Application Of Improved Particle Swarm Optimization In Solving Nonlinear Equations

The problem of solving nonlinear equations in optimization problems plays an important role in industrial engineering.And the mathematical model is needed to solve the problem of the system.In many solving methods,the algorithm of particle swarm optimization,genetic algorithm and Newton method are better than the accuracy and convergence of the solution,but there are some defects in the solution.In this thesis,the advantages and defects of various algorithms are combined to solve the problem of nonlinear equations.The main research results of this thesis are as follows:(1)The nonlinear equations are studied.The Newton method,ant colony algorithm and particle swarm optimization algorithm are applied to solve the nonlinear equations.The shortcomings of the particle swarm optimization algorithm and the Newton method are sensitive to the initial point.Newton's direction method,and then effectively mix the two algorithms,the convergence Newton direction and particle group hybrid algorithm is proposed,and improved particle swarm algorithm is more accurate and convergence speed is faster.(2)Using the MATLAB7.0 simulation tool,the method of the conjugate Newton direction and particle group hybrid algorithm is verified,and the efficiency of the three algorithms is analyzed from the accuracy and iteration number of the algorithm,the particle swarm algorithm and the improved particle swarm algorithm.The result proves that compared with other typical algorithms,the conjugate Newton direction and particle group hybrid algorithm is reduced by number of iterations in the solution,and the accuracy of the algorithm is improved.However,from the operation process of the algorithm,the conjugate Newton direction-particle swarm mixing algorithm is more complicated.