Research On Multimodal Multi-objective Optimization Algorithm With Two-stage Search

There are a large number of multimodal multi-objective optimization problems in real life,engineering application and scientific research.In such problems,two or more different Pareto optimal solution sets often correspond to the same Pareto frontier location.Solving all the Pareto solutions can provide more convenient and accurate choices for decision makers.However,traditional multi-objective evolutionary algorithms tend to ignore the distribution of decision space when solving such problems,which makes it impossible to solve multiple Pareto optimal solution sets simultaneously in multimodal multi-objective optimization problems.Therefore,this paper provided a general two-stage search framework to balance the search ability of the algorithm,and designed two two-stage search multimodal multiobjective evolutionary algorithms around spatial partition and clustering.The specific research contents are as follows.1)A multi-modal multi-objective differential evolution algorithm TS?MMODE based on partition and two-stage search is designed.The algorithm decomposes the evolution process into elite search stage dominated by divergent search and partition search stage dominated by depth search.In the elite search stage,the elite mutation strategy is used to generate high-quality individuals to ensure the search accuracy and efficiency of the population;In the partition search stage,the decision space is divided into several subspaces in the partition search stage.By dividing the decision space,the complexity of the problem is reduced,and the detected population is used to deeply explore each subspace,so as to improve the scalability and uniformity of the population in the decision space.The performance of the algorithm is verified by testing the function and a real addressing optimization problem.The experimental results show that TS?MMODE effectively balances the search ability of the algorithm through two-stage search,improves the distribution of the population in the decision space,and has certain application value in addressing optimization problems.2)Aiming at the characteristics of multi-modal multi-objective optimization problem with multiple PS,a two-stage search multi-modal multi-objective differential evolution algorithm TSSF?MMOEA?DE based on density clustering is designed.The algorithm divides the optimization process into two parts: global search and local search.In the global search,locate the approximate location of the optimal solution as much as possible,so as to provide a good population distribution for the next local search;In local search,DBSCAN clustering method is used to divide the population into multiple sub populations,and each sub population evolves independently,so as to reduce the adverse impact of multiple PS branches on population evolution,so as to strengthen the local search ability of the algorithm.In addition,in order to avoid the influence of clustering parameters on the performance of the algorithm,an adaptive neighborhood radius method is designed to adaptively determine the neighborhood radius of density clustering according to the size of decision space.At the same time,an individual selection mechanism based on the longest distance in two spaces is proposed to maintain the diversity of the population in the objective space and decision space.The performance of the algorithm is verified by testing the function and addressing optimization problem.The experimental results show that compared with other algorithms,the solution set searched by the TSSF?MOEA?DE has better convergence and diversity in both objective space and decision space.Its farthest-candidate approach with two spaces also effectively improves the ability of the algorithm to maintain population diversity.And a more complete and evenly distributed Pareto optimal region is searched in the addressing optimization problem.