关键词： 数学算法   计算机编程   编程优化  

摘要： 数学算法是计算机编程优化的基础,利用数学思维,可以提高编程效率及程序运行效率。文章首先对数学算法与计算机编程的关系进行分析,进而探讨数学算法在计算机编程优化中的作用,包括优化编程逻辑机构、数据结构、计算机编程语言等,以期为相关编程优化活动提供参考。

关键词： Variable message sign problem   Genetic algorithm   Self-adaption   Mathematical model   Vehicle routing   Pick-up/drop-off  

摘要： The Variable Message Sign Problem (VMSP) aims to optimise the delivery, collection and maintenance of Variable Message Signs. Firstly, the problem was formulated as a rigorous mathematical model. It was then reformulated using a permutation representation removing the need for some hard constraints and the formation of illegal sub-tours within the solution. The reformulated model was shown to be solvable using different artificial intelligence search techniques. The problem of parameter selection was then solved using self-adaption, which produced superior solutions with > 99.9% confidence by avoiding numerous local optima on the fitness landscape. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Lot sizing   Scheduling   Flexible flow shop   Mathematical models   Fruit fly algorithm  

摘要： This paper considers the lot scheduling problem in the flexible flow shop with limited intermediate buffers to minimize total cost which includes the inventory holding and setup costs. The single available mathematical model by Akrami et al. (2006) for this problem suffers from not only being non-linear but also high size-complexity. In this paper, two new mixed integer linear programming models are developed for the problem. Moreover, a fruit fly optimization algorithm is developed to effectively solve the large problems. For model's evaluation, this paper experimentally compares the proposed models with the available model. Moreover, the proposed algorithm is also evaluated by comparing with two well-known algorithms (tabu search and genetic algorithm) in the literature and adaption of three recent algorithms for the flexible flow shop problem. All the results and analyses show the high performance of the proposed mathematical models as well as fruit fly optimization algorithm. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Forward displacement analysis   Parallel mechanism   Conformal geometric algebra   Geometrical intuition   Closed-form solutions  

摘要： This paper presents an efficient graphical representation geometric algebra approach for the forward displacement analysis (FDA) of 3-PPS parallel mechanisms (PMs). Our approach based on conformal geometric algebra (CGA) reveals interesting intuitions and insight of the modelling and solution for FDA of this type PMs and reduces considerably computational burden and time. In this work, we first deduce the position of an arbitrary joint among three spherical joints on the moving platform through motors and represent it in terms of only one variable. Then, we formulate the position of either one joint of two remained spherical joints using the intersection of a sphere and two planes under the CGA framework. To obtain the geometric formulation of the third spherical joint position, we construct the outer product of two spatial balls with centers at two formulated spherical joints centers and two known planes. The positions of three spherical joints are all explicit geometric formulations of geometric entities of the parallel mechanisms. We achieve a coordinate-invariant equation expressed in terms of geometric entities via inner product of the last joint by itself. The symbolic 8th-degree univariate polynomial input-output equation is first proposed and all 8 sets of closed-form solutions can be obtained. The algorithm is the geometric algebra computation in a clear and coordinates-free way that avoids the use of rotation matrices, and complex algebraic modelling and nonlinear and multivariable elimination computations as most current approaches do. Finally, two numerical examples have been applied to demonstrate the efficiency of the algorithm comparing with the Dixon resultant method. The results show that this algorithm can simplify complexity of the problem and reduce computation time dramatically with strong geometrical intuition. The achieved symbolic univariate polynomial input-output equation can be applied directly to solve the DPA for all types of 3-PPS PMs i

关键词： 数学建模   智能算法   教学方法  

摘要： 优化数学模型在数学模型中具有重要地位,智能优化算法作为求解优化模型的常用方法,具有求解能力强,算法设计简单,易于实现等特点.但是学生在利用智能优化算法求解优化模型时往往会遇到很多困难.从教学内容中算法选择要有重点,教学设计要注重学生实际,教学手段要灵活多样3个方面探讨数学建模中智能优化算法的教学方法,对提高教学效果有一定的帮助.

关键词： ID3   Python   决策树   学生选拔  

摘要： 我国高等教育中,组织和参加学科竞赛是一种快速提高学生科研素养的途径。针对在高校中学科竞赛等选拔流程人工筛选周期长、工作主观性强、不利于公平性实现等问题,提出决策树方法。选用数学建模竞赛选拔学生的历史信息,使用适合离散数据运算、操作便捷的ID3决策树方法进行运算,训练出较为规范的决策树结果,最后验证准确性。此研究对相同类型的选择办法具有指导意义。

关键词： 儿童现实   儿童化   数学化   计算教学   知识建构   思维分析   算法建构  

摘要： 常态的计算教学课堂中所形成的算法,时常以教师“成人化”的认知经验和固有的计算法则直接替代学生的数学思考,抑制了学生“儿童化”思维探索算理的过程,忽略了“数学化”方法的自然建构,丧失了学生“算术”素养的培养和计算技能的形成。因此,数学课堂上“数学化”方法的形成,需要经历学生的“经验现实、认知现实、思维现实”等“儿童现实”的“儿童化”思维的过程,数学思考才能直接抵达学生的已有知识经验、思维起点以及动手操作等儿童认知。如此教学,学生的思维活动才能实现“数学化”的自然“蜕变”,数学知识才能真正实现从“儿童化”思维到“数学化”方法的自然建构。

关键词： 小学数学   简便算法   教学  

摘要： 《新课程标准》指出:“重视数与符号意义以及对数的感受,体会数字用来表示和交流的作用。通过探索丰富的问题情景发展运算的含义,在保持基本笔算训练的前提下,强调能够根据题目条件寻求合理、简捷的运算途径和运算方法,加强估算,引进计算器,鼓励算法多样化。”

关键词： 教学   学生   小学   数学   算法  

摘要： 教育实践小学数学算法教学不仅是培养学生数学能力,发展学生数学素养的必要条件,也是提升学生思维能力,促进学生个性发展的重要手段.因此,优化小学数学算法教学时,教师不妨通过创设情境、自主探究、问题推进等方法提升课堂学习趣味性,使算法教学不再是单纯的纸和笔的运算.