Application of linear programming to structural system reliability

Reliability of framed structures comprised of ductile components is studied assuming that loads and component strengths are random variables. A bounded variable simplex algorithm and duality in linear programming are used to determine the coefficients of strength terms in the failure mode expression (FME). The method is extended to identify an FME for a structure under simultaneous multiple load variables. It is shown that in the case of single load, Phase 1 of the simplex algorithm can be skipped since a trivial basic feasible solution is always available. Enumeration of FMEs is carried out using sensitivity and simulation approaches in conjunction with LP methods. The second moment format is used to find a measure of reliability for a structure. The significant modes are used in a Monte Carlo simulation to accurately obtain mean and variance of the safety margin of the system and consequently a safety index for the system is computed. Numerical examples are given to illustrate the methods presented in the paper.     

An improved initial solution of a long transportation problem

An efficient algorithm to obtain an improved initial feasible solution of a long transportation problem which saves 70–90% of simplex iterations executed by the “Most Negative Rule” as a basic change criteria is presented.     

A New Well-Solvable Class of PNS Problems

A manufacturing system consists of operating units which convert their input materials into their output materials. In the problem of designing a process network, we have to find a suitable network of operating units which produces the desired products from the given raw materials. If we consider this process network design problem from a structural point of view, then we obtain a combinatorial optimization problem called the Process Network Synthesis or (PNS) problem. It is known that the PNS problem is NP-complete. Here, a new method is presented to reduce the solution of some more difficult PNS problems to the solution of simpler ones, and using this method, a new well-solvable class of PNS problems is established. Received February 12, 1999; revised October 24, 2000     

An efficient search direction for linear programming problems

In this paper, we present an auxiliary algorithm, in terms of the speed of obtaining the optimal solution, that is effective in helping the simplex method for commencing a better initial basic feasible solution. The idea of choosing a direction towards an optimal point presented in this paper is new and easily implemented. From our experiments, the algorithm will release a corner point of the feasible region within few iterative steps, independent of the starting point. The computational results show that after the auxiliary algorithm is adopted as phase I process, the simplex method consistently reduce the number of required iterations by about 40%.Scope and purposeRecent progress in the implementations of simplex and interior point methods as well as advances in computer hardware has extended the capability of linear programming with today's computing technology. It is well known that the solution times for the interior point method improve with problem size. But, experimental evidence suggests that interior point methods dominate simplex-based methods only in the solution of very large scale linear programs. If the problem size is medium, how to combine the best features of these two methods to produce an effective algorithm for solving linear programming problems is still an interesting problem. In this research we present a new effective ε-optimality search direction based on the interior point method to start an initial basic feasible solution near the optimal point for the simplex method.     

Modification and implementation of two-phase simplex method

We investigate the problem of finding the initial basic feasible solution in the simplex algorithm. Two modifications of the two-phase simplex method are presented. Implementations of the two-phase simplex method and its modifications in the programming package MATHEMATICA and the programming language Visual Basic are written. We report computational results on numerical examples from the Netlib test set.     

一种基于IPSO-SVM算法的网络入侵检测方法

网络入侵检测一直是计算机网络安全领域的研究热点,当前网络面临着诸多的安全隐患。为了提高网络入侵检测的准确性,首先对粒子群优化(Particle Swarm Optimization,PSO)算法进行了改进,然后利用改进的PSO算法(IPSO算法)对支持向量机(Support Vector Machine,SVM)的参数进行了优化,并在此基础上设计了一种新型的基于IPSO-SVM算法的网络入侵检测方法。实验结果表明,相比于经典的SVM和PSO-SVM算法,IPSO-SVM算法不仅 明显改善了网络训练的收敛速度,而且其网络入侵检测的正确率分别提高了7.78%和4.74%,误报率分别降低了3.37%和1.19%,漏报率分别降低了1.46%和0.66%。     

A dynamic version for the Network Simplex Algorithm

In most practical environments, scheduling is an ongoing reactive process where the presence of real time information continually forces reconsideration and revision of pre-established schedules. The objectives of the research reported in this paper are to respond to changes in the problem, to solve the new problem faster and to use some parts of the previous solution for the next problem. In this paper, based on Network Simplex Algorithm, a dynamic algorithm, which is called Dynamic Network Simplex Algorithm (DNSA), is presented. Although the traditional network simplex algorithm is at least one hundred times faster than traditional simplex algorithm for Linear Programs (through specialization), for dynamic scheduling with large scale problems it still takes time to make a new graph model and to solve it. The overall approach of DNSA is to update the graph model dynamically and repair its spanning tree by some strategies when any changes happen. To test the algorithm and its performance, an application of this algorithm to Dynamic Scheduling of Automated Guided Vehicles in the container terminal is used. The dynamic problem arises when new jobs are arrived, the fulfilled jobs are removed and the links or junctions are blocked (which results in distances between points being changed). The results show considerable improvements, in terms of reducing the number of iterations and CPU time, to solve randomly generated problems.     

