蚁群算法在方程求根中的应用

The Application of Ant Colony Optimization Algorithm to Solving Equations

列举了传统方程求根方法的不足,介绍了当前若干人工仿生优化算法在方程求根领域的应用。模拟蚂蚁的群体智能,即选择最短路径觅食,提出了一种基于网格划分的连续域改进蚁群算法,用来求解超越方程和复系数高次代数方程的根。通过仿真计算,算法可以找到两类方程的所有根,对于两类方程的差异性而言,算法较稳定。算法给出的复系数高次代数方程的根的误差分布不太均匀,个别根精度太高或者太低。

Traditional algorithms have several disadvantages in the course of finding the roots of equations. Recently, some artificial biological modeling optimization algorithms have been applied to solving equations. Ant Colony Optimization algorithm is inspired from ant＇s intelligence, that is to say, choosing the most short-path to find food. In this paper, we provide a new Ant Colony Optimization algorithm which is based on grid computation, to solve transcendental equations and complex coefficient higher-order algebraic equations. Experiments show that the algorithm can solve all the roots. The algorithm is compatible with the two different equations. Finally, it is presented that the error distribution of the roots from complex coefficient higher-order algebraic equations is not even.