Clustering-Based Evolutionary Multimodal Multi-Objective Optimization Algorithm Research

There are many multimodal multi-objective optimization problems(MMOPs)in practical,and most of the existing multi-objective multi-modal evolutionary algorithms(MMOEAs)focus on the global Pareto Front of the problem,while it is difficult to give satisfactory solutions for multi-objective multi-modal problems with both global and local Pareto Front.And the problem of uniform distribution of individuals has also received little attention from researchers.To address the two problems mentioned above,the following two innovations are proposed in this paper.Innovation point one: an improved decision space density adaptive adjustment algorithm.The density adjustment algorithm proposed in this paper takes into account both the global Pareto Front and the local Pareto Front,and uses the information of the individuals around the least dense individual when performing the density adjustment,which has less impact on the convergence of the population.Innovation point two: a clustering algorithm for population based on sorting rank.The algorithm clusters the individuals in the population according to the non-dominated sorting rank,and after completing the clustering,the whole population is divided into one or more sub-populations according to the sorting rank,allowing the sub-populations to evolve individually and eventually being able to retain the local Pareto Front and the lobal Pareto Front.A Population Clustering Multimodal Multi-Objective Evolutionary Algorithm(PCMMOEA)is proposed for solving multimodal multi-objective problems with local Pareto Front by combining the two algorithms mentioned above.In the first step,the individuals in the population are explored locally and adjusted to the diversity of the population in the decision space and the distribution of individuals is improved by using improved decision space density adjustment algorithm.The algorithm then performs a convergence operation,allowing the population to converge to global Pareto Front and local Pareto Front.Then the population is divided into local and global Pareto Front by using population clustering algorithm based on sorting ranks and allowing all subpopulations to evolve separately without interference from each other.Step two,convergence and diversity of the decision space and an improved decision space density adaptive adjustment is performed.Finally,the decision space and objective space diversity and convergence are adjusted.In this way,the final result that not only finds the local Pareto Front and the global Pareto Front,but also maintains the diversity and convergence of the decision space and the objective space,and the density adjustment makes the distribution of individuals in the Pareto Sets more uniform,improving the quality of the solution.The proposed algorithm also performs well in problems with only global Pareto Front.This paper also compares the proposed PC-MMOEA with six other state-of-the-art algorithms using the CEC 2019 MMOPs.The experimental results show that the proposed algorithm outperforms the comparative algorithms,not only in finding local Pareto Front but also in obtaining solution sets with good convergence and diversity.In addition,the algorithm is also applied to solve a real-world map-based test problem,and the result shows that the proposed algorithm has a certain practical value in solving real-world problems.