关键词： Supply chain scheduling   Non-dominated sorting genetic algorithm   Multi-objective particle swarm optimization   Transportation modes  

摘要： In this study, a bi-objective optimization problem for a supply chain with different transportation modes is addressed. The first objective function is minimizing costs imposed by production, batching, due date assignment and transportation. The second one is minimizing inventory and tardiness costs. Also, a heuristic rule is developed to choose non-dominated transportation modes. Three metaheuristic algorithms including multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm (NSGA-II) and hybrid NSGA-II (HNSGA-II) are customized to solve the problem. In addition, a theoretical improvement in the non-dominated sorting procedure called improved efficient non-dominated sorting (IENS) is proposed. Computational tests are used for comparing and evaluating the proposed methods and algorithms. The results show that IENS reduces running time compared to the modern method of non-dominated sorting, the efficient non-dominated sorting method, and this reduction is statistically significant. Also, the HNSGA-II has an average but robust performance compared to the other two algorithms.

关键词： Lexicographic bottleneck   Assembly line balancing   Mixed-model lines   Mathematical model   Artificial bee colony algorithm  

摘要： Typically, the total number of required workstations are minimised for a given cycle time (this problem is referred to as type-1), or cycle time is minimised for a given number of workstations (this problem is referred to as type-2) in traditional balancing of assembly lines. However, variation in workload distributions of workstations is an important indicator of the quality of the obtained line balance. This needs to be taken into account to improve the reliability of an assembly line against unforeseeable circumstances, such as breakdowns or other failures. For this aim, a new problem, called lexicographic bottleneck mixed-model assembly line balancing problem (LB-MALBP), is presented and formalised. The lexicographic bottleneck objective, which was recently proposed for the simple single-model assembly line system in the literature, is considered for a mixed-model assembly line system. The mathematical model of the LB-MALBP is developed for the first time in the literature and coded in GAMS solver, and optimal solutions are presented for some small scale test problems available in the literature. As it is not possible to get optimal solutions for the large-scale instances, an artificial bee colony algorithm is also implemented for the solution of the LB-MALBP. The solution procedures of the algorithm are explored illustratively. The performance of the algorithm is also assessed using derived well-known test problems in this domain and promising results are observed in reasonable CPU times.

关键词： Welding   Scheduling   Discrete artificial bee colony algorithm   Welding shop scheduling  

摘要： The welding process which is one of the most important assembly processes is widespread in the modern manufacturing industry, including aerospace, automotive and engineering machinery. The welding shop scheduling greatly impacts the efficiency of whole production system. However, few studies on the welding shop scheduling problem (WSSP) were reported. In this paper, a mathematical model and an improved discrete artificial bee colony algorithm (DABC) are proposed for the WSSP. Firstly, it is defined where multi-machine can process one job at the same time in the WSSP. Secondly, the mathematical models of WSSP have been constructed. Thirdly, an effective DABC is proposed to solve the WSSP, considering job permutation and machine allocation simultaneously. To improve the performance of proposed DABC algorithm, the effective operators have been designed. Three instances with different scales are used to evaluate the effectiveness of proposed algorithm. The comparisons with other two algorithms including genetic algorithm and grey wolf optimizer are also provided. Experimental results show that the proposed model and algorithm achieve good performance. Finally, the proposed model and DABC algorithm are applied in a real-world girder welding shop from a crane company in China. The results show that proposed model and algorithm reduces 55.17% production time comparing with the traditional algorithm and the scheduled machine allocation provides more reasonable arrangements for workers and machine loads.

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： 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.