一种线性约束规划问题的神经网络模型及其应用

提出了一种基于梯度投影矩阵下的求解线性约束下规划问题的神经网络。针对解的稳定性问题,导出了该网络相关参数之间的关系。由文中定义可知,该网络不但适合于求解线性约束下线性或非二次规划问题,而且也用于求解线性或非线性方程组问题,比其它规划问题的神经网络方法更具有一般性。     

求解线性约束的二次规划神经网络学习新算法

提出了一种基于0.618法求解具有线性约束的二次规划问题的神经网络学习新算法。与已有的求解线性约束的二次规划问题的神经网络学习算法相比,该算法的适用范围更广,计算精度更高。其目的是为具有线性约束的二次规划问题的求解提供一种新方法。仿真实验验证了新算法的有效性。     

等式约束凸二次规划解析的新型神经网络方法*

针对不同于传统基于梯度法的递归神经网络定义一种基于标量范数取值的非负能量函数,通过定义一种基于向量取值的不定无界的误差函数,构建了一种能实时求解具有线性等式约束的凸二次规划问题。基于Simulink仿真平台的计算机实验结果表明,该新型神经网络模型能够准确有效地求解此类二次规划问题。     

一种求解线性约束的非线性规划神经网络方法

针对线性约束的非线性规划的求解问题,利用罚函数求解优化问题的思想将其转化为二次凸规划,基于神经网络的结构特性,定义所需的能量函数,从而使网络收敛于唯一稳定点最终实现线性约束的非线性规划的求解。实验仿真结果表明,该方法是有效和正确的,且能推广到含参的非线性规划和多目标规划中去。     

二次规划问题的变时滞神经网络模型的全局指数稳定

研究等式约束下二次规划问题最优解神经网络模型的稳定性,提出一种变时滞Lagrange神经网络求解方法.利用线性矩阵不等式(LMI)技术,得到两个变时滞神经网络模型全局指数稳定的条件.分析表明,此稳定判据能够适应慢变时滞和快变时滞两种情况,具有适用范围宽、保守性小且易于验证等特点.数值仿真结果验证了所提方法的有效性.     

二次规划问题的神经网络方法及其数值仿真

针对具有边界约束的凸二次规划问题,利用离散神经网络模型的建模原理,构造了一个新的离散投影神经网络模型.为了优化求解,运用李亚普诺夫稳定性理论,通过构造一个新的广义李亚普诺夫函数,得到了神经网络模型全局指数稳定的线性矩阵不等式条件.同时将结果的保守性与传统方法所得结果进行了比较.数值仿真表明,改进方法采用新条件,有求解方便,保守性弱的特点,具有较强的实用性.     

求解线性约束二次优化问题的神经计算模型

本文提出了一种求解线性约束二次优化问题的神经模型 ,研究了该神经网络的稳定性和收敛性 ,给出了电路框图 ,并通过算例证明了该神经网络的可行性。     

基于动态规划的约束优化问题多参数规划求解方法及应用

结合动态规划和单步多参数二次规划, 提出一种新的约束优化控制问题多参数规划求解方法. 一方面能得到约束线性二次优化控制问题最优控制序列与状态之间的显式函数关系, 减少多参数规划问题求解的工作量; 另一方面能够同时求解得到状态反馈最优控制律. 应用本文提出的多参数二次规划求解方法, 建立无限时间约束优化问题状态反馈显式最优控制律. 针对电梯机械系统振动控制模型做了数值仿真计算.     

基于神经网络模型的有约束的FMS资源调度

本文介绍了用神经网络求解ＦＭＳ中有约束的资源调度问题的方法，有约束的资源调度问题首和无被分解成一系列多维背包模型并且为背包模型建立了一个等价的Ｈｏｐｆｉｅｌｄ神经网络，然后通过扩展Ｈｏｐｆｉｅｌｄ网络，给出了一种求解有约束的资源调度问题的方法。这咱方法可以避免通常神经网络所具有的不稳定性和容易陷入局部极小点的缺陷。     

一种基于动态规划策略的离散动态大系统递阶优化神经网络

给出了一种具有集成化特征的、快速求解大规模系统动态规划问题的神经网络模型 (LDPNN),该神经网络将大系统的各子系统的动态方程约束嵌入局部优化子网络,使得整个 网络的结构简洁、紧凑,便于硬件实现,该神经网络计算模型克服了数值方法迭代计算的缺 陷,求解效率高,适宜于大规模动态系统实时优化应用.     

Using fuzzy numbers in linear programming

Managers, decision makers, and experts dealing with optimization problems often have a lack of information on the exact values of some parameters used in their problems. To deal with this kind of imprecise data, fuzzy sets provide a powerful tool to model and solve these problems. This paper studies a linear programming (LP) problem in which all its elements are defined as fuzzy sets. Special cases of this general model are found and reproduced, and it is shown that they coincide with the particular problems proposed in the literature by different authors and distinct approaches. Solution methods are also provided. They show how it is possible to address and solve linear programming problems with data given in a qualitative form, instead of the usual quantitative and precise way.     

