并行矩阵多分裂迭代算法的收敛速度与发散速度比较

本文对于矩阵多分裂ＡＯＲ，ＳＯＲ，Ｇａｕｓｓ－Ｓｅｉｄｅｌ。外插Ｊａｃｏｂｉ以及Ｊａｃｏｂｉ迭代算法的敛散速度做了细致的比较。     

非线性最小二乘问题的一个分裂开关算法

本文对非线性最小二乘问题的分裂Ｂｒｏｙｄｅｎ凸类公式进行研究，为使修正矩阵具有某种最优性，给出一个新的开关算法，以根据问题表现出来的特性，在分裂ＢＦＧＳ与分裂ＤＦＰ之间进行选择，这一方法同样适用于一般的无约束最优化问题。     

三维定常/非定常Stokes方程的维数分裂算法（英文）

本文针对三维柱形区域提出了定常/非定常Stokes方程基于一致分裂格式的维数分裂算法(DSA).文章推导了三维定常/非定常Stokes方程维数分裂方法的数值迭代格式.新算法的优势在于一系列的二维问题能够并行执行,而且数值计算中避免了三维网格的生成.大量的数值结果表明新算法既能获得最优收敛阶,而且能获得比采用四面体元求解更精确的逼近解.最后,通过采用并行求解新算法能够得到比较好的加速比和并行效率.     

求解混合互补问题的一种内点算法

针对混合互补问题,提出了一种在数值上具有稳健性质的内点算法,并证明了其收敛性定理,数值例子表明这一算法是有效的。     

关于量子概率论的若干研究(英文)

本文证明了以下结论:算子关于一秩投影的绝对方差的绝对值的上确界等于这个算子到所有数乘算子的距离的平方;一个密度算子是忠实的当且仅当它是单射;算子列在密度算子ρ的值域的闭包上的强收敛性蕴含它关于ρ的a.s.收敛性;如果算子列关于每个密度算子是a.s.收敛的,那么它一定是强收敛的;算子列{An}强收敛于A当且仅当它是一致有界的且关于某个忠实的密度算子ρa.s.收敛于A。     

约束优化一个结合积极集识别的强收敛模松弛SQP算法(英文)

本文考虑了非线性不等式约束优化问题的求解问题,并结合模松弛SQP方法、强次可行方向法和积极集识别技术,提出了一个SQP算法.该算法在每一次迭代中,模松弛QP子问题的约束函数个数只决定于相应的识别集.不引进罚参数线搜索便可将阶段I(初始化)和阶段II(最优化)统一起来.在MFCQ条件下,得到算法的全局收敛性,若满足二阶充分条件,则算法具有强收敛性,且识别集能精确识别积极约束集.最后,我们给出了初步的数值结果.     

星图上最短路改进问题的组合算法

给定星图中一个非中心点到其余所有非中心点之间的n对点对,当要求网络中边的权重只允许减少且减少量有上界,并且这n对点对的最短路长度都不超过给定的n个上界的条件下,研究了l1模下星图的最短路改进问题,得到了解该问题的强多项式时间的组合算法,算法的时间复杂度为O(|E|log|E|).     

一种基于形状分析的R树节点分裂算法

基于对最小边界矩形(MBR)形状的分析,提出了一种线性时间复杂度的R树空间索引节点分裂算法。该算法将节点及其记录的最小边界矩形按形状分类,并根据分类情况确定节点分裂策略。首先提出了一种基于形状分析的基本节点分裂算法,然后针对其可能产生的不平衡分裂结果,提出了一种分裂结果平衡算法。最后提出了一种考虑兄弟节点的联合分裂策略以进一步提升算法的效果。对比实验表明,无论在索引的创建过程还是查询过程,此算法效率都优于对比算法,并且具有易实现和适应性强等特点,可以应用于各种空间数据库和地理信息系统(GIS)。     

三维定常/非定常Stokes方程的维数分裂算法

本文针对三维柱形区域提出了定常/非定常Stokes方程基于一致分裂格式的维数分裂算法(DSA).文章推导了三维定常/非定常Stokes方程维数分裂方法的数值迭代格式.新算法的优势在于一系列的二维问题能够并行执行,而且数值计算中避免了三维网格的生成.大量的数值结果表明新算法既能获得最优收敛阶,而且能获得比采用四面体元求解更精确的逼近解.最后,通过采用并行求解新算法能够得到比较好的加速比和并行效率.     

求解非线性互补问题的一个光滑信赖域算法

基于半光滑性和Jacobi相容性,提出了求解非线性互补问题的一个光滑信赖域算法,并在一定条件下证明了该算法的全局收敛性和局部超线性收敛性。     

带装载能力的需求依背包拆分车辆路径问题

以最小化总的旅行时间为优化目标,以单车场、单车型、装载能力和需求依背包拆分等为约束条件,将以往客户需求不可拆分的条件松弛为依背包来离散拆分,建立了带装载能力的需求依背包拆分VRP（CVRPSDB）的单目标数学模型。设计了一个自适应禁忌搜索算法（ATSA）对模型进行求解。该算法采用了自适应惩罚机制,构建了一个多邻域结构体,并针对客户点与背包都设计了相应的邻域操作算子,较好地适应了客户需求量的离散拆分程度。经算例测试与文献对比,验证了所设计模型与算法的有效性。     

