Modified particle swarm optimization for solving systems of equations

The paper presents a modified particle swarm optimization (PSO) for solving systems of equations problem (SEP). With the hope to improve the global performance of PSO, the modified method adopts traditional controller to control the search dynamics, such as PI or PID controller. Through the introduction of traditional controller, the modified PSO can feed back the search information to adjust the inertia weight adaptively, which in turn balances the global exploration and the local exploitation validly. Further more, the modified PSO takes advantage of a single neuron network as a learner to get appropriate parameters for the traditional controller. The modified PSO with controller has been applied to solve some systems of equations. The experimental results show the proposed method is efficient and robust for optimization.