图的最大二等分问题的投影梯度算法

本文基于图的最大二等分问题已有的半定规划松弛模型,给出了原问题的等价模型及其新的半定规划松弛模型,利用投影梯度算法求解该半定规划松弛模型,最后使用随机扰动算法求得原问题的近似最优解。理论和数值试验表明该方法不仅可以在较高的精度下求解中小规模的图的最大二等分问题,而且特别适合求解大规模的图的最大二等分问题。     

非负权图的最大二等分问题的0.488算法

本文给出了非负权图的最大二等分问题的一种近似算法,并从理论上证明了这种算法是0.488近似算法.数值实验表明这种算法能得到图的最大二等分问题近似程度很高的次优解,是一种非常有效的算法.     

图的最大二等分问题的秩二松弛算法的改进

本文在吸取半定规划松弛和秩二松弛方法的优点,克服其缺点的基础上,针对模型目标函数非凸的特点,提出了图的最大二等分问题的秩二松弛模型。由于该模型变量的数目没有增加,因此该方法对求解大规模问题很有优势。数值实验表明,这种算法无论是与半定规划松弛还是原秩二松弛算法相比,在获得目标函数值相当的情况下,运行时间较短。     

拉压不同模量材料的参变量变分原理和有限元方法

对具有拉伸和压缩不同模量的材料,建立了平面静力问题的参变量变分原理.基于参变量变分原理,并结合有限元方法,将拉压不同模量平面问题转化为互补问题求解.经典的Lemke算法被用于求解此互补问题.该方法避免了应力状态的假设和刚度矩阵的更新,算法稳定,且收敛速度快.     

压电材料修正后的H-R混合变分原理及其层合板的精确法

将三维弹性体的Hellinger-Reissner(H-R)混合变分原理引入到具有机-电耦合效应的压电材料静力学问题中,建立了压电材料修正后的H-R混合变分原理,通过变分运算和分部积分得到了压电材料的状态向量方程.给出了四边简支的压电材料层合板静力学状态向量方程的精确求解方法,数值实例的结果证明了方法是正确性的.这里的理论和求解方法同样适应于纯弹性材料板和压电材料板混合的层合板静力学问题的分析.变分原理将有利于压电材料问题相应的半解析法或有限元法的推导.     

二等控温标准电池的测量不确定度

本文主要阐述了二等控温标准电池的测量不确定度的分折和计算 ,并给出了合成标准不确定度、扩展不确定度     

利用Excel实现对标准铂电阻温度计正温段分度表的计算

标准铂电阻温度计由于准确度高、性能稳定、使用方便,因此在对二等标准水银温度计的检定过程中,大有取代一等标准水银温度计的趋势.我国2003年新发布的JJG128-2003《二等标准水银温度计》检定规程直接说明了可以采用二等标准铂电阻温度计对二等标准水银温度计进行检定,使得SPRT的应用更加广泛.我们在送上级部门进行检定时,或者新购买的SPRT,往往只给出固定点电阻比和a8、b8的值,为了更好的解决测量中遇到的实际问题,我们分别用Visual Basic和Excel编制了计算方法,并与ITS1990温标进行了验证。     

代替二等标准水银温度计的数字温度计校准结果不确定度评定

二等标准水银温度计在中温测量中占据着重要的地位,由于国际上禁用水银的要求,研究数字温度计代替二等标准水银温度计作为中温测量的标准器变得尤为重要.本文通过对代替二等标准水银温度计的数字温度计校准过程中影响分量的分析,给出其校准结果的不确定度评定.     

基于哈密顿体系求解空间粘性流体问题

本文通过变分原理,将哈密顿体系引入到小雷诺数空间粘性流体问题中,导出一套哈密顿算子矩阵的本征函数向量展开求解问题的方法.基于直接法求解流体力学基本方程,通过求零本征解及其约当型,得到几种常见的基本流动;求解非零本征值及本征向量的叠加,继可分析流场端部效应.从而在该领域用哈密顿体系辛几何空间中研究问题的方法代替了传统在拉格朗日体系欧氏空间分析问题的方法.     

电路二等分问题的强化半定规划松弛

将表示电路的超图转化成带权值的无向图，从而将电路二等分问题转化成图的划分问题，图的划分问题存在已知的半定规划松弛，在此半定规划松弛基础上增加两个非线性结束，得到了强化半定规划松弛，定理和数值试验保证了强化半定规划松弛给出原问题一个更好的下界。     

求解二进制二次规划问题的一种连续化方法

本文提出了一种求解二进制二次规划问题的连续化方法。首先利用NCP函数方法,将二进制变量转化为等价的非光滑方程,再用凝聚函数法对其进行光滑化处理,从而把原来的组合优化问题转化成了一般的可微非线性规划问题。通过对一些标准考题进行计算,表明了该连续化方法的可行性、高效性以及稳定性。     

求解非线性系统的信赖域方法

本文给出了一个求解非线性系统的信赖域方法。通过引入松驰变量将非线性系统问题转化为带非负约束的非线性最优化问题,新算法借助于KKT条件和F-BNCP函数,在每次迭代时,不必求解二次信赖域子问题,只需求解一个线性方程组。在一定的假设条件下,该算法还是全局收敛和局部超线性收敛的。数值试验结果表明该算法是有效的。     

一类极大极小优化问题的信赖域算法

借助于K-T条件和NCP函数,提出了处理一类极大极小优化问题的信赖域算法。数值实验结果表明该方法足行之有效的。     

供应链中生产和运输协调调度问题初探

提出了解决供应链中生产和航空运输协调调度问题的理论框架.基于对生产调度和航空运输调度彼此制约关系的分析,协调调度问题被分解为两个子调度问题.建立了航空运输子调度问题的整数规划模型,并证明了该问题为NP完全问题.提出了基于倒排调度方法(backward scheduling method)的调度算法解单机生产调度子问题.     