Binary Fruit Fly Swarm Algorithms for the Set Covering Problem

Currently, the industry is experiencing an exponential increase in dealing with binary-based combinatorial problems. In this sense, metaheuristics have been a common trend in the field in order to design approaches to solve them successfully. Thus, a well-known strategy consists in the use of algorithms based on discrete swarms transformed to perform in binary environments. Following the No Free Lunch theorem, we are interested in testing the performance of the Fruit Fly Algorithm, this is a bio-inspired metaheuristic for deducing global optimization in continuous spaces, based on the foraging behavior of the fruit fly, which usually has much better sensory perception of smell and vision than any other species. On the other hand, the Set Coverage Problem is a well-known NP-hard problem with many practical applications, including production line balancing, utility installation, and crew scheduling in railroad and mass transit companies. In this paper, we propose different binarization methods for the Fruit Fly Algorithm, using S-shaped and V-shaped transfer functions and various discretization methods to make the algorithm work in a binary search space. We are motivated with this approach, because in this way we can deliver to future researchers interested in this area, a way to be able to work with continuous metaheuristics in binary domains. This new approach was tested on benchmark instances of the Set Coverage Problem and the computational results show that the proposed algorithm is robust enough to produce good results with low computational cost.     

物流运输系统货郎问题算法及应用

针对物流运输系统运送时间与运输成本问题,本文对运筹学领域货郎问题的算法进行了探讨,比较了货郎问题的匈牙利算法、填数破圈算法及填数破圈表上作业算法三种算法,通过矩阵变换,对各种算法作了分析并加以改进优化。结合实例应用,结果提示解决物流货郎问题更简便适用的方法是填数破圈算法。     

带准备时间的作业车间分批调度算法

研究了带有准备时间的作业车间分批排序问题,通过模拟计算将3种算法进行了对比分析.结果表明,遗传退火两阶段算法不受等分批限制,产生的各子批大小可以不同,这使得解空间更大,因而得到满意解的可能性大大增加.     

A Grafted Genetic Algorithm for the Job-Shop Scheduling Problem

The standard genetic algorithm has limitations of a low convergence rate and premature convergence in solving the job-shop scheduling problem. To overcome these limitations, this paper presents a new improved hybrid genetic algorithm on the basis of the idea of graft in botany. Through the introduction of a grafted population and crossover probability matrix, this algorithm accelerates the convergence rate greatly and also increases the ability to fight premature convergence. Finally, the approach is tested on a set of standard instances taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.     

不确定车数的随机车辆路径问题模型及算法

研究了一类有时间约束、车辆数量不确定的随机车辆路径问题;建立了该类问题的随机规划数学模型;设计了模型求解的遗传算法、禁忌搜索算法和遗传-禁忌混合算法.禁忌算法采用了对当前解的车辆-顾客分配结构和解的路径顺序分别禁忌的双层禁忌算法,使算法全局性更好,同时也降低了搜索时间.把禁忌算法作为变异算子应用于遗传算法形成了混合算法.最后给出了计算示例,对算法进行了比较分析.     

考虑加班因素的订单接受问题优化模型与算法

加班是制造商在面对客户需求增多时经常会采取的一种临时扩大产能的方法。本文将加班因素引入订单接受问题,考虑到加班容易导致生产线的工位间同时存在产能不足与产能过剩的情况,建立了以总利润最大化和生产线产能均衡为优化目标的数学模型。根据模型特征,本文采用两种分布式估计算法,即基于节点矩阵抽样算法和基于节点的偶合算法来实现问题求解。实验结果表明,基于节点的偶合算法具有良好的求解效果,并且产能均衡这一优化目标的设定可以在保证生产线产能平衡的同时有效地提高产品利润。     

Hilbert空间中一般强混合变分包含的迭代算法

研究了Hilbert空间中求一般强混合变分包含逼近解的迭代算法。这类变分包含概括了若干熟知的变分不等式与变分包含成特例。结果是刘理蔚与李育强(2001)及Noor(1998)的结果的推广和改进。     

Solution of Inverse Boundary Optimization Problem by Trefftz Method and Exponentially Convergent Scalar Homotopy Algorithm

The inverse boundary optimization problem, governed by the Helmholtz equation, is analyzed by the Trefftz method (TM) and the exponentially convergent scalar homotopy algorithm (ECSHA). In the inverse boundary optimization problem, the position for part of boundary with given boundary condition is unknown, and the position for the rest of boundary with additionally specified boundary conditions is given. Therefore, it is very difficult to handle the boundary optimization problem by any numerical scheme. In order to stably solve the boundary optimization problem, the TM, one kind of boundary-type meshless methods, is adopted in this study, since it can avoid the generation of mesh grid and numerical integration. In the boundary optimization problem governed by the Helmholtz equation, the numerical solution of TM is expressed as linear combination of the T-complete functions. When this problem is considered by TM, a system of nonlinear algebraic equations will be formed and solved by ECSHA which will converge exponentially. The evolutionary process of ECSHA can acquire the unknown coefficients in TM and the spatial position of the unknown boundary simultaneously. Some numerical examples will be provided to demonstrate the ability and accuracy of the proposed scheme. Besides, the stability of the proposed meshless method will be validated by adding some noise into the boundary conditions.     

Comparison of Two Algorithms for Decoding Alternant Codes

We compare the key equation solving algorithm introduced by Fitzpatrick to the Berlekamp-Massey algorithm. Our main result is that the two algorithms have the same computational complexity. It follows that in practice Fitzpatricks algorithm improves on Berlekamp-Massey since it uses less storage and has a simpler control structure. We also give an improved version of Fitzpatricks algorithm and a new simplified proof of the central inductive step in the argument. Received: June 6, 1997