关键词： 信息安全数学基础   网络空间安全   教学改革   工程教育认证   新工科教育  

摘要： 针对目前信息安全数学基础课程教学存在的重理论、轻实践的问题,结合工程教育认证和新工科教学改革理念,梳理了信息安全数学基础的知识点和学习脉络,提出以算法为核心的信息安全数学基础教学新模式.通过分析RSA和ElGamal加密算法的实现,引出课程教学内容,并以数论和抽象代数中的相关算法为核心展开教学内容,设计了相应的实践教学环节和考核方式等,从而更好地实现了对专业毕业要求指标点达成的支撑.

关键词： Assembly lines   Rebalancing   Worker assignment   Variable task times   Metaheuristics  

摘要： In real life, some situations such as demand fluctuations, changes in product structure, and workstation failures affect the existing balance of assembly lines, resulting in the need for these lines to rebalance. In the assembly line rebalancing problem (ALRBP), it is assumed that the processing time of a task does not depend on the worker performing it. Nevertheless, in practice, the time each worker requires to execute a task varies owing to several reasons, including the experience, skill, and disability of some individuals. In this study, the assembly line worker assignment and rebalancing problem (ALWARBP), which considers task times diversify in terms of workers, is introduced to fill this gap. The ALWARBP consists of the reassignment of tasks and workers to non-disrupted workstations after disruptions occur due to breakdowns or shutdowns of workstations to minimize variability in terms of cycle time and workstation assignments of tasks relative to the initial line balance. The aims of this paper are to i) describe the ALWARBP, ii) develop a mixed-integer linear programming (MILP) model, and iii) propose an artificial bee colony (ABC) algorithm to tackle the considered problem. The numerical experiments have been designed and conducted using 120 problem instances. The experimental results indicate that both methods managed to obtain optimal solutions in small-sized instances. In large-sized test instances, the proposed ABC algorithm showed higher performance in terms of solution value and computation time.

关键词： 高中数学   算法教学   信息技术   结合  

摘要： 新课标的实施对原有的高中信息数学做出了部分调整,并且明确了高中数学课程的内容、性质、理念以及课程学 习目标。在新时代背景下,算法教学部分在高中课程中扮演着重要的角色,将数学算法教学与信息技术有效结 合,不仅可以唤起学生学习高中数学的热情,也能够提升高中数学水平。本文重点阐述促进高中数学算法教学与 信息技术有效结合教学实践的意义和价值,并根据目前存在的问题提出一些具体的策略。

关键词： 数学法则   数学概念   导数运算   教学设计与实践  

摘要： 长期以来,数学概念或法则教学常常存在重结果轻过程、重传递轻建构的问题.具体地,从知识本身角度来看,数学概念或法则常被看作是现存的、结果性的知识,学生所要掌握的只是数学概念或法则的内涵、表示等结果性的要素.也正因为如此,数学概念或法则课的教学中常会出现只有10分钟"玩概念",30分钟"练概念"的现象.

关键词： 飞蛾火焰优化算法   Tent混沌映射   维数学习   二次插值   K-means聚类  

摘要： 针对K-means算法对初始聚类中心敏感和容易陷入局部最优的问题,首先提出一种基于维数学习和二次插值的飞蛾火焰优化算法以提高基本算法的求解精度和收敛速度,即采用Tent混沌映射产生多样性较好的初始种群,增强算法的全局搜索能力;对火焰位置采用维数学习策略生成更优良的火焰来指导飞蛾寻优,以提高算法的搜索效率;把二次插值引入基本飞蛾火焰算法,每次迭代利用二次函数的极值点产生新的飞蛾个体,增强算法的局部开发能力,更好地平衡算法的探索与开发能力,从而改善了解的精度.选取CEC 2017测试函数进行数值实验测试所提算法的性能,并与5个先进的元启发式算法比较,结果表明:所提出的算法具有更高的求解精度和更强的鲁棒性.然后,将改进的飞蛾火焰算法用来优化聚类中心的位置,5个UCI数据集的实验结果表明改进的算法适用于求解K-means聚类问题,且取得了好的聚类效果.

关键词： 运算法则   演绎推理   程序化   创造性  

摘要： 运算法则是运算的依据,是推理的基础,是运算结果唯一性的保障.深刻理解数学运算法则,分析二项式定理的结构性证明思路和应用法则进行程序化解题以及平行向量基本定理及结论应用,促进学生数学思维能力发展.

关键词： Metaheuristic algorithms   Bayesian approach   Structural and mathematical optimization   problems  

摘要： Metaheuristic algorithms are general optimization techniques that demonstrate remarkable performance in solving different classes of optimization problems. However, equipping their stochastic search mechanisms with auxiliary logical strategies can still increase their search capability. Based on this fact, in the current study, the search performance of the Interactive Search Algorithm (ISA), as a metaheuristic search method, is improved by adding a new Bayesian regulator strategy to adjust its search behavior. In this regard, the search patterns of the ISA method are unified and classified according to the memory and learning concepts. Subsequently, during the optimization process, the developed Bayesian module dynamically regulates the ratio of the exploration and exploitation search behaviors by tuning the effect of memory concept. The recent technique is named Bayesian Interactive Search Algorithm (BISA), and its search performance tested on a suite of unconstraint mathematical functions and constrained engineering problems. Acquired outcomes indicate that the proposed BISA considerably speeds up the convergence rate, and improves the stability of the process as well as the accuracy of the solutions, for both engineering and mathematical problems.

关键词： Mathematical model   Protocols   Hilbert space   Distributed algorithms   Convex functions   Network topology   Topology   Asynchronous   distributed algorithm   linear algebraic equations   random graphs  

摘要： This article considers the problem of solving linear algebraic equations of the form Ax=b among multiagents, which seek a solution by using local information in presence of random communication topologies. The equation is solved by m agents where each agent only knows a subset of rows of the partitioned matrix [A,b]. The problem is formulated such that this formulation does not need the distribution of random interconnection graphs. Therefore, this framework includes asynchronous updates and/or unreliable communication protocols. The random Krasnoselskii-Mann iterative algorithm is applied that converges almost surely and in mean square to a solution of the problem for any matrices A and b and any initial conditions of agents' states. The algorithm is a totally asynchronous algorithm without requiring a priori B-connectivity and distribution dependency assumptions. The algorithm is able to solve the problem even if the weighted matrix of the graph is periodic and irreducible for synchronous protocol. It is demonstrated that the limit point to which the agents' states converge is determined by the unique solution of a convex optimization problem regardless of the distribution of random communication graphs. Finally, some numerical examples are given to show the results.