中文摘要：

将几何约束问题转化为非线性方程组的形式。传统的求解几何约束问题的牛顿法具有较好的局部收敛性,但是对于一些强非线性方程,传统数值法容易导致求解失败,有效性较低。而遗传算法具有较好的全局收敛性。将遗传算法和牛顿法结合起来,引入牛顿-遗传混合算法来求解几何约束问题。在遗传算法中嵌入一个牛顿算子,以发挥传统数值算法在计算速度与计算精度上的优势。将该混合算法应用于几何约束求解,实验表明该算法在解决完备约束和欠约束问题上都获得令人较满意的结果。

英文摘要：

The geometric constraint problem was transferred into non-linear equation group. The traditional Newton Method for the geometric constraint problem has a good local convergence. But for some strong no-linear equations, the traditional numerical method can result failure easily, The validity is very low. The Genetic Algorithm has a good global convergence. Combining Newton algorithm and Genetic Algorithm, Newton-Genetic Algorithm was introduced to solve the geometric constraint problems. A Newton operator was embedded into the genetic algorithm so that the advantages could be employed in the calculating speed and calculating precision of the traditional numerical algorithm. The experiment indicates that the hybrid algorithm can gain satisfying results in both good-constraint and under-constraint problems.