遗传规划和最小二乘法在数据拟合中的应用(英文)

Application of Genetic Programming and Least Square Method on Data Fitting

为了分析和预测数据,需要预先确定其拟合函数模型.最小二乘法是一种常用的对测量数据进行数据拟合的方法,但当拟合函数模型未知时,该方法即失效.提出了一种联合遗传规划和最小二乘法寻求拟合模型的方法.利用遗传规划方法只需给出数据点及允许误差即可得到匹配的拟合函数式,并可对复杂函数式合理地简化.以此结果作为最小二乘法的拟合函数模型,进一步估计其中的参数,实现了对测量数据的更精确拟合.文中给出了应用实例,说明了本方法的有效性.

A function that closely matches an unknown expression based on a finite set of sample data should be given in order to analyze and forecast data. Least square method is a commonly used method to solve the problem when the function expression is provided and it fails when no function expression can be provided. A new method for getting the fitting model by combining genetic programming and least square method is stated. Genetic programming can obtain the matched function expression by only giving the data points and the acceptable error. It can also simplify complex parts of the function. Furthermore, the parameters in the matched function expression are estimated by least square method to give more accurate fitting model. An example is given to prove the effectiveness of above method.