Research On Solving Multimodal Multi-Objective Optimization Problems With Evolutionary Computation Algorithms

There are a lot of complex optimization problems in applications,and they usually include multiple simultaneous optimization and mutual restriction goals.In order to solve this multi-objective optimization problem,a large number of multi-objective evolutionary algorithms have been proposed by researchers to find a set of compromise solutions in the objective space.With the development of society,changes in business,and researches on optimization problems in applications,the needs of decision makers for multi-objective solutions have become more complex and diverse.Therefore,more and more multimodal multi-objective optimization problems are discovered and abstracted from applications.The problem is characterized by multiple equivalent Pareto optimal solutions in the decision space corresponding to the same Pareto front in the objective space.So traditional multi-objective evolutionary algorithms cannot solve this problem well.Compared with the multi-objective evolutionary algorithm,which only focuses on the performance of the objective space,the multimodal multi-objective evolutionary algorithm can not only find the balance of the solution in the objective space and the decision space,but also find the balance between the local optimal problems and the global optimal problems.Therefore,the multimodal multi-objective evolutionary algorithm is very suitable for solving multimodal optimization problems.Through our research,this paper finds that although both multimodal multi-objective optimization problems and multi-objective optimization problems are similar in the objective space,they are quite different in decision space.Equivalent Pareto optimal solution sets will compete with each other during the evolutionary process,resulting in the lack of PSs.Secondly,the local optimal solution set is dominated due to the pressure of the global optimal solution set,and it is difficult to survive in environment selection.Therefore,for these two difficulties,this paper proposes the corresponding improved algorithms,including the following two main tasks:First,this paper proposes a multimodal multi-objective optimization using a density-based one-by-one update strategy(MMOEA-GD).This algorithm uses a calculation method of the harmonic average distance to improve the accuracy of the density estimation in the decision space,which can improve the algorithm's ability to optimize solutions and ensure the distribution of the population.In addition,the algorithm uses the one-by-one update strategy to improve the accuracy of the algorithm's update strategy,to avoid the equivalent Pareto optimal solutions being deleted by mistake,so as to ensure the distribution of the equivalent Pareto optimal solutions in the decision space.Secondly,this paper proposes a multimodal multi-objective evolutionary algorithm based on a mean-shift clustering method and a dual-mode update strategy with local optimal monitoring(MMOEA-LC&DU).The algorithm uses a mean-shift clustering method to classify populations into several clusters in the decision space,avoiding or reducing competition between equivalent Pareto solutions.At the same time,the algorithm uses a local optimal monitoring mechanism to determine whether there may be a local Pareto optimal solution set in the population.If there exist local Pareto optimal solutions,the algorithm uses the update strategy based on hierarchical clustering,which uses a clustering method to distinguish between the local Pareto front and the global Pareto front in the objective space.This mode is used to perform population update,avoiding the local Pareto optimal solutions being dominated.Otherwise the algorithm executes global optimal update strategy based on niche density,which uses the method of dividing niche in the objective space and decision space,respectively.Considering the density in the objective space and decision space at the same time,it is able to obtain the balance between diversity and convergence of population.With this method,the algorithm improves its performance and successfully solves the current multimodal multi-objective optimization problems.