椭球体易拉罐形状和尺寸的优化设计模型

从材料最省、外观最美、放置稳定的角度设计了"椭球体"易拉罐的形状,然后通过建立非线性规划模型Ⅰ,求出了"椭球体"易拉罐的中腰半径、底面半径和高度.然后从手感舒适的角度建立了优化模型Ⅱ,从而确定了两种型号的"椭球体"易拉罐的最优尺寸.     

易拉罐的优化设计

本文讲述了"易拉罐形状和尺寸的最优设计"问题的命题、建模和求解,评述了学生递交的论文中的优缺点,提出了若干建议.     

功能梯度空心及实心圆柱体旋转时的弹性及粘弹性解

逐步分析了旋转的功能梯度空心及实心长圆柱体问题的解.假设圆柱体的弹性模量和材料密度沿径向呈指数变化,Poisson比为常数.由平衡方程、相容方程、弹性变形理论及应力-应变关系,导出了统一的控制方程.根据超几何函数,求解该二阶微分控制方程,得到旋转功能梯度圆柱体的弹性变形.检验并讨论了圆柱体中的应力与非均质参数、几何、边界条件之间的相互关系.将旋转功能梯度空心及实心圆柱体的分析结果,与旋转均质各向同性圆柱体的结果进行了对比分析.同时,提出了旋转粘弹性圆柱体的粘弹性解,并验证了空心及实心圆柱体中应力与时间参数间的依赖关系.     

易拉罐的设计方案

在日常生活中,我们总会买些易拉罐装的饮料或食品.殊不知,这易拉罐的设计便包含了一定的数学道理. 对易拉罐的设计,经营者总是考虑让成本最低.如:设计一个体积固定为V的圆柱形易拉罐,什么样的设计方案最优? 要比较易拉罐优劣的标准,有下面两种不同的标准进行考虑. 第一种标准:根据制造过程中消耗铁皮的多少来判别优劣,即最优易拉罐应该具有的最小表面S. 分析设易拉罐的高为h,底面半径为r.由圆柱的体积公式V=πr2h,得h=V/πr2.又易拉罐的表面积S=2πr2 2πrh ①     

易拉罐形状和尺寸的最优设计

从用料最省的角度研究了易拉罐的形状和尺寸的优化设计问题,首先通过多次测量取平均值的方法得到了题目所需的数据．然后就问题二和问题三分别建立了优化模型,并借助数学软件进行了求解,得到了最优设计的尺寸．最后设计出了椭球形状的易拉罐作为自己的最优设计．     

无限圆柱体旋转运动时的热应力

研究旋转对确定边界条件下无限圆柱体的影响.当热荷载沿径向作用时,给出了旋转圆柱体中热应力、位移和温度的分析过程.当无限弹性圆柱体部分弯曲界面有常温作用,而其余界面维持零温度时,讨论其热动应力的分布.圆柱体表面绝缘材料熔化时出现这种情况.得到了应力分量、位移分量和温度的解和数值结果.提出的半解析法所得到的结果,与早期采用方法所得到的结果比较,发现两者显示出很好的一致性.     

易拉罐形状和尺寸的最优设计

研究易拉罐形状及尺寸的最优设计分析问题.首先,根据实际测量的数据,利用拉格朗日乘子法,验证了市售易拉罐设计尺寸的合理性与实用性.其次,给出了个性化的创新型美观设计方案,力求以节约材料和使用方面的优势征服厂家和消费者.最后,利用辛普生公式近似算法,得到了新造型设计的具体尺寸.     

功能梯度压电圆柱体的旋转分析及其应用——内压和热荷载作用下的力学传感器

对旋转的功能梯度压电(FGP)圆柱体,进行了精确的热弹性分析．圆柱体同时承受电、热和力学荷载的作用,这是一个旋转传感器或者调节器的简化模型．应用能量法得到系统的控制微分方程．为了正确地评估能量函数,引进了一个被称为“附加能量”的新项．在两种边界条件下:自由旋转的圆柱体和受内压作用的圆柱体,求解所得到的控制方程．研究角速度对各个物理量沿半径分布的影响．所研究的结构也可以认为是,在压力及热荷载作用下,测量圆柱体角速度的一个传感器．结果表明,电势与角速度成正比例关系．     

饮料罐尺寸的最优解证明及其优化设计

为了发掘节省原料的潜力,对销量很大的饮料易拉罐进行优化设计.建立起具有通用性的优化模型;运用压缩变量技术,解决了模型复杂不易求解的困难;给出了便于实施计算的一整套显式求解公式.通过方向导数分析和流动极值分析,证明了解的最优性,指出了目标函数的退化特征及其临界状态;结合数学理论分析、具体数值计算和实际工艺条件,形成了层层递进式的优化设计途径.     

基于非傅里叶的有限空圆柱体的温度场解析解及其在谐波均匀的圆柱体上的应用

在有限空圆柱体的热冲击问题中引进非傅里叶分析,考虑了在极端热传递条件下的非稳态热传递过程中热量传播速度的有限性,建立了有限空圆柱体的轴对称非傅里叶温度场的数学模型,利用分离变量法和杜哈尔积分求得有限空圆柱体双曲型热传导问题的精确解析解.并将结果应用于外表面是谐波均匀的热通量的有限空圆柱体,得到其瞬态温度场及其径向、轴向温度分布规律.     

