关键词： Intermodal transportation   Pick-up routing with three-dimensional loading   Train loading   Heuristic approach   Mathematical model, Machine learning  

摘要： This paper presents a combinatorial problem called a pick-up routing problem with a three-dimensional (3D-PRP) loading constraint, clustered backhauls at the operational level, and train loading at the tactical level for an intermodal transportation network. A two-phase approach, called clustering first, packing-routing second, is proposed for use during the first stage. The clustering of backhauls is carried out using the k-means algorithm. A hybrid approach is provided, which combines the packing of orders by first solving a 3D loading problem for each cluster using machine learning with a best-fit-first strategy, with routing using a genetic algorithm. During the second stage, the train-loading problem is solved using a mixed integer programming approach to minimise the total costs by incorporating various cost types, in which detention and demurrage costs are taken into account. All solution approaches are computationally evaluated on real-world data provided by an international logistics firm and new randomly generated instances. Comparisons are carried out using both exact solution methods and heuristic approaches, and the proposed approach was shown to be more effective for real-world problems. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： 数学算法   计算机编程优化   相关思考  

摘要： 数学算法是一种数学领域非常精华的内容,也是在计算机领域比较基础的应用。数学算法可以将一些问题展开总结和归纳,从而进行统一数学计算,因此数学算法这种数学思想,对解决实际问题是有重要意义的。在编程领域,数学算法也是有非常重要的应用,对编程优化是有重要价值的。本文分析在编程优化方面对数学算法的实际应用,希望对数学算法在编程方面的发展是有促进作用的。

关键词： 小学数学   算法多样化   数学教学  

摘要： 随着国家教育制度不断改革,社会十分关注小学数学教育的发展。在此条件下,"算法多样化"的出现,使得小学数学教学的发展更加迅速。 “算法多样化”在小学数学教学中具有更为广阔的内涵,小学数学教师需了解“算法多样化”对于小学数学教学的重要意义,从而有效地开展数学教学活动。本文主要探究教师如何在小学数学教学中应用“算法多样化”,便于小学数学教师能够更好地展开教学工作,为其提供部分教学意见。

关键词： Speeded-Up robust features (SURF)   Interest points   Geometric algebra (GA)   Multispectral image  

摘要： Speeded-Up Robust Features (SURF) can be used for tasks such as object recognition, image registration, classification or 3D reconstruction. However, existing SURF algorithm cannot be directly applied to deal with multispectral images. In this paper, based on SURF and the theory of Geometric Algebra (GA), a novel feature extraction algorithm named GA-SURF is proposed for multispectral images. First, a Hessian matrix based on GA is calculated for locating interest points in spatial and spectral space. The box filters based on GA are used to simplify the calculation of Hessian matrix and generate image pyramids. Then, following the procedures of SURF, interest points are located by the image pyramids and described in GA space. Experimental results demonstrate that, compared with other feature extraction algorithms for multispectral images, GA-SURF can be computed much faster and are more robust and distinctive. (C) 2018 Elsevier B.V. All rights reserved.

关键词： 分数指数幂   同课异构   导入设计   备课组   运算法则   议课   教学思考   教学呈现  

摘要： 近日备课组开展了一次"同课异构"活动,课题是苏教版《高中数学》必修①"分数指数幂",笔者也有幸参与了评课议课活动,过后又查阅了与本课相关的文献,对于以下问题感触颇深:如何让数学问题的出现和解决更自然?如何使教学呈现的认知方式获得学生更多的认同?如何真正做到数学思想的渗透?本文笔者将结合执教教师的一些案例对比,从导入设计和分数指数幂意义探究方法的辨析谈谈对以上问题的一些个人想法,以供大家讨论参考.

