Research On Intelligent Optimization Algorithms To Solve Nonlinear Equation Systems

Nonlinear equation system is one of the most representative optimization problems in the fields of scientific research and engineering practice.Thus,research on how to solve a nonlinear equation system has great theoretical and practical significance.The traditional optimization method is used to solve the nonlinear equation system,which needs the derivability of functions,the dependence of the initial point.Only one optimal solution can be obtained in a single run,which cannot meet the actual needs.Due to their huge application potentials and development prospects,intelligent optimization algorithms have been widely applied to diversified fields.After years of development,relatively mature algorithm frameworks have been formed.Intelligent optimization algorithms for solving nonlinear equation systems have attracted wide attention by researchers.This thesis studies how to simultaneously locate multiple optimal solutions based on intelligent optimization algorithms in a single run.The main works are as follows:1.An evolutionary algorithm based on multiobjective technology is proposed to solve nonlinear equation systems.The algorithm combines combines a diversity indicator,multiobjective optimization technique,and clustering technique.First,a nonlinear equation system is transformed into a single-objective optimization problem.And a diversity indicator based on Gaussian kernel functions is designed to improve the diversity.During the evolutionary,in order to effectively screen a lot of candidate solutions,a K-means clustering-based selection strategy is introduced to select the most promising solution set.Moreover,local search is used to quickly locate multiple optimal solutions.30 nonlinear equation systems are used to test the performance of the proposed algorithm in this paper.Through simulation comparison,this algorithm has competitive overall performance compared with several algorithms.2.An evolutionary algorithm based on decomposition is proposed to solve nonlinear equation systems.This is the attempt of decomposition in this field.First,a nonlinear equation system is transformed into a biobjective optimization problem.Next,we use the decomposition-based multiobjective technology to obtain the Pareto front of the transformation problem,that is,the optimal solutions of the nonlinear equation system.During the specific implementation,a biobjective optimization problem is decomposed into multiple single objective subproblems according to the Tchebycheff decomposition approach.The genetic algorithm is used to solve the optimal solution of each subproblem.And through the cooperation between the neighborhood subproblems,multiple optimal solutions of nonlinear equation systems are obtained eventually.30 nonlinear equation systems are used to test the performance of the proposed algorithm in this paper.Through simulation comparison,this algorithm has better performance than comparison algorithms.