Multiloop transportation simplex algorithm

In large-scale transportation problems (TPs), various methods have been developed to obtain an optimal solution. One of the methods is the transportation simplex algorithm (TSA), which obtains an optimal solution for TP. Various heuristic methods have been developed to find an initial basic feasible solution for transportation algorithms. These methods differ in terms of computational cost and finding good initial solution. In TSA, the better the basic feasible solution, the less the number of iterations the algorithm will run. At each step, it uses pivoting operation, where a loop involving the nonbasic variable with the largest cost reduction is determined. Then, it eliminates the entering basic variable. However, for large-scale problems, even the best basic feasible solution may result in high number of iterations. In this paper, we present a novel algorithm called multiloop transportation simplex algorithm which finds multiple independent loops during pivoting operation. This causes larger cost reductions in every iteration. We experimentally show that the average number of iterations and runtime to solve the TP are dramatically reduced.     

A gradient driven transportation algorithm

In this work we present a new algorithm for the solution of the transportation problem. Although the algorithm is gradient-directed, it does not use the classical gradient approach. Instead, it first computes a reduced gradient and then determines an improved feasible direction in the dual space, thereby extending the initial gradient. To accomplish this, we make use of a special diagonal ordering of the basic vectors. After obtaining the intial basic feasible solution, the algorithm may transfer, without any computational overhead, to a streamlined dual simplex routine, or continue on with the gradient method.     

模糊神经网络算法在倒立摆控制中的应用

本文利用一种可以进行结构和参数学习的模糊神经网络成功地控制一级倒立摆,该网络是一种多层前馈网络,它将传统模糊控制器的基本要件综合到网络结构中。从而使该网络既具备神经网络的低级学习能力,从而还具备模糊逻辑系统类似人的高级推理能力。因而,给定训练数据后,该网络不仅可以学习网络参数,同时还可以学习网络结构。结构学习确定了表示了模糊规则和模糊分段数的连接类型以及隐节点数目。对一级倒立摆的实际控制效果可以证明该算法的性能和实用性。     

无级电话网非线性单纯形动态路由策略及算法评估方法

无级电话网动态路由技术是充分利用现有设备、提高服务质量的关键技术．为了提高求解速度和求解质量，本文提出一个基于非线性单纯形动态路由策略及其评估方法；介绍了在离散的解空间中根据链路负载均方差构造动态路由最优化问题和算法的具体实现；并根据话务溢出率和网络阻塞率对网络正常或网络异常情况下的算法求解结果进行评估；分析了系统运行情况和话务模拟结果．仿真实验与评估结果说明该策略能够在很短的时间内得到质量较优的全局优化的路由方案，该策略正应用于广东省电话网智能管理系统．     

A linear algorithm for the pos/neg-weighted 1-median problem on a cactus

The 1-median problem on a network asks for a vertex minimizing the sum of the weighted shortest path distances from itself to all other vertices, each associated with a certain positive weight. We allow fornegative weights as well and devise an exact algorithm for the resulting ‘pos/neg-weighted’ problem defined on a cactus. The algorithm visits every vertex just once and runs thus in linear time. This research has been supported by the Spezialforschungsbereich F 003 ‘Optimierung und Kontrolle’, Projektbereich Diskrete Optimierung.     

一种改进的药代动力学参数优化方法及其应用

基于药代动力学参数优化方法PKAIN人工免疫网络算法,提出了迭代分组并发单纯形算子,并实现了线性网络抑制函数以简化人工免疫网络的参数设置。为了加快算法的搜索速度和搜索精度,提出了新型的人工免疫网络单纯形混合算法（PKAIN_spx）,用人工免疫网络实现粗粒度全局搜索,随后用单纯形进行精确搜索。仿真实验对改进的PKAIN算法（PKAIN_in）、人工免疫网络单纯形混合算法（PKAIN_spx）以及PKAIN算法进行了比较分析,结果表明PKAIN_spx算法在药代动力学参数优化中取得良好的实验效果。     

An Optimal Algorithm for Bound and Equality Constrained Quadratic Programming Problems with Bounded Spectrum

An implementation of the recently proposed semi-monotonic augmented Lagrangian algorithm for solving the large convex bound and equality constrained quadratic programming problems is considered. It is proved that if the algorithm is applied to the class of problems with uniformly bounded spectrum of the Hessian matrix, then the algorithm finds an approximate solution at O(1) matrix-vector multiplications. The optimality results are presented that do not depend on conditioning of the matrix which defines the equality constraints. Theory covers also the problems with dependent constraints. Theoretical results are illustrated by numerical experiments.     

