【作者】 陈炜；

【导师】 张卫国；

【作者基本信息】 宁夏大学 ， 应用数学， 2004， 硕士

【摘要】 遗传算法是一种模拟自然界生物进化的搜索算法，由于它的简单易行、鲁棒性强尤其是其不需要专门领域的知识，而仅用适应度函数作评价来指导搜索过程，从而使它的应用范围极为广泛，并且已在众多领域得到了实际应用，取得了许多令人瞩目的成果，引起了广大学者和工程人员的关注。 本文的主要内容是对遗传算法理论及其在证券投资组合中的应用进行了一些研究和分析工作，并对这类问题的求解提出了可靠、高效的算法。 首先介绍了遗传算法的基本概念和基本理论，对遗传算法的各个组成部分，特别是对选择策略、杂交策略、变异策略以及遗传算法的基础定理-模式定理作了详细的介绍。其次，在对传统遗传算法的基本结构和基本流程的研究分析基础之上，对传统遗传算法作了一些改进：对确定初始群体的改进，提出了一种改进的选择方法，利用范数来度量群体中各个染色体之间差异的选种方法；针对传统遗传算法的缺点，设计了三种通用遗传算法-TNGA、GATS、IAGA；接着，在随后的章节中，本文从理论上用泛函分析的数学方法证明了TNGA的收敛性，并在Markov链分析的基础上分析了标准遗传算法的收敛性；最后，本文做了一些实践应用方面的研究工作，提出了用遗传算法求解最佳证券投资组合的算法，并实际编程求解最佳证券投资组合，从而说明了这三种改进算法的有效性和可行性。更多还原

【Abstract】 The genetic algorithm is a kind of searching method which simulates the natural evolution.lt is simple and easy to implement,especially it doesn’ t need the special field knowledge , but simply uses fitness function as an assessment to instruct the search process,so it has been used in very broad fields. Now the genetic algorithm has got a lot of fruits and scholars begin to pay attention to it .The main content of the paper is discussing the theory of the genetic algorithm and the application of the genetic algorithm in portfolio investment . In addition, I propose reliable and efficient algorithm to solve relevant problem.Firstly, this paper gives a brief introduction to the basic conception and theories of the genetic algorithm .And it also provides a detailed explanation on the components of the genetic algorithm , with the emphasis on the strategies of selection, crossover,mutation and the basic theorem -Schema theorem. Secondly, based on the study of the basic structure and flow diagram of the traditional genetic algorithm, some improvement is given:A selection method is proposed about the settled initiated population improvement and the norm is used to measure the selection method of the difference of chromosome;to overcome the disadvantage of the genetic algorithm, a general genetic algorithm is designed桾NGA, GATS and IAGA;in the following chapters, the paper proves the convergence of the genetic algorithm ,using the functional analysis and the convergence of simple genetic algorithm is illumiunated by the analysis of the Markov chain. Finally, the paper does some research work on the practical application and puts forward three improved genetic algorithm to solve the best portfolio investment . Some programs are designed to find out the best portfolio investment ,and this shows the feasibility and validity of these methods.更多还原