Abstract: The genetic algorithm is usually selected as an optimization tool for the least square fitting about ordered plane data by B-spline curves. But the result easily falls into the local optimum with random initial choice, and more control points are required to assure higher accuracy. The adaptive genetic algorithm was proposed to overcome the shortcoming during the parameter optimization for B-spline curves. The average fitness of the initial populations was improved obviously by the average data parameter value method, which built the relationship between the data parameters and the knots. In the algorithm, the evolution of populations was accelerated through the optimization for the genetic strategy. The experimental results show that the algorithm can do with minimum control points and better precision within lower iterations.

Key words: adaptive genetic algorithm, B-spline curve, least square fitting, parameters optimization

摘要： 在B样条曲线的最小二乘拟合平面有序数据问题中，经常采用遗传算法进行优化。但随机选取初始种群的遗传算法，容易使得结果陷入局部最优。要达到较高的拟合精度，则需要增加更多的控制顶点。为克服这一缺点，提出了一种自适应的遗传算法对B样条曲线的参数优化。用平均有序数据参数法,将数据参数和节点建立关联，极大提高初始种群的平均适应度；通过优化遗传策略,加快种群进化。实验表明，该算法能用最少的控制顶点和进化代数进行B样条曲线的拟合，得到的拟合曲线逼近效果更好。

关键词: 自适应遗传算法, B样条曲线, 最小二乘拟合, 参数优化