多指标动态规划

本文在相当广泛前提下,证明了动态系统多指标最优化问题的有效解具有某种连锁性质,并导出了多指标动态规划基本方程,这是通常意义下动态规划基本方程的推广.相应地,也推广了动态规划最优化原理.在这基础上,建立了某种广义的动态系统最优化模型以及相应的广义动态规划基本方程.     

管理科学中的一个数学方法

功态规划是管理科学中的一个数学方法。本文首先应用动态规划的最优性原理来求解一类特殊结构的函数的最小值,从而研究了动态规划求解这类函数优化问题所具有的基本特点。其次又推导了一类多阶最优决策问题的递推基本方程,最后还简要引进一个微分动态规划并与动态规划作了相应的比较。     

二维动态规划模型及其在陕西省七·五技改规划中的应用

在—般情况下,动态规划的阶段变量是一维的。但在实际工作中存在一类多阶段决策问题,由于这类问题的约束条件较多,造成状态变量的转移方向比较复杂,因而无法用一维动态规划模型求解。本文将动态规划数学模型中的阶段变量扩展到二维,通过建立二维动态规划模型对以上问题进行了研究。并且应用所建立的模型求解了一个实际的资源分配问题。     

动态规划中的最优性原理及方法的进一步研究

本在对求解多阶段决策问题的动志规划的基本理论，最优性原理进行严格证明的同时还通过实例介绍了动态规划的基本方法一逆序递推法的具体应用。     

集值状态的动态规划

本文的目的是建立一个一般集上的动态规划模型,并给出它的存在性的证明,随着抽象分析的进展,抽象状态空间的动态规划不断有人涉及(例如[1]—[3]),本文的结果是在较弱的条件下给出的,本文使用的术语与未给证明的结果均来自[4]。     

GM(1,1)模型在粮食产量预测中的应用

本文根据灰色系统理论，利用安徽省１９８８—１９９５年粮食产量资料，运用ＧＭ（１，１）灰色预测模型方法，对“九五”期间安徽省粮食产量进行动态预测，为实现“九五”规划中的粮食产量提供科学的理论依据．     

混合动力公交车能量控制策略的优化模型

针对混合动力公交车在循环工况内功率需求的特点,建立了未来功率需求贝叶斯预测模型;利用2-阶段随机动态规划模型将大规模的随机动态规划问题简化为多个小规模的随机动态规划问题和一个确定型动态规划问题;对于随机动态规划模型的求解,给出了稀疏表示的降维方法,将复杂的泛函极值问题转化为常规的随机动态优化问题,并采用分布估计算法和计算资源最优配置算法的计算机仿真优化算法对随机动态优化问题进行求解;给出了基于查表的在线控制策略,为模型的实际应用进行了有益的探索。     

考虑时间效应的机器负荷分配模型

机器人高低负荷分配问题是动态规划的应用之一，但该问题的动态规划模型一般都没有考虑资金，产值的时间价值效应，本在机器负荷分配的原动态规划模型基础之上，加入了时间因索，建立了考虑时间效应的机器高低负荷分配的动态规划模型，从而扩大了原模型的适应范围。     

连续型凸动态规划的离散近似迭代法研究

为解决连续型凸动态规划的“维数灾”问题,提出了一种新的算法—离散近似迭代法.该算法的基本思路为:首先,将连续型状态变量离散化,根据网络图的构造方法将动态规划问题转化为多阶段有向赋权图;其次,运用极大代数求出起点至终点的最短路,即获得模型的一个可行解;最后,以该可行解为基础,继续迭代直到前后两个可行解非常接近.文章还证明了该算法的收敛性和线性收敛,并以一个具体例子验证了算法的有效性.     

动态规划的单增量搜索算法

本文首先对现有的三种动态规划迭代算法：微分动态规划、渐进优化算法、状态增量动态规划作了简单评述。针对如何进一步减少计算工作量和加快收敛速度，提出单增量搜索算法。通过理论阐述和实例分析，说明这种新的迭代算法优于上述三种常用方法。最后，本文把这种方法推广到连续型动态规划问题。     

Normal subsystems of fusion systems

The notion of a fusion system was first defined and exploredby Puig in the context of modular representation theory. Later,Broto, Levi, and Oliver significantly extended the theory offusion systems as a tool in homotopy theory. In this paper webegin a program to establish a local theory of fusion systemssimilar to the local theory of finite groups. In particular,we define the notion of a normal subsystem of a saturated fusionsystem, and prove some basic results about normal subsystemsand factor systems.     

