爬山算法构造小阶广义Howell设计

发布时间：2018-03-02 16:05

本文选题：爬山算法　切入点：广义Howell设计　出处：《北京交通大学》2017年硕士论文　论文类型：学位论文

【摘要】：广义Howell设计是组合设计理论的一个重要的研究方向,是一类双可分解的组合设计,广义Howell是编码理论中用到的重要工具之一,可以用来构造最优双常重码,多常重码等,并且可以用来构造置换阵列,进而用于构造置换码,在通信领域中有着重要的应用.爬山算法是一种局部择优的启发式随机搜索算法,是对深度优先搜索的一种改进,该算法每次从当前解的临近解空间中选择一个最优解作为当前解,直到达到一个局部最优解.爬山算法虽然有会陷入局部最优的缺陷,但是效率比较高,本文给出利用爬山算法构造小阶广义Howell设计的方法.本文分四个章节进行介绍:第一章,对爬山算法进行简单介绍,并综述了有关广义Howell设计的研究背景及研究现状,给出相关概念及符号表示,同时给出爬山算法在组合设计中的应用实例.第二章,详细介绍爬山算法在构造因子分解中的应用,广义Howell设计实际上是两个因子分解正交的结果,本节给出利用爬山算法构造两个正交的因子分解,进而构造出广义Howell设计,并给出利用该算法找到的广义Howell设计结果.第三章,对该算法在构造广义Howell设计的细节进行详细介绍及分析,并对算法进行优化.第四章,对本文的主要内容进行总结。
[Abstract]:Generalized Howell design is an important research direction of combinatorial design theory. It is a kind of bidecomposable combinatorial design. Generalized Howell is one of the important tools used in coding theory. And it can be used to construct permutation array and then to construct permutation code, which has important applications in the field of communication. Mountain climbing algorithm is a locally optimal heuristic random search algorithm, which is an improvement to depth first search. The algorithm selects an optimal solution as the current solution every time from the adjacent solution space of the current solution until a local optimal solution is reached. Although the mountain climbing algorithm has the defect of falling into the local optimum, it is more efficient. In this paper, a method of constructing small order generalized Howell design by using mountain climbing algorithm is presented. This paper is divided into four chapters: chapter 1, a brief introduction of mountain climbing algorithm, and a review of the research background and research status of generalized Howell design. The related concepts and symbolic representations are given, and the application examples of mountain climbing algorithm in combinatorial design are given. In chapter 2, the application of mountain climbing algorithm in constructing factorization is introduced in detail. The generalized Howell design is actually the result of orthogonal two factorizations. In this section, two orthogonal factorizations are constructed by using the mountain climbing algorithm, and then the generalized Howell design is constructed, and the result of the generalized Howell design obtained by the algorithm is given. This paper introduces and analyzes the details of the algorithm in constructing the generalized Howell design and optimizes the algorithm. Chapter 4th summarizes the main contents of this paper.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.2

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