomly generated benchmarks which demonstrate the efficiency of both methods: the second method is competitive compared to the best previous methods. It can be seen that our new relaxation allows an efficient detection of non-feasible instances.     

基于遗传算法的最佳摄动量法在反问题中的应用

抛物型方程参数的反演在工程中有重要的应用价值,针对最佳摄动量法对初始模型依赖性的严重不足,给出遗传算法对最佳摄动量法的改进的新算法并进行了数值模拟．从模拟结果可以看到模拟结果与估算值曲线图基本吻合,体现了该方法的有效性和高精度性,且新算法弥补了对初始数据严重依赖的不足以及保证了区域收敛的全局性．     

二层线性规划的自适应遗传算法

提出了一种自适应遗传算法来求解二层线性规划问题.该方法克服了难以确定合适的交叉概率和变异概率的困难.另外,在该方法中还采用了其它一些技巧不仅解决了在采用遗传算法经常出现的有些个体不可行的问题,而且还改进了算法的效率.     

Performance Analysis of Adaptive Genetic Algorithms with Fuzzy Logic and Heuristics

In this paper, we propose some genetic algorithms with adaptive abilities and compare with them. Crossover and mutation operators of genetic algorithms are used for constructing the adaptive abilities. All together four adaptive genetic algorithms are suggested: one uses a fuzzy logic controller improved in this paper and others employ several heuristics used in conventional studies. These algorithms can regulate the rates of crossover and mutation operators during their search process. All the algorithms are tested and analyzed in numerical examples. Finally, a best genetic algorithm is recommended.     

试探算法与SSOR预处理共轭梯度算法的拟最佳因子

1引言在求解系数矩阵为对称正定的大型线性代数方程组Au=b (1．1)的迭代法方面,七十年代以来发展了各种预处理共轭梯度法．由于SSOR分裂中具有对称因子,可用于加速共轭梯度法,称为SSOR预处理共轭梯度法(简记为;SSORPCG．同时,由于当松弛因子ω∈(0,2)时,SSOR迭代法收敛,从而进一步发展了m步SSOR预处理共轭梯度法(简记为:m-step SSORPCG．胡家赣证明,经过最优的SSOR预条件,预优     

三维Poisson方程的一个块松弛法

在许多物理、工程问题中,都涉及到Poisson方程的数值求解。在二维情形,人们已经对规则区域研究出一些快速求解方法(如快速富氏变换,循环约简算法等)。这些算法具有稳定、计算量小等优点。特别是循环约简算法,更充分地体现了这些优点。我们曾在每秒五万次左右的机器上用此方法求解了1200多阶的方程组,仅用50秒便得准确结果,足见其计算量之少。但如何将此方法应用于一般区域,尚待进一步研究。在将循环约简     

New geometry-inspired relaxations and algorithms for the metric Steiner tree problem

Determining the integrality gap of the bidirected cut relaxation for the metric Steiner tree problem, and exploiting it algorithmically, is a long-standing open problem. We use geometry to define an LP whose dual is equivalent to this relaxation. This opens up the possibility of using the primal-dual schema in a geometric setting for designing an algorithm for this problem. Using this approach, we obtain a 4/3 factor algorithm and integrality gap bound for the case of quasi-bipartite graphs; the previous best integrality gap upper bound being 3/2 (Rajagopalan and Vazirani in On the bidirected cut relaxation for the metric Steiner tree problem, 1999). We also obtain a factor \({\sqrt{2}}\) strongly polynomial algorithm for this class of graphs. A key difficulty experienced by researchers in working with the bidirected cut relaxation was that any reasonable dual growth procedure produces extremely unwieldy dual solutions. A new algorithmic idea helps finesse this difficulty—that of reducing the cost of certain edges and constructing the dual in this altered instance—and this idea can be extracted into a new technique for running the primal-dual schema in the setting of approximation algorithms.     

An efficient algorithm for the parallel solution of high-dimensional differential equations

The study of high-dimensional differential equations is challenging and difficult due to the analytical and computational intractability. Here, we improve the speed of waveform relaxation (WR), a method to simulate high-dimensional differential-algebraic equations. This new method termed adaptive waveform relaxation (AWR) is tested on a communication network example. Further, we propose different heuristics for computing graph partitions tailored to adaptive waveform relaxation. We find that AWR coupled with appropriate graph partitioning methods provides a speedup by a factor between 3 and 16.     

约束装箱问题的混合遗传算法求解

本将最佳适应法和遗传算法相结合，提出了一种新的启发式混合遗传算法对具有时间约束的装箱问题进行求解，给出了具体的算法步骤，试算结果表明基于启发式算法的混合遗传算法适合于求解各种约束条件下的大规模装箱问题。