Computer system for kinematic and dynamic analysis synthesis of rigid and flexible multibody systems

In the paper an overview of a general numerical algorithm and program system library for deriving the kinematic constraint equations and dynamic equations of motion, as well as, computation of their first and second order partial derivatives with respect to kinematic parameters of motion, design parameters and mass and inertia characteristics for rigid and flexible multibody systems is presented. These are the main basic computational modules for implementation of kinematic and dynamic synthesis, optimization and design. The main theoretical basis consists in matrix methods for deriving the kinematic constraints and dynamic equations, as well as, the generalized Newton – Euler dynamic equations for rigid and flexible bodies, and finite element discretization in relative coordinates. Block–scheme of the computational procedures and problem oriented program compilation is presented. An example of kinematic synthesis of six–link path generating mechanism with singular points is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A hierarchy of relaxations for nonlinear convex generalized disjunctive programming

We propose a framework to generate alternative mixed-integer nonlinear programming formulations for disjunctive convex programs that lead to stronger relaxations. We extend the concept of “basic steps” defined for disjunctive linear programs to the nonlinear case. A basic step is an operation that takes a disjunctive set to another with fewer number of conjuncts. We show that the strength of the relaxations increases as the number of conjuncts decreases, leading to a hierarchy of relaxations. We prove that the tightest of these relaxations, allows in theory the solution of the disjunctive convex program as a nonlinear programming problem. We present a methodology to guide the generation of strong relaxations without incurring an exponential increase of the size of the reformulated mixed-integer program. Finally, we apply the theory developed to improve the computational efficiency of solution methods for nonlinear convex generalized disjunctive programs (GDP). This methodology is validated through a set of numerical examples.     

Research on closed-loop supply chain coordination control model based on difference equation load model

ABSTRACT

This paper systematically summarizes the basic theory of closed-loop supply chain, expounds the difference equation model and the parameter dispersion of differential equation load model, and uses the difference equation to describe the dynamic model based on closed-loop supply chain network. Then the dynamic model of closed-loop supply chain network is established, and the basic theory of model predictive control is expounded. Finally, an inventory balance state space model is established for a closed-loop supply chain considering recycling centre, and a case study is carried out. Get the performance curve of production and inventory. Through the model predictive control method, it is proved that in the case of control variable production/order, the whole system is gradually stable, and when the stock level is controlled at a certain position, the cost can be reduced.     

Nonstandard tools of nonsmooth analysis

This is an overview of the basic tools of nonsmooth analysis which are grounded on nonstandard models of set theory. By way of illustration we give a criterion for an infinitesimally optimal path of a general discrete dynamic system.     

粘性流体两相多孔介质非线性动力问题的罚有限元法

采用基于混合物理论的多孔介质模型,给出粘性流体饱和两相多孔介质非线性动力问题的控制场方程以及相应边值和初值问题的提法,用Galerkin加权残值法导出罚有限元公式,并给出该非线性方程组的迭代求解方法。考虑了体积分数和渗透率与变形相关的情况。用编制的有限元程序计算分析了一维多孔柱体在脉冲载荷作用下的瞬态响应,数值结果表明文中方法正确有效。     

Symbolic computation of normal form for Hopf bifurcation in a retarded functional differential equation with unknown parameters

Based on the normal form theory for retarded functional differential equations by Faria and Magalhães, a symbolic computation scheme together with the Maple program implementation is developed to compute the normal form of a Hopf bifurcation for retarded functional differential equations with unknown parameters. Not operating as the usual way of computing the center manifold first and normal form later, the scheme features computing them simultaneously. Great efforts are made to package this task into one Maple program with an input interface provided for defining different systems. The applicability of the Maple program is demonstrated via three kinds of delayed dynamic systems such as a delayed Liénard equation, a simplified drilling model and a delayed three-neuron model. The effectiveness of Maple program is also validated through the numerical simulations of those three systems.     

A NEW LOOK AT WHOLE-FOREST MODELING

The harvest scheduling problem customarily known as Model II can be reformulated using a dynamic equation, and solved in two ways using linear programming. Viewing the problem in this way offers many insights and is convenient for deriving extensions to the basic problem. Extensions include the risk of catastrophic loss through fire, the problem of a changing land base, and the imposition of area constraints on the forest. An economic interpretation of certain dual variables in one of the solution methods is given. The mathematical equivalence of the standard Model II linear program, and the dynamic equation formulation, is demonstrated and the numerical efficiency of the various methods is examined for simple problems.     

JavaStat: a Java/R-based statistical computing environment

Architectures are described which allow a Java-based front-end to run R code on a server. The front-end described here is a Java application called JavaStat (). JavaStat is a highly-interactive program for data analysis and dynamic visualization with data management capabilities. The objective is to bring the high-level functions of R to JavaStat, without excessive duplicative development work. Results returned from R are wrapped and then displayed using linked, dynamic plots in JavaStat. The principal idea is to use Remote Method Invocation to communicate with a Java server program (JRIServer), which in turn communicates with R using Java/R Interface (JRI). Two versions have been implemented. The first (basic) architecture maintains a connection between the client and server in order to return the results from R. This is suitable for small to moderate data sets in which relatively simple models are run. The second (enhanced) architecture queues the requests and uses polling to fetch the results. It is suitable for large data sets and complex models, e.g., those encountered in genomic studies. JavaStat supports the basic architecture out of the box, but a user account is required to enable the enhanced architectures. The enhanced architecture supports workflows, e.g., genomic and modeling workflows.