Hybrid particle swarm optimization algorithm for solving systems of nonlinear equations

A hybrid particle swarm optimization (HPSO) algorithm, which combines the advantages of Nelder-Mead simplex method (SM) and particle swarm optimization (PSO) algorithm, is put forward to solve systems of nonlinear equations, and it can be used to overcome the difficulty in selecting good initial guess for SM and inaccuracy of PSO due to being easily trapped into local optimal. The algorithm has sufficiently displayed the performance of PSO´s global searching and SM´s accurate local search. Numerical computation results show that the approach has great robust, high convergence rate and precision, it can give satisfactory solutions of nonlinear equations.