Control applications of nonlinear convex programming

Since 1984 there has been a concentrated effort to develop efficient interior-point methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important property of these interior-point methods (beyond their efficiency for LP): they extend gracefully to nonlinear convex optimization problems. New interior-point algorithms for problem classes such as semidefinite programming (SDP) or second-order cone programming (SOCP) are now approaching the extreme efficiency of modern linear programming codes. In this paper we discuss three examples of areas of control where our ability to efficiently solve nonlinear convex optimization problems opens up new applications. In the first example we show how SOCP can be used to solve robust open-loop optimal control problems. In the second example, we show how SOCP can be used to simultaneously design the set-point and feedback gains for a controller, and compare this method with the more standard approach. Our final application concerns analysis and synthesis via linear matrix inequalities and SDP.     

A new neural network for solving linear programming problems andits application

Presents a new neural network which improves existing neural networks for solving general linear programming problems. The network, without setting parameter, uses only simple hardware in which no analog multipliers are required, and is proved to be completely stable to the exact solutions. Moreover, using this network the author can solve linear programming problems and its dual simultaneously, and cope with problems with nonunique solutions whose set is allowed to be unbounded.     

改进和声搜索算法求解一般整数规划问题

设计了一种改进的和声搜索算法对一般的整数规划问题进行求解,在计算机上予以实现。经实验测试,相对遗传模拟退火算法和混合遗传算法,获得了同样甚至更好的解。由于改进和声搜索算法使用灵活,因此对于线性和非线性的整数规划问题都能进行求解。     

单纯形法求解与Excel规划求解

利用单纯形法求解线性规划问题在产品品种问题、合理配料问题、开料问题等问题中有着极其广泛的应用,但整个计算过程非常繁杂,而且容易计算错误。对Excel规划求解的研究发现,利用Excel中的规划求解工具可以实现单纯形法求解线性规划的问题,大大提高了求解的速度和准确性。     

Fuzzy mathematical programming

Fuzzy linear programming (FLP) was originally suggested to solve problems which could be formulated as LP-models, the parameters of which, however, were fuzzy rather than crisp numbers. It has turned out in the meantime that FLP is also well suited to solve LP-problems with several objective functions. FLP belongs to goal programming in the sense that implicitly or explicitly aspiration levels have to be defined at which the membership functions of the fuzzy sets reach their maximum or minimum. Main advantages of FLP are, that the models used are numerically very efficient and that they can in many ways be well adopted to different decision behaviors and contexts.     

SCPIP – an efficient software tool for the solution of structural optimization problems

This paper describes SCPIP, a FORTRAN77 subroutine that has been proven to be a reliable implementation of convex programming methods in an industrial environment. Convex approximation methods like the method of moving asymptotes are used nowadays in many software packages for structural optimization. They are known to be efficient tools for the solution of design problems, in particular if displacement dependent constraints like stresses occur. A major advantage over many but not all classical approaches of mathematical programming is that at an iteration point a local model is formulated. For the solution of such a model no further function and gradient evaluations are necessary besides those at the current iteration point. The first versions of convex approximation methods used all a dual approach to solve the subproblems which is still a very efficient algorithm to solve problems with at most a medium number of constraints. But it is not efficient for problems with many constraints. An alternative is the use of an interior point method for the subproblem solution. This leads to more freedom in the definition of the linear systems where most of the computing time to solve the subproblems is spent. In consequence, large-scale problems can be handled more efficiently.     

Computation of probabilistic linear programming problems involving normal and log-normal random variables with a joint constraint

A method for solving single- and multi-objective probabilistic linear programming problems with a joint constraint is presented. It is assumed that the parameters in the probabilistic linear programming problems are random variables, and the probabilistic problem is converted to an equivalent deterministic mathematical programming problem. In this paper the parameters are generally considered as normal and log-normal random variables. A non-linear programming method is used to solve the single-objective deterministic problem, and a fuzzy programming method is used to solve the multi-objective deterministic problem. Finally, a numerical example is presented to illustrate the methodology.     

基于Matlab的线性规划问题求解

线性规划是运筹学中研究较早、发展较快、应用广泛、方法成熟的一个重要分支,它是辅助人们进行科学管理的一种重要的数学方法.文章首先介绍了线性规划的基本概念及标准形式,着重讨论了线性规划问题的三种常用解法:单纯形法、直接搜索法以及遗传算法,最后在Matlab R2009a环境下进行了仿真.通过结果可以看出,用Matlab求解线性规划问题,可以避免手工的烦琐计算,大大地提高工作效率和结果的准确性.