Research On Multi-modal Multi-objective Optimization Algorithm For Improving Search Ability In Decision Space

The multi-objective optimization problem is an optimization problem with two or more conflicting objectives.When multiple Pareto optimal solution sets in the decision space of the multi-objective problem are mapped to the same Pareto frontier,the problem is transformed into a more complex multi-modal multi-objective optimization problem.The evolutionary method has been widely used in the study of multi-mode and multi-objective.Most of the existing studies consider the search performance of decision space or target space separately,and the fusion of decision space and target space can effectively improve the convergence and diversity of the algorithm.Therefore,based on the in-depth analysis of the existing research on multi-modal multi-objective optimization,this paper proposes a new environment selection strategy and propagation strategy to improve the performance of the algorithm with the aim of combining the state of the target space to improve the search ability of the decision space.The main research contents are as follows:(1)Most of the existing multi-modal multi-objective optimization algorithms try to search the entire Pareto optimal set(PS)in the decision space,and there are still incomplete Pareto solution sets,which may increase the calculation cost and may retain the solutions with poor effect.Thus,the diversity of decision space deteriorates.Based on this,this paper proposes a new environment selection strategy based on individual conditions in decision space and target space to improve the performance of the algorithm.This strategy takes into account both convergence and diversity.In this environment selection strategy,the combined parent and child populations are sorted by non-dominant order,and the non-dominant individuals in all the combined populations are retained,so as to improve the convergence ability of the algorithm.If the number of retained non-dominant individuals exceeds the set population number,the diversity is further optimized,and the next generation population is selected through the distribution of target space and decision space.On the contrary,if the number of retained non-dominated individuals does not reach the set population number,all the non-dominated individuals in the merged population will be retained at first,and then the remaining individuals in the merged population will be selected for other individuals in the next generation population based on their distribution in the target space and decision space.In order to verify the effectiveness of the proposed strategy,11 multimodal multiobjective test functions are tested.Experimental results show that the proposed environment selection strategy can effectively solve the convergence and diversity problems in multi-modal multi-objective optimization.(2)In order to ensure that the algorithm can find more solutions,a new propagation strategy is proposed which takes into account the performance of decision space and target space.Through the analysis of population diversity and convergence(adaptive),suitable mutation operator is selected to take into account the performance of decision space and target space,which can improve the convergence on the premise of ensuring diversity.By comparing with other algorithms on 11 multimodal and multiobjective test functions,the experimental results show that the proposed propagation strategy has better performance.