关键词： Interior-point algorithm   Sufficient linear complementarity problem   Algebraic equivalent transformation   Polynomial complexity  

摘要： We present a short-step interior-point algorithm (IPA) for sufficient linear complementarity problems (LCPs) based on a new search direction. An algebraic equivalent transformation (AET) is used on the centrality equation of the central path system and Newton's method is applied on this modified system. This technique was offered by Zsolt Darvay for linear optimization in 2002. Darvay first used the square root function as AET and in 2012 Darvay et al. applied this technique with an other transformation formed by the difference of the identity map and the square root function. We apply the AET technique with the new function to transform the central path equation of the sufficient LCPs. This technique leads to new search directions for the problem. We introduce an IPA with full Newton steps and prove that the iteration bound of the algorithm coincides with the best known one for sufficient LCPs. We present some numerical results to illustrate performance of the proposed IPA on two significantly different sets of test problems and compare it, with related, quite similar variants of IPAs.

关键词： Process planning   Mixed-integer linear programming model   Hybrid evolutionary algorithm   Benchmark  

摘要： Process planning is an essential part of the manufacturing system linking the designing and practical manufacturing. However, the reported process planning models are too simple to describe all characteristics because of the complexity of process planning. Therefore, a new mixed-integer linear programming (MILP) mathematical model is established based on OR-node of the network graph. In the model, the linear expression of the OR-node controlling function as well as three types of changing costs are first established. Beside, considering the OR-node selection state in the encoding and decoding method, a hybrid evolutionary algorithm (HEA) is designed to combine a genetic algorithm with a simulated annealing algorithm. The tournament selection method is adopted in the proposed HEA, and the discussion on the tournament size is conducted on the open problems to make the algorithm designing more reasonable and scientific. The HEA and the new MILP model are both tested on series of numerical experiments which are carried on the existing benchmarks as well as some randomly generated cases. The behavior of both two methods can verify their effectiveness and superiority successfully.

关键词： Engineering communication   pedagogy   teaching  

摘要： Most textbooks and trade press books on engineering communication are genre based, proscription based, or some are a combination of the two. Henderson takes a different approach to teaching the rules of English grammar and how to apply those rules to craft effective sentences. His approach is mathematics based, presenting the rules of English grammar as sentence equations. This approach makes the book particularly intriguing as a resource for teaching students of engineering and science. Henderson's "A Math-Based Writing System for Engineers: Sentence Algebra & Document Algorithms" presents a distinctive approach and methodology for clear engineering communication, particularly suited to its specific audience. Henderson's methodology, grounded in the "universal language" of mathematics, is unique and refreshing. The book is a welcome addition to available resources for these students and their instructors.

关键词： Distance metric learning   Classification   Mahalanobis distance   Dimensionality   Similarity  

摘要： Distance metric learning isa branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this topic and a comprehensive experimental analysis of the most-known algorithms. We start by describing the distance metric learning problem and its main mathematical foundations, divided into three main blocks: convex analysis, matrix analysis and information theory. Then, we will describe a representative set of the most popular distance metric learning methods used in classification. All the algorithms studied in this paper will be evaluated with exhaustive testing in order to analyze their capabilities in standard classification problems, particularly considering dimensionality reduction and kernelization. The results, verified by Bayesian statistical tests, highlight a set of outstanding algorithms. Finally, we will discuss several potential future prospects and challenges in this field. This tutorial will serve as a starting point in the domain of distance metric learning from both a theoretical and practical perspective. (c) 2020 Elsevier B.V. All rights reserved.

关键词： 铁路工程   箱梁预制   砂石料供应   运输方式   线性规划   合理运距  

摘要： 箱梁预制场的砂石料供应方案是箱梁预制的重要环节,合理的砂石料供应方案对降低工程建设项目的冗余成本具有重要意义。文章主要通过实际调查资料,分析了汽车运输和船舶运输砂石料的运距分界点,通过运筹学线性规划模型解决箱梁预制场的砂石料供应问题,并通过实际算例验证数学模型解决箱梁预制场碎石供应的可行性,对比供应方案和不同运输方式碎石供应的差异,便于施工管理企业进行箱梁预制场的当地料供应决策。

关键词： 模糊数学   非线性   二层规划问题   求解算法   寻优  

摘要： 为了提高非线性二层规划寻优和运筹能力,提出基于模糊数学的非线性二层规划问题求解算法。建立非线性二层规划的线性方程组,采用最大Lyapunov泛函方法进行非线性二层规划过程中的最优参数辨识,建立非线性二层规划寻优的自动搜索模型,通过建立非线性二层规划的双曲微分方程组,进行非线性二层规划的最优解向量分析,实现非线性二层规划优化。实验结果表明,采用该方法进行非线性二层规划的自适应性较好,收敛性和输出稳定性较好。

关键词： 量子计算机   超级计算机   科学术语   中国科学技术大学   数学算法   潘建伟   九章   计算能力  

摘要： 2020年12月4日,中国科学技术大学宣布该校潘建伟等人成功构建76个光子的量子计算原型机“九章”,求解数学算法高斯玻色取样只需200秒,而目前世界最快的超级计算机要用6亿年。这一突破使我国成为全球第二个实现“量子优越性”的国家。算力新离度技术三优势“量子优越性”是一个科学术语:作为新生事物的量子计算机,一旦在某个问题上的计算能力超过了最强的传统计算机,就证明了量子计算机的优越性,跨过了未来多方面超越传统计算机的门槛。

关键词： 数学模型   成本计算   路线规划   航线设计  

摘要： 在原有的船舶航线规划数学建模求解算法的使用过程中,其对航向目标函数构建能力较差,导致航向运行成本较高。因此,设计船舶航线规划数学建模及求解的人工智能算法。在航线规划数学模型构建前,需要对路线规划问题进行描述与假设,并设定合理的目标函数。根据此目标函数,选定线性函数作为蓝本,构建约束条件过滤器,同时使用此约束条件过滤器处理结果对可行航线展开分析,得到最优航线方案。构建仿真实验环节,通过与目前使用的求解方法对比可知,此算法的航线选择结果最佳,且成本最低。

关键词： 数学算法   计算机   程序设计与优化  

摘要： 本文讨论了计算机编程优化中各种数学算法在求解效果上存在的问题,并进一步强调了各种数学算法的精确度和它们对计算机编程优化的重要意义。伴随着现代社会的科技、信息技术以及电子计算机等新兴技术的发展,大多数计算机和计算机软件已经需要在开发过程中对计算机进行编程,正是因为“计算机编程”一词的出现,才促使计算机和计算机软件发挥其应有的作用。电脑程式设计的优劣直接影响到每一个软件功能的发挥,因此电脑程式设计工具需要不断地优化、改进,从而使电脑程式设计与软件设计的程序得到不断的优化、完善,从而提高电脑程式设计的效果。数学是伴随着人们走向近代的社会而产生的,有着悠久的历史。