An exact penalty function method for optimising QAP formulation in facility layout problem

A quadratic assignment problem (QAP), which is a combinatorial optimisation problem, is developed to model the problem of locating facilities with material flows between them. The aim of solving the QAP formulation for a facility layout problem (FLP) is to increase a system’s operating efficiency by reducing material handling costs, which can be measured by interdepartmental distances and flows. The QAP-formulated FLP can be viewed as a discrete optimisation problem, where the quadratic objective function is optimised with respect to discrete decision variables subject to linear equality constraints. The conventional approach for solving this discrete optimisation problem is to use the linearisation of the quadratic objective function whereby additional discrete variables and constraints are introduced. The adoption of the linearisation process can result in a significantly increased number of variables and constraints; solving the resulting problem can therefore be challenging. In this paper, a new approach is introduced to solve this discrete optimisation problem. First, the discrete optimisation problem is transformed into an equivalent nonlinear optimisation problem involving only continuous decision variables by introducing quadratic inequality constraints. The number of variables, however, remains the same as the original problem. Then, an exact penalty function method is applied to convert this transformed continuous optimisation problem into an unconstrained continuous optimisation problem. An improved backtracking search algorithm is then developed to solve the unconstrained optimisation problem. Numerical computation results demonstrate the effectiveness of the proposed new approach.     

A SINGULAR-ARC APPROXIMATION TO A DYNAMIC SAILPLANE FLIGHT PATH OPTIMIZATION PROBLEM

A dynamic sailplane performance problem is investigated using optimal control theory. The problem is to minimize the total flight time between successive thermals subject to zero altitude loss. From the original nonlinear optimal control problem, a singular linear/quadratic problem is derived and solved.

A relationship between the original optimal control problem and a certain parameter optimization problem is explored, and it is shown that the solution to this parameter optimization provides a lower bound for the minimum flight time of the original optimal control problem. The parameter optimization solution is adopted as the reference trajectory for the linear/quadratic problem. Finally, the linear/quadratic problem is shown to provide a good approximation to the original optimal control problem at a small fraction of the computing cost.     

Stress intensity solutions for the interaction between a hole edge crack and a line crack

The principle of superposition is used to solve the problem and the original problem is converted into two particular hole edge crack problems. The remote stresses are applied at infinity in the first problem. Meantime, a dislocation distribution is assumed outside the hole contour in the second problem. Singular integral equation is proposed for the solution of the second problem, in which the right hand side of the integral equation is obtained from the solution of the first problem. The first problem as well as the elementary solution of the second problem are solved by means of the rational mapping approach. Finally, numerical examples with the calculated results of stress intensity factors are presented.     

An improved approach for determination of index positions on CNC magazines with cutting tool duplications by integrating shortest path algorithm

Optimisation of automatic tool changer (ATC) indexing problem, where cutting tools are allocated to the stations on a turret magazine of a CNC machine, is one of the challenging problems in machining. The aim of the problem is to minimise the total indexing time of ATC. This problem becomes even more challenging if duplication of cutting tools is allowed and a bidirectional ATC is used. The problem has a unique feature which has not been stressed yet by other researchers, that is, although ATC indexing (master problem) is the main optimisation problem, objective function evaluation of this problem is a standalone optimisation problem (sub problem) indeed. Although an approximation algorithm does not guarantee optimality for the master problem, the subproblem must be solved optimally; otherwise, deficiencies arising from ill-defined objective function might be encountered. Considering this interesting future, a novel methodology, which employs a shortest path algorithm, is developed. Thus, the subproblem of this complicated problem can be optimally solved. Moreover, two metaheuristics, based on threshold accepting and descent first improvement greedy methodologies, are proposed for generating efficient solutions. Finally, several benchmarking instances are generated and solved to test the proposed algorithms.     

基于遗传算法的高校教室调度问题

对高校教室调度问题进行研究,能使教室和课程达到一种合理的优化配置。类似问题的研究在制造业或生产系统中都占有非常重要的地位。研究首先采用三元组方式,将教室调度问题描述为一类具有机器适用限制的并行多机问题,以最小化Cmax（即集中时间提高教室利用效率）和滞后时间总和为调度目标,建立了对应的数学模型。根据问题的特性,设计了包含分派规则和遗传算法的启发式调度算法求解该类问题。研究结合问题特性在编码,个体适应度函数,交叉及变异等方面进行了设计。以实例分析验证了所设计算法的可行性和有效性。