应用数学硕士论文——关于全局优化理论算法优化的研究

发布时间:2012-03-08 09:02:31 论文编辑:代写作业经验总结

  应用数学硕士论文——全局优化理论几种算法的改进与研究
  
        目录:
  致谢 4-5
  摘要 5-6
  Abstract 6-7
  1绪论 11-18
  1.1课题的背景和意义 11-12
  1.2国内外研究现状 12-16
  1.3本文的主要工作 16-17
  1.4本文的组织 17-18
  2全局优化的基本理论 18-31
  2.1优化问题简介 18-19
  2.2优化模型的建立 19-20
  2.3优化问题的分类 20
  2.4凸集与凸函数 20-21
  2.5优化算法简介 21-27
  2.5.1优化算法的基本迭代 21-22
  2.5.2解决优化问题的基本算法 22-23
  2.5.3优化算法的收敛问题 23-24
  2.5.4搜索方向确定 24-25
  2.5.5算法步长确定 25-27
  2.6局部最优与全局最优 27-29
  2.7全局优化问题的特点 29-30
  2.7.1优化方法的发展 29-30
  2.7.2全局优化问题的性质 30
  2.8智能优化 30-31
  3混沌优化和粒子群优化 31-51
  3.1混沌优化 31-37
  3.1.1混沌的产生 31
  3.1.2混沌的定义 31-32
  3.1.3一般混沌映射特性 32-34
  3.1.4典型混沌映射点集的概率分布 34-35
  3.1.5混沌优化概述 35-36
  3.1.6其它改进的混沌优化算法 36-37
  3.2粒子群优化算法的原理 37-51
  3.2.1描述PSO的关键术语 37-38
  3.2.2基本粒子群优化算法 38-43
  3.2.3标准粒子群优化算法 43-45
  3.2.4粒子群优化算法的研究现状 45-48
  3.2.5与其它智能算法的比较分析 48-49
  3.2.6粒子群算法的不足 49-50
  3.2.7粒子群优化算法小结 50-51
  4粒子群优化算法的改进研究 51-73
  4.1粒子群优化存在的问题和改进分析 51-53
  4.1.1粒子群优化算法中存在的问题 51-52
  4.1.2粒子群优化算法的改进分析 52-53
  4.2基于混沌的自适应粒子群全局优化方法 53-60
  4.2.1混沌粒子群算法基本思想 54-55
  4.2.2一种基于混沌的自适应粒子群优化算法 55-57
  4.2.3数值仿真实验 57-60
  4.2.4小结 60
  4.3基于混沌的弹性粒子群全局优化算法 60-65
  4.3.1优化算法分析 60-61
  4.3.2弹性处理粒子速度 61-62
  4.3.3基于混沌的弹性粒子群全局优化算法流程 62-63
  4.3.4仿真研究 63-65
  4.3.5小结 65
  4.4基于梯度的弹性粒子群全局优化方法 65-72
  4.4.1梯度法 66
  4.4.2早熟收敛程度评价与自适应调整策略 66-67
  4.4.3一种基于梯度的弹性粒子群优化算法流程 67
  4.4.4数值实验和结果分析 67-71
  4.4.5小结 71-72
  4.5三种改进算法的比较分析 72
  4.6本章小结 72-73
  5填充函数方法的改进研究 73-86
  5.1填充函数方法 73-78
  5.2一类无参数填充函数的构造与性质 78-82
  5.2.1无参数填充函数的构造与填充性质 78-81
  5.2.2无参数填充函数的全局优化算法 81-82
  5.3基于混沌和填充函数的全局优化算法 82-85
  5.3.1算法分析 82
  5.3.2基于混沌和填充函数的全局优化算法 82-84
  5.3.3数值实验 84-85
  5.3.4小结 85
  5.4本章总结 85-86
  6结论与展望 86-88
  参考文献 88-91
  附录 91-99
  作者简历 99-101
  学位论文数据集 101-102

