基于改进遗传规划算法的数据拟合*

针对传统数据拟合方法需预先估计基函数、依赖于应用领域等问题,基于遗传规划的动态可变特性,提出将遗传规划与最小二乘法结合,设计具有一定通用性和自适应能力的数据拟合算法。在分析传统遗传规划算法的基础上,详细介绍了算法改进方法,并针对各种类型的拟合数据进行了对比实验。实验结果表明,该算法不仅可以应用到多种场合,而且可以提高拟合效率与精度。     

遗传规划和进化策略混合算法及应用

文中把函数拟合建模看作是模型结构和参数的优化搜索过程,将遗传规划和进化策略结合起来对函数拟合的结构和参数共存且相互影响的复杂解空间进行全局最优搜索实现拟合结构和参数的共同识别。克服了传统的函数拟合完全依赖于数据、精度低、结构与参数分别确定这样一“串行”计算结构等缺陷。实验数据表明,该方法得到的拟合函数比传统方法得到的拟合函数,具有较高的精度和推广预测能力。     

工程实验数据的非线性拟合方法

在EXCEL软件中,拟合非线性实验数据有4种方法。其中规划求解方法与随机抽样方法的最大优点是不要变换方程,且适合任何实验数据非线性拟合。规划求解方法最为简便,但精度相对要差,结果有时难以把握。后者加入了VBA混合编程,达到筛选与优化目的,提高了拟合精度。另2种方法为函数公式方法和回归分析方法,前者根据最小二乘法原理仅仅在电子表格中输入函数公式即可得到精度极高的拟合结果。后者利用了EXCEL自带的数学分析工具完成拟合,精度最高。但它们在应用之前,需要对实验数据进行多元多项式方程变换,对难于变换的非线性实验数据不适合。处理工程实验数据,掌握这4种非线性实验数据的拟合方法很有必要。     

遗传算法在l1数据拟合中的应用

采用l1范数准则函数对测试数据进行数据拟合的方法，称为l1数据拟合。介绍了遗传算法及其在数据拟合中的应用，并且给出了应用实例。     

遗传程序设计算法中选择调整参数的光滑拟合方法

对遗传程序设计(GP)算法中的适应度评价函数光滑拟合问题进行了研究,结合LAM(Linear Association Memory)和HJ(Hook和Jeevs)两种方法,估计GP树数值权值,以减少GP树适应度值评价的计算代价。提出了一种选择调整参数的新方法,同时,给出了一个数学例子,并与广义交叉实验B一样条函数仿真比较验证。     

GP算法中适应度函数的光滑拟合与调整参数方法研究

研究了遗传程序设计(GP)算法中适应度函数的光滑拟合问题,结合LAMs(Linear association memorys)方法和HJ(Hook和Jeevs)方法两种方法,估计GP树数值权值,以减少GP树适应度值评价的计算代价.光滑拟合的好坏关键取决于调整参数的选择.提出了一种选择调整参数的新方法,同时,给出了两个数学例子,并与广义交叉实验B-样条函数仿真比较验证.     

情境自适应的RSSI分段异构拟合定位方法

室内定位在公共安全、健康监护、定位服务等领域具有重要价值,提高定位精度和模型对环境的适应性已经成为室内定位的核心问题。其中通过接收信号强度指示RSSI值来获取距离是比较通用的方法。针对室内复杂环境中传统的对数距离损耗路径模型适用性不高的情况,提出了一种情境自适应的RSSI分段异构拟合定位方法。该方法利用信号在不同应用情境下传播损耗的差异性,将RSSI数据分为多个不同的拟合段,根据RSSI数据的区分特性寻找最优的分段拟合点,并为每个分段选择最优的拟合函数,使得分段数、分段位置和每个分段的拟合函数都适应相应的应用场景,从而实现高精度的RSSI信号拟合。实验结果表明,本文所提出的方法在RSSI拟合精度上均优于传统的单一拟合函数,可明显提高定位算法的精度。     

一种径向基函数神经网络的参数求解方法

为了求解径向基函数神经网络的权值,首先分析了传统基于训练误差的方法,发现该方法容易造成数据过拟合,原因在于训练误差是风险函数的下偏估计;因此,文中提出采用缺一交叉验证得分代替训练误差,来实现无偏估计风险函数;实验对摩托数据与玻璃数据进行拟合,证实了基于缺一交叉验证的方法优于传统基于训练误差的方法,且所得到的径向基函数网络能够较光滑地拟合数据,不会造成过拟合.     

小生境技术在遗传规划中的应用

为了提高遗传规划算法的性能,把遗传算法中的小生境技术运用到遗传规划中,提出了改进的遗传规划算法（NGP）。该算法首先对原始训练集进行数据拟合,然后应用小生境技术跟踪拟合函数的极值点,并根据拟合函数的维数的不同,分别计算极值点在自变量维上的欧氏距离并排序,选取欧式距离较大且数量不超过原始训练集10%的极值点,加入到原始训练集中作为新的训练集,最后用遗传规划算法处理新训练集。在符号回归实验中对NGP 的准确率进行了测试,说明了该算法的准确性和有效性。     

基于小波函数的数据拟合方法

本把小波函数引入离散数据拟合领域，将小波函数与数据拟合的常用方法－最小二乘法相结合，给出了一种新型的数据拟合工具，中详细讨论了该方法的处理论和实施步骤，由于小波函数具有良好的局部性质，该方法在提高似合精度方面具有传统方法不可替代的优点。     

Accelerated Genetic Programming of Polynomials

An accelerated polynomial construction technique for genetic programming is proposed. This is a horizontal technique for gradual expansion of a partial polynomial during traversal of its tree-structured representation. The coefficients of the partial polynomial and the coefficient of the new term are calculated by a rapid recurrent least squares (RLS) fitting method. When used for genetic programming (GP) of polynomials this technique enables us not only to achieve fast estimation of the coefficients, but also leads to power series models that differ from those of traditional Koza-style GP and from those of the previous GP with polynomials STROGANOFF. We demonstrate that the accelerated GP is sucessful in that it evolves solutions with greater generalization capacity than STROGANOFF and traditional GP on symbolic regression, pattern recognition, and financial time-series prediction tasks.     