关键词： 图像边缘检测   图像噪声   数学形态学   形态学滤波  

摘要： 边缘检测算法在图像识别领域具有不可替代的作用。边缘检测在实现的过程中需要考虑边界增强的效应,边缘检测算法的研究有着丰富的理论和经验。但是,图像压缩和图像识别中图像通常被噪声破坏,需优化处理,才能获取较好质量的图像。文中首先介绍了边缘检测算法,依次阐述这些经典算法的优缺点,引入数学形态学这一观点,对边缘检测算法进行结合,将其应用到图像的识别中,通过C++语言编程实现图像效果,最后进行总结与展望,该成果对于图像的处理具有积极的意义。

关键词： Manufacturing sector   organizational indicators   performance optimization   Data Envelopment Analysis (DEA)   Fuzzy DEA (FDEA)  

摘要： This study presents an integrated algorithm for the evaluation and optimization of manufacturing systems by considering managerial and organizational performance indicators. The proposed algorithm is composed of data envelopment analysis (DEA), fuzzy DEA and statistical methods. In order to achieve the goals of this study, a set of 12 criteria were chosen to indicate the application of the integrated method. The results showed DEA results have lower mean absolute percentage error (MAPE) than that of the fuzzy DEA. This study also analyzes and weights the indicators, and the results showed "research and development investment to production value" and "education and training investment per employee" indicators are the most effective indicators. This is the first study that introduces a unique algorithm for managerial and organizational factors. Second, it can handle data uncertainty due to existence of fuzzy mathematical programming in the algorithm. Third, weights of indicators are identified through robust statistical algorithm.

关键词： Spline   Welding procedure specification   Interpolation   Bead sequence   Piecewise cubic Hermite interpolation  

摘要： This study proposes an algorithm by using bead sequences and drawing techniques for multi-pass V-groove welding. Several points were prepared to form the weld bead shape. Then, a spline method called piecewise cubic Hermite interpolation was applied to describe the smooth curve shape of the multi-pass weld beads in Cartesian coordinates. This study simply considers the physical behavior of weld pool, such as surface tension, to describe the bead shapes differently along the layer position bead sequence. These techniques are useful to improve the welding procedure specification and thus reduce the time consumed in drawing the bead shapes to 1 s for thick-plate welding process.

关键词： Relation algebra   Prime fields   Representation  

摘要： A proper (simple) relation algebra is a collection A of binary relations on a set U such that the top element of the algebra is U x U, and A is closed under union, intersection, complementation, composition, converse and contains the identity relation on U. Proper relation algebras can be constructed using U = Z/pZ as a base set using a method due to Corner. The cycle structure of such an algebra must, in general, be determined a posteriori, normally with the aid of a computer. In this paper, we give an improved algorithm for checking the cycle structure that reduces the time complexity from O(p(2)) to O(p). (C) 2019 Elsevier B.V. All rights reserved.

关键词： walking workers   multi-manned   assembly line balancing   electromagnetic field optimisation  

摘要： Assembly lines are widely used in industrial environments that produce standardised products in high volumes. Multi-manned assembly line is a special version of them that allows simultaneous operation of more than one worker at the same workstation. These lines are widely used in large-sized product manufacturing since they have many advantages over the simple one. This article has dealt with multi-manned assembly line balancing problem with walking workers for minimising the number of workers and workstations as the first and second objectives, respectively. A linear mixed-integer programming formulation of the problem has been firstly addressed after the problem definition is given. Besides that, a metaheuristic based on electromagnetic field optimisation algorithm has been improved. In addition to the classical electromagnetic field optimisation algorithm, a regeneration strategy has been applied to enhance diversification. A particle swarm optimisation algorithm from assembly line balancing literature has been modified to compare with the proposed algorithm. A group of test instances from many precedence diagrams were generated for evaluating the performances of all solution methods. Deviations from lower bound values of the number of workers/workstations and the number of optimal solutions obtained by these methods are concerned as performance criteria. The results obtained by the proposed programming formulations have been also compared with the solutions obtained by the traditional mathematical model of the multi-manned assembly line. Through the experimental results, the performance of the metaheuristic has been found very satisfactory according to the number of obtained optimal solutions and deviations from lower bound values.