Preference modelling by estimating local utility functions for multiobjective optimization

This paper is intended to design goal programming models for capturing the decision maker's (DM's) preference information and for supporting the search for the best compromise solutions in multiobjective optimization. At first, a linear goal programming model is built to estimate piecewise linear local utility functions based on pairwise comparisons of efficient solutions as well as objectives. The interactive step trade-off method (ISTM) is employed to generate a typical subset of efficient solutions of a multiobjective problem. Another general goal programming model is then constructed to embed the estimated utility functions in the original multiobjective problem for utility optimization using ordinary nonlinear programming algorithms. This technique, consisting of the ISTM method and the newly investigated search process, facilitates the identification and elimination of possible inconsistent information which may exist in the DM's preferences. It also provides various ways to carry out post-optimality analysis to test the robustness of the obtained best solutions. A modified nonlinear multiobjective management problem is taken as example to demonstrate the technique.     

一个新的解线性规划的神经网络

本文提出一个新的解线性规划的Hopfields-型网络。该网络基于线性规划的对偶理论,并使用了Sigmoid函数,但不需要预先给定的罚参数和乘法模拟器,我们证明该网络不仅全局收敛到线性规划的精确解,而且能同时解原规划和对偶规划。由于在该网络中没有使用乘法模拟器而利用了Sigmoid函数,因此该模型是很容易用硬件实现的。     

输油管道的布置

本文建立了非线性规划模型,解决了输油管线布置问题,并给出了输油管线铺设的最佳方案.     

Design of electronic assembly lines: An analytical framework and its application

The design of component assembly lines in Printed Circuit Board (PCB) manufacturing environments is a challenging problem faced by many firms in the electronics industry. The main design approaches to such component assembly lines are the Mini-Line, Flexible Flow Line, and Hybrid Line designs. In this paper, we discuss the operational trade-offs associated with these design alternatives and present a mathematical programming framework that captures relevant system design issues. Each of the design alternatives can be viewed as a special case of the stated mathematical programming model. We develop effective algorithms to solve these mathematical programs. We have used the framework in a specific PCB manufacturing environment to advise managers on the best configuration of their lines. The models were used as sensitivity analysis tools. The results of our computational experiments, combined with qualitative comparisons of different design approaches developed by a crossfunctional team (engineers, manufacturing and product managers), have led to the development of a set of managerial guidelines for the selection of the design plan for component assembly lines in the studied environment.     

An Integrated Plant Design and Scheduling Problem in the Food Industry

An integrated plant design and scheduling problem in the food industry is discussed, and a solution is proposed. This involves the use of two models. The first model is an integer programming model that deals with long-term decisions. The second model deals with decisions that have to be made instantly.     

Diverse Imprecise Goal Programming Model Formulations

The goal programming (GP) model is probably the best known in mathematical programming with multiple objectives. Available in various versions, GP is one of the most powerful multiple objective methods which has been applied in much varied fields. It has also been the target of many criticisms among which are those related to the difficulty of determining precisely the goal values as well as those concerning the decision-maker's near absence in this modelling process. In this paper, we will use the concept of indifference thresholds for modelling the imprecision related to the goal values. Many classical imprecise and fuzzy GP model formulations can be considered as a particular case of the proposed formulation.     

A Multi-criteria Approach to Formulating International Project-financing Strategies

Despite their commercial feasibility, many international projects have failed primarily because of poor financial planning. When formulating a project-financing strategy, financial managers of multinational corporations must consider a variety of conflicting objectives. The existence of conflicting goals makes the design of international project-financing strategies very difficult. A goal programming model is presented as an aid to financial managers for analysing trade-offs among conflicting financing goals and identifying the best multi-source financing package for major international projects.     

An Algorithm of Gas Turbine Components in Aircraft

This paper presents a case study of mathematical modelling,algorithm design,and computer implementation for a decisionproblem arising in the assembly of gas turbine engines for jetaircraft. Turbine assembly involves the bolting together ofa series of cylindrical components; each component may be positionedin one of 16 orientations relative to its neighbours. Owingto manufacturing imperfections, the cylinder faces may be slightlyskewed and the h l t holes located slightly offcentre. The problemis to find the set of orientations which minimizes the deviationof the individual cylinder axes from the bearing axis of thewhole turbine. Standard results of coordinate geometry are usedto formulate the problem as one in nonlinear integer programming,and a search algorithm based on the branch-and-bound techniqueis proposed. It is shown how the calculations may be simplifiedby ignoring second-order terms, and results, including computerrun-times, are given for sample problems.     

Solution approaches for the soft drink integrated production lot sizing and scheduling problem

In this paper we present a mixed integer programming model that integrates production lot sizing and scheduling decisions of beverage plants with sequence-dependent setup costs and times. The model considers that the industrial process produces soft drink bottles in different flavours and sizes, and it is carried out in two production stages: liquid preparation (stage I) and bottling (stage II). The model also takes into account that the production bottleneck may alternate between stages I and II, and a synchronisation of the production between these stages is required. A relaxation approach and several strategies of the relax-and-fix heuristic are proposed to solve the model. Computational tests with instances generated based on real data from a Brazilian soft drink plant are also presented. The results show that the solution approaches are capable of producing better solutions than those used by the company.     

Multi-objective stochastic programming for portfolio selection

Generally, in the portfolio selection problem the Decision Maker (DM) considers simultaneously conflicting objectives such as rate of return, liquidity and risk. Multi-objective programming techniques such as goal programming (GP) and compromise programming (CP) are used to choose the portfolio best satisfying the DM’s aspirations and preferences. In this article, we assume that the parameters associated with the objectives are random and normally distributed. We propose a chance constrained compromise programming model (CCCP) as a deterministic transformation to multi-objective stochastic programming portfolio model. CCCP is based on CP and chance constrained programming (CCP) models. The proposed program is illustrated by means of a portfolio selection problem from the Tunisian stock exchange market.