超越方程的全局优化解法

The Global Optimization Method to Transcendental Equation

现有的粒子群算法在求解超越方程时具有局部搜索能力差、后期收敛速度较慢的缺陷,导致了粒子群算法无法得到较为精确的超越方程的根。在粒子群算法的基础上,加入局部搜索能力较好、后期收敛速度较快的拟牛顿算法,依照算法的进程自动甄选粒子群算法和拟牛顿算法,充分发挥粒子群算法的全局搜索性能和拟牛顿法的局部搜索性能,进而将超越方程转化为了纯粹的函数优化问题,并基于此方法进行求解实验,结果表明该方法具有极高的收敛速度和求解精度。

The existing PSO(particle swarm optimization)algorithm has many problems in solving the transcendental equation,such as poor local search ability,post-convergence slower,which causes that PSO algorithm can not get more precise transcendental equation roots.In this article,based on particle swarm optimization algorithm,and adding quasi-Newton algorithm with better local search ability and faster post-convergence,the particle swarm algorithm and quasi-Newton method have been automatically selected and given full performance in local search ability abut this two algorithms.Thus the transcendental equation has been transformed into purely function optimization problem.Based on this method,a solution experiment has been made,and the results show that this method has the very high convergence speed and solution accuracy.