Improvement And Application Of Multimodal Multi-Objective Particle Swarm Optimization Algorithm

There are a large number of multimodal multi-objective optimization problems in practical applications,and there are multiple Pareto optimal solution sets in the decision space of such problems corresponding to the same Pareto frontier in the objective space.Obtaining multiple Pareto-optimal solution sets can uncover the potential characteristics of the problem while providing multiple feasible solutions for decision makers,and how to search for these Pareto-optimal solution sets has been the focus of attention in the optimization field.Traditional multi-objective optimization algorithms focus on the search of the objective space and can only find a set of optimal solution sets in a single run,thus making it difficult to solve such problems effectively.In this paper,we study the improvement and application of multimodal multi-objective particle swarm optimization algorithm,which is mainly as follows:(1)Aiming at the problem that the traditional particle swarm optimization algorithms has poor diversity of solution sets and convergence of algorithm when solving multimodal multiobjective optimization problems,a dynamic neighborhood based multimodal multi-objective particle swarm optimization algorithm(DN-MMOPSO)is proposed.In order to change the limitation of fixed neighborhoods on the exchange of information between particles and also to reduce the possibility of the population falling into premature convergence,a dynamic neighborhood selection strategy is proposed.This strategy divides the whole population into multiple dynamic sub-swarms and selects new neighboring particles for each particle to produce a more diverse solution set.To improve the search efficiency of the algorithm,an isolated sub-swarm reorganization strategy is introduced.To verify the effectiveness of the proposed algorithm,10 multimodal multi-objective test problems are solved using it and compared with four existing multi-objective optimization algorithms.The experimental results of each algorithm on three evaluation metrics,IGDX,PSP and HV,for the same test problem illustrate the convergence of this algorithm in the decision space and objective space,respectively,and the diversity of the solution sets obtained.The results show that this algorithm can improve the diversity of solution sets and the convergence of the algorithm.(2)Aiming at the problem that the traditional multi-objective optimization algorithm does not fully consider the distribution of solutions in the decision space,resulting in premature convergence and incomplete Pareto sets.To solve the above problem,a multimodal multiobjective particle swarm optimization algorithm using ring topology and search disturbance is proposed.To better balance exploration and development,the optimization process is divided into 2 phases.In phase 1,the entire population is divided into multiple small sub-swarms and one inferior sub-swarms.The small sub-swarms uses a spatial distance-based non-overlapping ring topology to increase the diversity of the population and enable the algorithm to search for more Pareto optimal solutions.The disadvantaged sub-swarms are updated using the global optimal solutions to improve the search efficiency.In phase 2,all particles follow the global optimal solution for searching to improve the search accuracy of the algorithm.To avoid premature convergence of the algorithm,cycle recombination and a new global optimal solution updating strategy are introduced.To verify the effectiveness of the proposed algorithm,it is used to solve 10 multimodal multi-objective test problems and compared with five existing multi-objective optimization algorithms,and the results show that this algorithm can obtain a better convergence and a more complete set of Pareto solutions.(3)The application of multimodal multi-objective particle swarm optimization algorithm in feature selection is studied.Considering both the number of features and classification accuracy,the feature selection is considered as a multimodal multi-objective optimization problem and solved.Considering that the continuous particle swarm optimization algorithm cannot be directly used to deal with discrete optimization problems,this paper adopts a real number encoding method to transform the continuous position vector into a binary feature string,so as to establish a mapping between particles and potential solutions of the problem.The proposed algorithm is applied to 7 data sets and compared with 2 existing algorithms on the same data set for the average classification accuracy and the number of equivalent feature combinations obtained.The comparison results show that the algorithm can effectively reduce the redundancy of the feature set and can find more equivalent feature combinations while ensuring the classification accuracy.