【摘要】 自然科学和社会科学中的许多问题都可归结为一个全局优化问题。全局优化问题广泛见于经济模型、金融计算、网络交通、系统控制、生物工程、环境工程等等。如何有效地求解这些全局优化问题已经成为影响这些领域发展的关键因素。由于存在多个不同于全局最优解的局部最优解,而传统的非线性规划方法都只能求其局部最优解,所以不能顺利地求解全局最优化问题。近年来,随着全局最优化在许多领域的重要应用,全局优化备受关注,其理论和方法也得到了很大的发展。这些方法主要包括确定性方法和随机性方法。本文主要研究随机方法中的粒子群优化方法和确定性方法中的填充函数方法。本文的创新之处如下:对粒子群优化算法,在对粒子群优化算法本身存在缺陷分析的基础上,以提高种群多样度、最优解精度和优化效率为目标,首先,提出早熟判断机制,以群体早熟收敛程度和个体适应值来调整惯性权重,并采用逻辑自映射函数来产生混沌序列,提出了基于混沌的自适应粒子群全局优化方法;其次,在计算各粒子的速度时,不考虑它与最优粒子之间距离的大小,而只利用其方向信息,采用一种自适应策略弹性地修正粒子速度的幅值,同时把混沌机制融入粒子群优化,提出了基于混沌的弹性粒子群全局优化算法;同时,把经典的梯度下降算法与上面提出的弹性修正粒子速度有机结合,互为补充,提出了基于梯度的弹性粒子群全局优化方法,利用标准测试函数,通过数值实验证明了各改进算法能有效提高算法的效率和优化结果的精确度。最后对改进的三种算法进行了比较分析。对填充函数方法,提出了一类新的无参数填充函数,从理论上证明了新填充函数的填充性质,给出了相应的填充函数全局优化算法,并把混沌优化与填充函数方法有机结合,提出了基于混沌和填充函数的全局优化方法,数值实验验证了算法的优越性。最后,对全文进行全面的总结,对相关领域的几种全局优化算法的继续改进和研究方向给出了展望。

代写数学硕士论文-【Abstract】 A lot of problems of natural science and social science can boil down to global optimization problems which often discovered in the field of economic planning models, finance, traffic transportation, engineering design and so on. Efficient global optimization methods affect the development of these subjects. Owing to there being many local optimal solutions which are different from global ones, we can only get the local optimal solutions using the methods of traditional nonlinear programming, therefore we can’t receive the global optimal solution successfully. As the global optimization is applied importantly in many fields, the global optimization comes under comprehensive attention. With the speedy development of computer and the hard work of scientists,the theoretic analysis and computational methods on optimization have been highly improved.This paper mainly research the particle swarm optimization and the filled function optimization algorithm. The innovation of this paper as follows:About the particle swarm optimization, based on the analyses with the present particle swarm optimization algorithm in detail, in order to improve the multiplicity, the solution precision and the algorithm efficiency, first of all, bringing forward judgement mechanism about precocity, adjusting inertia weight using the degree of precocity and the individual value adaptively, getting the sequence of chaos making use of the logic function, a adaptive particle swarm global optimization algorithm based on chaos is proposed. Secondly using a strategy in which the velocity is not dependent on the size of distance between the individual and the optimal particle but only dependent on its direction, an adaptive scheme is adopted to adjust the magnitude of the velocity resiliently, a resilient particle swarm global optimization algorithm based on chaos is proposed. Simultaneity, combining the classical gradient method with the resilient modification of the velocity, complementarity each other, a resilient particle swarm global optimization algorithm based on gradient method is proposed. Simulation results show these algorithms can improve the algorithm’s performance effectively as well as make the algorithm practical. Both the quality of global convergence and the algorithm efficiency of the algorithms are improved. About the filled function optimization algorithm. A kind of parameter-free filled function is proposed. The filled properties are discussed and proved. Then we improve it using the chaos theory and propose a global optimization algorithm based on chaos and filled function. Numerical experiments show that the method is effective.The last part concludes the research in this paper and presents the future research on the relative global optimization algorithms.

【关键词】 填充函数; 混沌; 粒子群优化; 弹性; 局部最优解; 全局优化;

【Key words】 filled function; chaos; particle swarm optimization; resilient; local optimal; global optimization;

 

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