改进的粒子群算法在非线性方程求根中的应用

Application of Improved Particle Swarm Optimization Algorithm for Finding Roots of Nonlinear Equation

在关于算法的研究中,针对粒子群算法局部搜索能力差,在真实解附近收敛速度慢,并求解精度不高和传统的数值解法只有当迭代初值在真实解附近时较快,为解决上述问题,提出了一种改进的粒子群算法。算法从优化的角度求解代数方程和超越方程,首先利用粒子群算法进行大范围搜索,为拟牛顿法提供一个好的初始点,然后使用拟牛顿法进行精细搜索,从而找到方程较高精度的根。数值仿真表明,算法有极好的稳定性、较高的收敛速度和精度,有效地克服了粒子群算法后期搜索效率低的缺点。

Some drawbacks such as poor local searching ability,slow convergence speed near the real solution and low precision exist in particle swarm optimization algorithm.Only when initial point is near the real solution,can the traditional optimization algorithms give their faster performance of local search.In view of this,an improved particle swarm optimization algorithm is proposed in this paper.Algebraic equation and transcendental equation are solved from optimization angle with this algorithm.First,this algorithm carries out the large-scale searching using particle swarm algorithm in order to provide a good initial point for quasi-Newton method.Then,quasi-Newton method makes refined search to find the higher precision roots of equation.Numerical experiments show that this algorithm has extremely stability,high convergence rate and precision.At the same time,it effectively overcomes the problem of high sensitivity to initial point of quasi-Newton method and shortcoming of PSO which reduces the searching efficiency in later period.