基于多目标粒子群优化的虚拟网络映射算法

在虚拟网络映射中,多数研究只考虑一个映射目标,不能体现多方的利益。为此,将多目标算法和粒子群算法结合,提出了一种基于多目标粒子群优化（PSO）的虚拟网络映射算法（VNE-MOPSO）。首先,在基本的粒子群算法中引入交叉算子,扩大了种群优化的搜索空间;其次,在多目标优化算法中引入非支配排序、拥挤距离排序,从而加快种群的收敛;最后,以同时最小化成本和节点负载均衡度为虚拟网络映射目标函数,采用多目标粒子群优化算法求解虚拟网络映射问题（VNMP）。实验结果表明,采用该算法求解虚拟网络映射问题,在网络请求接受率、平均成本、平均节点负载均衡度、基础设施提供商的收益等方面具有优势。     

WSN中基于分布式的覆盖洞修复算法

无线传感器网络(WSN)中存在因节点能量耗尽和移动节点撒播不均而出现的覆盖洞问题,覆盖洞的出现会降低网络的覆盖率和连通性,严重影响网络性能。为解决该问题,构造一种既有静态节点又有移动节点的混合网络模型,并提出一种WSN中基于分布式的覆盖洞修复算法。利用静态节点指导移动节点移动到最优位置,达到修复覆盖洞目的。仿真实验结果证明,该算法能在空洞覆盖率和节点代价之间取得最佳平衡。     

基于神经网络的并联3自由度机器人位置正解

并联机器人位置正解是机器人运动学中难点问题之一，常规求解方法比较复杂且难度较大，通常需要对大量的非线性方程组进行推导计算且得到的解不唯一。该文提出了一种将人工神经网络用于并联机器人位置正解求解的通用方法，并结合实际机构对并联3自由度机器人进行了具体求解。通过对神经网络拓扑结构的设计以及选取有效的学习算法并用大量的位置反解数据对神经网络进行训练，获得了用于求解位置正解的神经网络模型，该网络可以实现位置正解问题的求解计算，从而避免了复杂的推导和演算。计算机仿真与实验结果表明了该方法的有效性与可行性。     

基于球形矩匹配与特征判别的图像超分辨率重建

由于网络训练不稳定,基于生成对抗网络（GAN）的图像超分辨率重建存在模式崩溃的现象。针对此问题,提出了一种基于球形几何矩匹配与特征判别的球面双判别器超分辨率重建网络SDSRGAN,通过引入几何矩匹配与高频特征判别来改善网络训练的稳定性。首先,生成器对图像提取特征并通过上采样生成重建图像;接着,球面判别器将图像特征映射至高维球面空间,充分利用特征数据的高阶统计信息;然后,在传统判别器的基础上增加特征判别器,提取图像高频特征,重建特征高频分量和结构分量两方面;最后,对生成器与双判别器进行博弈训练,提高生成器重建图像质量。实验结果表明,所提算法能有效收敛,其网络能够稳定训练,峰值信噪比（PSNR）为31.28 dB,结构相似性（SSIM）为0.872,而与双三次差值、超分辨率残差网络（SRResNet）、加速的卷积神经网络超分辨率（FSRCNN）、基于GAN的单图像超分辨率（SRGAN）和增强型超分辨率生成对抗网络（ESRGAN）算法相比,所提算法的重建图像具有更加逼真的结构纹理细节。所提算法为基于GAN的图像超分辨率研究提供了球形矩匹配与特征判别的双判别方法,在实际应用中可行且有效。     

A simplex algorithm for minimum fuel problems of linear discrete control systems

A simplex algorithm for solving the minimum fuel problem for linear discrete control systems is described. In this algorithm an initial basic feasible solution is available with no artificial variables needed. Also minimum computer storage is required. The algorithm is a simple and fast one. A numerical example is given     

Derivative Free Optimization in Higher Dimension

Non-linear optimizations that do not require explicit or implicit derivative information of an objective function are an alternate search strategy when the derivative of the objective function is not available. In factorial design, the number of trials for experimental identification method in E^m is about ( m + 1). These ( m + 1) equally spaced points are allowed to form a geometry that is known as regular simplex. The simplex method is attributed to Spendley, Hext and Himsworth. The method is improved by maintaining a set of ( m + 1) points in m dimensional space to generate a non-regular simplex. This study suggests re-scaling the simplex in higher dimensions for a restart phase. The direction of search is also changed when the simplex degenerates.
The performance of this derivative free search method is measured based on the number of function evaluations, number of restart attempts and improvements in function value. An algorithm that describes the improved method is presented and compared with the Nelder and Mead simplex method. The performance of this algorithm is also tested with artificial neural network (ANN) problem. The numbers of function evaluations are about 40 times less with the improved method against the Nelder and Mead (1965) method to train an ANN problem with 36 variables.