Multimodal Multi-objective Differential Evolution Algorithm And Its Application In Nonlinear Equations

Most algorithms on multi-objective optimization focus on improving the distribution of Pareto front,while Pareto sets which affect Pareto front have not yet attracted much attention.At present,multimodal multi-objective optimization problems possess more than one Pareto subsets in the decision space that correspond to the same Pareto front,so it can solve the balance between Pareto sets and Pareto front according to studying these problems.However,when dealing with these problems,existing evolutionary algorithms easily get trapped into local optimum,which will lead to insufficient solutions and uneven distribution.To reduce these difficulties,this thesis proposes a multimodal multi-objective differential evolution algorithm.It designs a preselection mechanism and a mutation boundary processing method,which can not only increase the number of solutions in the Pareto sets,but also improve their distribution.At the same time,this thesis also constructs some new multimodal multi-objective optimization problems with different Pareto sets and Pareto front shapes.By comparing this proposed algorithm with the currently popular four algorithms,the experimental results show that the performance of the proposed algorithm has statistical superiority.In addition,in order to further verify the performance of the proposed algorithm,it is also applied to solve the nonlinear equations.The experimental results show that the proposed algorithm has a larger number of solutions and success rate than the other algorithms significantly.The main contents of this thesis are as follows:First,it introduces the research background and significance of multimodal and multi-objective optimization,and it also describes the steps of differential evolution.Due to the shortcomings and deficiencies in the current state of research,a multimodal multi-objective differential evolution algorithm is proposed.Second,it introduces the proposed algorithm in detail and illustrates the motivation and innovation.It also emphatically describes the preselection mechanism and mutation boundary processing method.Third,the multi-modal multi-objective differential evolution algorithm is tested on the test functions.The experiments include the comparison of the test results between the proposed algorithm and the compared algorithm,the comparison of graphics,the comparison of statistical results,the comparison between the proposed algorithm and its corresponding variants,the influence of the population size and the proposed strategy.Hence,the proposed algorithm is applied to nonlinear equations.The experiments include the enumeration of the graphic results,the comparison of evaluation results,the statistical comparison of results and analysis.Finally,it introduces the main functions and results of a graphical user interface.It can be used for intuitive algorithm comparison and parameter analysis.In addition,the work of this thesis is summarized and it gives a prospect in the shortcomings and directions of improvement in the future.