Research On Diversity Preserving Strategy In Multi-modal Multi-objective Algorithms

In recent years,with the increasing complexity of industrial production links and the continuous improvement of people's quality of life,a single solution strategy has been difficult to meet the needs of decision makers.Multi-modal optimization is used to find multiple sets of equivalent solutions to the same optimization problem and provide them to decision makers.However,previous studies only focused on the multimodal single-target problem,and there are relatively few multimodal problems in the multi-objective problem.Multimodal multi-objective optimization problems(MMOPs)refer to a Pareto frontier(PF)in the corresponding target space that often contains two or more Pareto optimal solution sets(PS)in the decision space.Providing all the PS found in the production life to decision makers can improve decision flexibility and reduce unnecessary difficulties.Such problems require a high diversity of solutions in decision space.However,the current mainstream multi-objective evolutionary algorithms pay little attention to the diversity of solutions in decision space,they pay more attention to the diversity and convergence in the target space.It appears that it does not have the ability to search for multiple sets of solutions in decision space.In order to improve the diversity of population in decision space,this paper designs two multimodal multi-objective algorithms which can effectively maintain the spatial diversity of decision space.The main contents are as follows:1)A multimodal multi-objective differential evolution algorithm based on spectral clustering is designed and implemented.This algorithm emphasizes the local search of subpopulations,uses spectral clustering algorithm to divide the population in decision space into several subpopulations in each generation according to their distribution,and makes each subpopulation fit different PS as much as possible to increase the search efficiency for different PS.In addition,the algorithm uses a differential evolution algorithm based on external archives and an individual selection mechanism based on decision spatial diversity to enhance the diversity of population distribution in decision space.2)A multimodal multi-objective optimization algorithm based on grid selection is designed and implemented.This algorithm designs a new individual selection mechanism for the problem characteristics of multimodal multi-objective optimization problems,and uses an adaptive grid selection strategy in decision space to ensure the uniformity of population distribution in decision space.At the same time,the number of individuals in the subpopulation is adjusted reasonably in the target space by generating reference vectors to maintain the distribution of the population in the target space.This enables the final solution that the algorithm finds to have a degree of diversity in both decision space and target space.