将数学建模引入高等数学教学中的典型案例

首先阐述了将数学建模思想融入高等数学教学内容中的意义,接着从高等数学中的基本概念和基本定理出发,通过具体案例说明如何将数学建模案例融入在高等数学教学中。最后给出了根据高等数学内容选编的典型建模案例。     

不确定环境下的地震应急救援路径优化研究

针对地震应急救援的特点,引入不确定理论,在地震灾害的背景下,研究震后动态网络环境下的应急救援路径选择问题。用不确定变量表示网络中各路段的破坏程度,综合考虑路径破坏程度及车辆路径连续性等约束条件,以救援时间最短为目标,基于不确定理论建立了动态优化模型,并用改进的遗传算法求解,最后设计算例验证了模型和算法的有效性。     

中国货币国际化的趋势预测与人民币的范式选择

货币国际化是一个动态的历史过程。通过对其历史进程的考察,可以清晰地对未来货币国际化进程加以预测。文章认为,中国的人民币国际化进程刚刚起步,但却面临与以往世界货币迥异的道路、环境和结构,迫切需要走出一条符合中国国情的货币国际化道路。     

Searching for empirical linkages between demographic structure and economic growth

Demographic structure could affect economic growth through many channels. However, little is known about how demographic structure affects economic growth since no study has examined an extensive collection of channels through which demographic structure could affect economic growth in a single context. This paper overcomes this limitation by examining 45 potential mediating variables between demographic structure and economic growth. A causal search algorithm is used to identify channels through which demographic structure affects economic growth. Our results suggest that demographic structure affects economic growth differently between developed and developing countries. For developed countries, we find that an increase in the share of middle-aged workers has a positive effect on economic growth through institutions, investment and education channels. On the other hand, an increase in the share of the senior population has a negative effect on economic growth through institutions and investment channels. For developing countries, we find (but with weak evidence) that an increase in the share of young workers has a negative effect on economic growth through investment, financial market development and trade channels.     

Forecasting technology diffusion: a new generalisation of the logistic model

The present research proposes a new generalisation of the logistic model aiming at technology diffusion forecasting. Regarding criticisms and failures reported in the literature to apply logistic function for long-term forecasting, in our work we focused on short-term accuracy of forecast. To formulate the model, based on mathematical approximation, at first the differential equation governing the diffusion process is found and then by solving the derived differential equation, the forecast function is obtained. In all steps, mathematical tools from numerical analysis are used. We compared the New Generalized Logistic Model with eight of the most renowned models in the literature. The model led to more accurate fits and forecasts than those obtained from other models we applied for comparison.     

基于成本优化的制造业生产物流装配线排序问题分析

为了降低制造业的生产成本，提高收益，在分析生产物流配线闲置和超载成本的基础上，采用粒子群算法对其进行优化，并利用模糊自适应改进惯性权值，通过实证研究表明该方法实用，可操作性强，可以有效降低制造业生产物流成本，具有广泛的应用价值。     

Numerical Maximisation of Likelihood: A Neglected Alternative to EM?

There is by now a long tradition of using the EM algorithm to find maximum‐likelihood estimates (MLEs) when the data are incomplete in any of a wide range of ways, even when the observed‐data likelihood can easily be evaluated and numerical maximisation of that likelihood is available as a conceptually simple route to the MLEs. It is rare in the literature to see numerical maximisation employed if EM is possible. But with excellent general‐purpose numerical optimisers now available free, there is no longer any reason, as a matter of course, to avoid direct numerical maximisation of likelihood. In this tutorial, I present seven examples of models in which numerical maximisation of likelihood appears to have some advantages over the use of EM as a route to MLEs. The mathematical and coding effort is minimal, as there is no need to derive and code the E and M steps, only a likelihood evaluator. In all the examples, the unconstrained optimiser nlm available in R is used, and transformations are used to impose constraints on parameters. I suggest therefore that the following question be asked of proposed new applications of EM: Can the MLEs be found more simply and directly by using a general‐purpose numerical optimiser?     

The trade-off between fixed vehicle costs and time-dependent arrival penalties in a routing problem

This paper introduces the vehicle routing problem with soft time windows (VRPSTW) in which problem definition differs from ones previously defined in literature. Branch-and-price approach is employed, resulting in a set partitioning master problem and its new subproblem. Novel techniques are consequently developed to solve this new subproblem. Experimental results report the comparisons of these solution techniques under the branch-and-price framework. The VRPSTW solutions have further been compared to the state-of-the-art literature, signifying the superiority of the VRPSTW on this issue.     

基于遗传算法的锅炉水位控制器设计

文章分析了锅炉水位控制系统的基本原理及结构,针对传统PID控制器的不足之处设计了基于遗传算法的新型锅炉水位控制器,在此基础上搭建了锅炉水位控制系统。最后,通过仿真验证了该水位控制器在改善水位系统稳态误差及动态超调方面均具有较好的作用。     

单车场无时间窗甩挂运输车辆调度的启发式算法

考虑了牵引车空驶、带空挂车行驶和带重挂车行驶所引起的成本差异，定义了牵引车运行成本的概念，将总运行成本最小作为调度方案优劣的判别指标，并同时考虑牵引车数量最少。将牵引任务分为四种类型，定义了任务链、虚拟任务、链内交叉和链间交叉的概念，提出了一种求解该类单车场甩挂运输车辆调度无时间窗约束的启发式算法，包括初始调运方案、链内优化、空车调运交叉、牵引车数量优化和链间交叉。最后给出了仿真算例，算法优化后的最终方案与初始方案相比，牵引车数量减少，总运行成本降低，验证了算法的有效性和可行性。