Applying Dynamic Training‐Subset Selection Methods Using Genetic Programming for Forecasting Implied Volatility

Volatility is a key variable in option pricing, trading, and hedging strategies. The purpose of this article is to improve the accuracy of forecasting implied volatility using an extension of genetic programming (GP) by means of dynamic training‐subset selection methods. These methods manipulate the training data in order to improve the out‐of‐sample patterns fitting. When applied with the static subset selection method using a single training data sample, GP could generate forecasting models, which are not adapted to some out‐of‐sample fitness cases. In order to improve the predictive accuracy of generated GP patterns, dynamic subset selection methods are introduced to the GP algorithm allowing a regular change of the training sample during evolution. Four dynamic training‐subset selection methods are proposed based on random, sequential, or adaptive subset selection. The latest approach uses an adaptive subset weight measuring the sample difficulty according to the fitness cases' errors. Using real data from S&P500 index options, these techniques are compared with the static subset selection method. Based on mean squared error total and percentage of non‐fitted observations, results show that the dynamic approach improves the forecasting performance of the generated GP models, especially those obtained from the adaptive‐random training‐subset selection method applied to the whole set of training samples.     

Polynomial genetic programming for response surface modeling Part 1: a methodology

The second-order polynomial is commonly used for fitting a response surface but the low-order polynomial is not sufficient if the response surface is highly nonlinear. Based on genetic programming (GP), this paper presents a method with which high-order smooth polynomials, which can model nonlinear response surfaces, can be built. Since in many cases small samples are used to fit the response surface, it is inevitable that the high-order polynomial shows serious overfitting behaviors. Moreover, the high-order polynomial shows infamous wiggling, unwanted oscillations, and large peaks. To suppress such problematic behaviors, this paper introduces a novel method, called directional derivative-based smoothing (DDBS) that is very effective for smoothing a high-order polynomial.The role of GP is to find appropriate terms of a polynomial through the application of genetic operators to GP trees that represent polynomials. The GP tree is transformed into the standard form of a polynomial using the translation algorithm. To estimate the coefficients of the polynomial quickly the ordinary least-square (OLS) method that incorporates the DDBS and extended data-set method is devised.Also, by using the classical Lagrange multiplier method, the modified OLS method enabling interpolation is presented.Four illustrative numerical examples are given to demonstrate the performance of GP with DDBS.     

Training genetic programming on half a million patterns: an example from anomaly detection

The hierarchical RSS-DSS algorithm is introduced for dynamically filtering large datasets based on the concepts of training pattern age and difficulty, while utilizing a data structure to facilitate the efficient use of memory hierarchies. Such a scheme provides the basis for training genetic programming (GP) on a data set of half a million patterns in 15 min. The method is generic, thus, not specific to a particular GP structure, computing platform, or application context. The method is demonstrated on the real-world KDD-99 intrusion detection data set, resulting in solutions competitive with those identified in the original KDD-99 competition, while only using a fraction of the original features. Parameters of the RSS-DSS algorithm are demonstrated to be effective over a wide range of values. An analysis of different cost functions indicates that hierarchical fitness functions provide the most effective solutions.     

动态系统的演化建模

针对采用传统方法解决动态系统的微分方程建模问题所遇到的困难和存在的不足,语文中设计了将遗传程序设计与遗传算法和相嵌套的混合演化建模算法,以遗传程序设计优化模型结构,以遗传算法优化模型参数,成功地实现了动态系统的常微分方程组建模过程自动化。     

软件可靠性的GP演化建模

为解决软件可靠性模型的不一致性,摆脱传统模型多种主观假设的束缚,提出了采用遗传程序设计(GP)的演化算法建立基于软件失效间隔时间序列的软件可靠性模型。针对装甲兵工程学院的某软件测试用例进行演化建模,并对其性能指标进行了分析评价,结果验证了GP算法的可行性以及拟合、预测的有效性,从而能有效地应用于软件系统测试,保障数据的有效性。     

A new approach of Romero’s extended lexicographic goal programming: fuzzy extended lexicographic goal programming

Goal programming (GP) is perhaps one of the most widely used approaches in the field of multicriteria decision making. The major advantage of the GP model is its great flexibility which enables the decision maker to easily incorporate numerous variations on constraints and goals. Romero provides a general structure, extended lexicographic goal programming (ELGP) for GP and some multiobjective programming approaches. In this work, we propose the extension of this unifying framework to fuzzy multiobjective programming. Our extension is carried out by several methodologies developed by the authors in the fuzzy GP approach. An interval GP model has been constructed where the feasible set has been defined by means of a relationship between fuzzy numbers. We will apply this model to our fuzzy extended lexicographic goal programming (FELGP). The FELGP is a general primary structure with the same advantages as Romero’s ELGP and moreover it has the capacity of working with imprecise information. An example is given in order to illustrate the proposed method.