Abstract: Multi-modal multi-objective optimization is a complex multi-objective optimization problem with multiple Pareto solutions on the same Pareto front.It has become an important research direction in the field of multi-objective optimization.Existing algorithms can solve this problem well,but they have certain limitations in terms of solution diversity,convergence and handling of target conflicts,such as difficulty in effectively covering all solution sets or premature convergence during the optimization process.To solve these problems,a new multi-modal multi-objective optimization algorithm based on the environment selection strategy of the growing neural gas(GNG) network is proposed.This method introduces an adaptive topological structure to dynamically adjust the population distribution,and uses weighted Euclidean distance to calculate the crowding degree for environment selection,thereby improving the diversity and uniformity of the population.In addition,the knowledge transfer mechanism is introduced to enhance the algorithm’s search ability and further improve the diversity and convergence of solutions.To verify the effectiveness of the algorithm,experiments are carried out on the HYL and MMF test function sets.The experimental results show that the proposed algorithm performs better than the five comparison algorithms in terms of solution distribution uniformity,Pareto front convergence and target space coverage.

Key words: Multi-modality, Multi-objective, Neural network, Knowledge transfer, Environmental selection