求解奇异非线性方程组的粒子群优化算法

奇异非线性方程组是一类十分重要也比较困难的问题,基于粒子群优化算法提出了一种求解奇异非线性方程组的新方法.先把奇异非线性方程组转化为无约束优化问题,然后与人工智能算法相结合,利用标准粒子群优化算法求解.此算法不但不受方程组的连续性、光滑性的限制,而且避免了大量的求导计算,得到了极为精确的数值解.数值仿真结果显示了算法的有效性和可行性.该方法为求解奇异非线性方程组提供了一种有效、可行的新算法,也扩大了粒子群算法的应用领域.

Particle swarm optimization algorithm for solving singular nonlinear equations

Singular nonlinear equations is a class of important and diffieuh problem. Based on particle swarm optimization algorithm, a method for solving singular nonlinear equations is proposed in this paper. The equatiollS are transformed into optimization problem without constraints, to be solved by particle swarm optimization algorithm. This algorithln, free fiom the limitation of the form of the equations, avoids such complicated processes as calculating derivative and finding inverse of a matrix, anti gives an exaet numerical solution. Simulation results show that the algorithm is feasible and effective. This algorithm not only provides a new algorithm for solving singular nonlinear equations, but also enlarges the application area of the particle swarm optimization algorithm.