【作者】 郭德龙；

【导师】 周永权；

【作者基本信息】 广西民族大学 ， 计算数学， 2008， 硕士

【摘要】 进化策略是模拟自然界的生物进化机制,人们设计出一种群智能搜索算法,该算法具有自组织、自适应和自学习等功能,它在不同学科领域已得到了广泛地应用。但在回归模型参数估计中应用并不多。回归模型参数估计是许多学科中常用的数学模型,如系统工程、自动化、机械工程、电力工程等,至今都是研究的重点问题之一。近年来,回归参数估计已有一些方法,如最小二乘法、极大似然法等,但是这些方法都是建立在具有连续导数的光滑搜索空间的假设基础上,并且沿梯度下降方向寻优的局部搜索技术在很多情况易陷入局部极值。基于此,本文将进化策略算法应用于回归模型参数估计,它可以弥补传统方法中一些不足。针对目前传统参数估计方法存在的一些问题,本文主要利用进化策略自适应搜索、全局收敛、鲁棒性等特性,并且做了一些改进。本文提出了一种进化策略算法,它通用性好、搜索效率高、收敛速度快,该算法主要对分布密度函数中的参数、线性回归分析中参数以及非线性回归分析中参数进行估计。所得到参数估计与传统方法相比具有求解精度高、收敛速度快等优点。该方法在数理统计,系统工程等方面具有重要的理论价值和实际应用背景。更多还原

【Abstract】 The evolution strategy is an algorithm which simulates the biological evolution mechanism, the people design a group intelligence search algorithm, it has intelligent characteristics of self-organizing, self-adapting, self-learning and so on, but the evolution strategy widely applied in many different scientific domains is less concerned in the regression model parameter estimation. The regression model parameter estimation is generally a mathematical model applied in many academics, such as systematic engineering, automation, mechanical engineering, electric power project and so on, To this day ,it is an important problem for research all the time. Recently, regression parameter estimation has already had some methods, such as least squares method, maximum likelihood method. But these methods are all based on the supposition that smooth searching space has continuous derivatives, and partial searching technology which seeks the optimization in the gradient dropping direction can easily lead to partial extreme value. Based on these, the evolution strategy algorithm is applied in carrying on the parameter estimation, which avoids some insufficiencies in the traditional methods.In view of some problems in traditional parameter estimation method, this article mainly makes use of some characteristics of evolution strategy, especially such as self-adapting searching, global convergence, robustness, moreover makes some improvements. An evolution strategy algorithm which has the advantages of good universal property,high searching efficiency and fast convergence rate is given in this paper. This algorithm are mainly used to estimate the parameters in the distributive density function, linear and non-linear regression analysis, the parameter estimation values compare those obtained by the traditional methods which has the solution precision high, the convergence rate quick and so on the merits .Therefore, this method in the mathematical statistic, aspects systems engineering and so on has the important theory value and the practical application background.更多还原