【摘要】 将几何约束问题转化为数值优化问题。把蚂蚁算法引入几何约束求解中。在所有的操作中,由于没有涉及到在 Newton-Raphson 中遇到的矩阵求逆操作,因此蚂蚁算法具有很强的鲁棒性。笔者在基本蚂蚁算中混入局部优化算法,对每代的最优解进行改进,进一步加快蚂蚁算法的收敛速度。为了避免蚂蚁一开始就失去解的多样性,笔者改进了选择策略。为了克服蚂蚁算法计算时间较长的缺陷,这里引入遗传算法中的变异算子,经过局部优化后,整个群体的性能会有明显改善,使得算法保持更好的多样性。由于该算法对方程的个数和变量的个数没有什么特殊的要求,因此可以处理欠约束问题。更多还原

【Abstract】 We transform the geometric constraint solving into the numerical optimization solving. We introduce ant algorithm into the geometric constraint solving. Because in all the operating it isn’t related to the inversion of the matrix by Newton-Raphson method, the ant algorithm is robust. We interfuse local optimization algorithm in the basic ant algorithm and improve the best solution of every generation, so it can improve the convergence speed of the ant algorithm. In order to avoid the loss of diversity of the solutions from the beginning, we improve the choosing method. In order to avoid the shortage of the long time computing, we introduce the variance operator of the genetic algorithm. After local optimization, the character of the colony can be improved greatly and the algorithm can keep better diversity. Because this algorithm hasn’t special need to the number of the equations and the variables, we can deal with under-constraint problem.更多还原