全局优化问题的填充函数方法研究

发布时间：2018-06-16 01:01

本文选题：全局优化 + 无约束优化问题　；参考：《宁夏大学》2017年硕士论文

【摘要】：填充函数法是求解全局优化问题的一种重要的算法,该算法在已有局部优化算法的基础上,通过构造适当的填充函数来实现优化过程,深受理论及实际工作者的欢迎.本文分析已有填充函数算法存在的问题,重点研究基于填充函数法求解一般无约束连续全局优化问题.全文共分为四章.第一章对全局优化问题的基本理论和填充函数算法的研究现状进行了简要介绍,并给出了本文的研究目的及主要工作.第二章针对已有填充函数存在多个参数的问题,构造了两类含有单参数的填充函数,并分别给出了理论证明和数值实验,实验结果表明这两类单参数填充函数算法均有效可行且算法II较算法I迭代步数少,求解精度高.第三章针对含参填充函数在参数调节过程中存在影响计算效果的问题,构造了两个不含参数的填充函数,并分别进行了数值实验,数值结果表明所构造的两个无参数填充函数形式正确,算法有效可行且算法II较算法I计算时间短,效果好.第四章总结了本文所做的主要工作,并对填充函数方法有待研究的问题进行了展望.
[Abstract]:The filling function method is an important algorithm for solving the global optimization problem. Based on the existing local optimization algorithm, the algorithm realizes the optimization process by constructing appropriate filling function, which is welcomed by both theoretical and practical workers. This paper analyzes the problems existing in the existing filling function algorithms, and focuses on solving the general unconstrained continuous global optimization problem based on the filling function method. The full text is divided into four chapters. In the first chapter, the basic theory of global optimization problem and the research status of filling function algorithm are briefly introduced, and the purpose and main work of this paper are given. In the second chapter, two kinds of filling functions with single parameter are constructed, and the theoretical proof and numerical experiment are given. The experimental results show that the two kinds of single-parameter filling function algorithms are effective and feasible, and the algorithm II has less iteration steps than the algorithm I, and the accuracy of the algorithm is high. In chapter 3, two nonparametric filling functions are constructed and numerical experiments are carried out to solve the problem that the parameter filling function has influence on the calculation results in the process of parameter adjustment. The numerical results show that the two nonparametric filling functions are correctly constructed, the algorithm is effective and feasible, and the computation time of algorithm II is shorter than that of algorithm I, and the effect is good. In chapter 4, the main work of this paper is summarized, and the problems that need to be studied in the method of filling function are prospected.
【学位授予单位】：宁夏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O224

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