New Method for Solving Nonlinear Equation Systems
Existing numerical methods for solving nonlinear equation systems often can not converge to all of the optimal solutions.In this paper,a hybrid niching genetic algorithm(HNGA) is presented for solving global solutions of nonlinear equation systems.Genetic drift of genetic algorithm(GA) is overcome by introducing deterministic crowing(DC) technique in GA.DC creates niches for subpopulation's evolution.Diversity in population is maintained and multi-solutions can be achieved at the same time.In addition,quasi-Newton method participates in the process of GA's evolution as a local searching operator.Convergent rate and accuracy of the algorithm are improved.Several specific examples with multi-solutions are selected to test the validity of HNGA.Results of numerical computations show that HNGA can converge to all solutions at the same time in the definition area of solutions with reliable global convergence characteristic,high convergence rate and accuracy of solutions.It is an effective method for solving nonlinear equation systems.