Conjugate direction particle swarm optimization solving systems of nonlinear equations

摘要

Solving systems of nonlinear equations is a difficult problem in numerical computation. For most numerical methods such as the Newton's method for solving systems of nonlinear equations, their convergence and performance characteristics can be highly sensitive to the initial guess of the solution supplied to the methods. However, it is difficult to select a good initial guess for most systems of nonlinear equations. Aiming to solve these problems, Conjugate Direction Particle Swarm Optimization (CDPSO) was put forward, which introduced conjugate direction method into Particle Swarm Optimization (PSO)in order to improve PSO, and enable PSO to effectively optimize high-dimensional optimization problem. In one optimization problem, when after some iterations PSO got trapped in local minima with local optimal solution x*, conjugate direction method was applied with x* as a initial guess to optimize the problem to help PSO overcome local minima by changing high-dimension function optimization problem into low-dimensional function optimization problem. Because PSO is efficient in solving the low-dimension function optimization problem, PSO can efficiently optimize high-dimensional function optimization problem by this tactic. Since CDPSO has the advantages of Method of Conjugate Direction (CD) and Particle Swarm Optimization (PSO), it overcomes the inaccuracy of CD and PSO for solving systems of nonlinear equations. The numerical results showed that the approach was successful for solving systems of nonlinear equations.