基于遗传算法求解分形无标度区的方法

Genetic Algorithm for Determining Scale Independent FractalsAssociated with Grinding Surface

分形无标度区的求取是分形应用研究的前提和基础．文中指出了目前求解无标度区算法的缺点，提出了一种基于遗传算法截取无标度区的方法．它将无标度区的起点和终点位置在全部数据范围内进行编码，以完成从可行解空间到染色体空间的映射，并用数据的平均残差平方和构成适应度函数，采用改进遗传算法对最优的起点与终点进行全局搜索．将此方法应用于磨削表面的分形研究，证明在获得同等精度的计算结果的条件下，大大地缩短了无标度区计算时间．这为进一步分形的实时测量提供了有力的支持．

A genetic algorithm is developed to determine scale independent fractals accociated with grinding surface. Obtained are the initial and terminal points that give the range of measuring points for describing the reflection from the feasible solution space to the chromosome space. The summation of the average variance could be applied for searching all the optimal position of the initial and terminal points. For the same accuracy, computational time of the proposed method is greatly reduced.