Evolutionary Algorithm For Solving Nonlinear Equations And Application

In engineering and science,a large number of problems can be described by nonlinear equation systems(NESs),such as circuit design,pulse width modulation strategies,protein structure design.It is of great practical importance to study how to solve NESs effectively.An NES generally has multiple roots,and traditional numerical methods are often unable to locate multiple roots in a single run.Evolutionary algorithms(EAs)are a class of population-based algorithms that have the ability to locate multiple roots simultaneously.With good robustness and globalization,EAs have been widely used to solve NESs.At present,the EA-based algorithms for solving NESs need further research in how to maintain the diversity of populations and how to design more effective transformation techniques.In this thesis,the methods of solving NESs based on EA will be studied,and the proposed algorithms will be applied to the pulse width modulation strategy.The main research contents and results are as follows.A multilayer bi-objective brainstorm optimization(MOBSO)algorithm is proposed.A multilayer bi-objective transformation technique is developed to convert an NES into a biobjective optimization problem,which is able to reduce the number of optimization objectives to two while maintaining no reduction in solution differentiation.A diversity conservation mechanism with aging is introduced to balance the number of individuals in each cluster.This mechanism avoids the problem of missing solutions due to slow evolution of clusters with fewer individuals.Compared with five advanced algorithms,the experimental results show that the root ratio and success ratio of the MOBSO algorithm are improved by 2.1% and 10.88%,respectively.An adaptive neighborhood particle swarm optimization(MNPSO)algorithm is designed.For the problem that particle evolution can be misled by individuals with other peaks,a distance-based adaptive neighborhood strategy is proposed.The strategy can eliminate individuals with other peaks in the neighborhood of the current individual.For the problem of poor convergence on high-dimensional problems,a discrete crossover operator is introduced to improve the accuracy of the roots in high-dimensional problems.On 30 test problems,the average success ratio for eight advanced algorithms such as FNODE is85.07%,and the success ratio of MNPSO algorithm reaches 96.40%.The proposed MNPSO algorithm is applied to selective harmonic elimination pulse width modulation(SHEPWM).In the SHEPWM,the NES about the switching angle has only two roots,and the difficulty in solving it does not lie in the diversity maintenances.Therefore,it is more suitable to solve this problem using the MNPSO algorithm.After establishing the system of harmonic elimination equations,the MNPSO algorithm successfully solves the NES with multiple sets of solutions.A two-level inverter is built using Matlab/Simulink simulation software,and the simulation experiments verify the effectiveness of the MNPSO algorithm in solving the NESs of SHEPWM.