Research On Population Angle Distance Based Evolutionary Many-objective Optimization Algorithm

Compared with Multi-Objective Optimization Problems(MOPs),Many-Objective Optimization Problems(MaOPs)with more than 3 objectives are more suitable for practical applications.Currently,with the increase of the number of objectives,decision variables and the complexity of the objective problems,the performance of multi-objective optimization algorithms degenerate in the many-objective space.For example,Dominance Resistant Solutions(DRSs)with poor performance may not be filtered out;absence of balance between convergence and diversity in MaOPs;adapting to the shapes of the Pareto Fronts(PF)become difficult,and a lack of good estimation methods for convergence and diversity.Therefore,the many-objective optimization problems become one of the hot and difficult research topics in the field of evolutionary computing.Aiming at the above-mentioned difficulties and the property of multi/many-objective optimization,this paper proposes two simple yet effective new Many-objective Evolutionary Algorithms(MaOEAs)by dealing with the above difficulties.We compare them with the state-of-the-art algorithms on a number of test problems.The research in this paper is as follows:(1)In order to enhance the balance between the convergence and diversity of the population in the many-objective space,and improve the overall performance,a many-objective evolutionary algorithm based on new angle penalized distance is proposed in this paper,which is termed MaOEA-NAPD.In MaOEA-NAPD,it could dynamically balance the convergence and diversity of the population concerning their importance degree during the evolutionary process based on new angle penalized distance.In environmental selection,we use new angle penalized distance to eliminate poor individuals to improve performance.In addition,this paper uses a type of binary tournament selection strategy based on Pareto dominance in the bi-goal domain as the mating mechanism,and introduces new convergence measures and distribution measures,which are the achievement scalarizing function and angle based crowding degree estimation,respectively,which improves the selection ability of the mating pool.Experimental results show that MaOEA-NAPD outperforms the state-of-the-art algorithms in test problems ranging from 3 objectives to 15 objectives.It is worth mentioning that MaOEA-NAPD also has some advantages: adaptive reference vector generation and a lower time complexity.(2)In order to enhance the ability to evaluate the convergence and diversity of the population in the many-objective space,and select elite individuals accurately,this paper proposes an angle distance based many-objective evolutionary algorithm with separation and clustering(ADMaOEA-SC).In environment selection,the angle priority strategy is firstly introduced to select the individuals with the best diversity of the current population,which is used as the center of the objective subspace to achieve the purpose of separation.Then,the individuals with similar characteristics of the center are clustered by the max-min-distance.Finally,the elite individuals are selected according to the aggregation function value,that is,the elite individuals with the best convergence and diversity are selected into the next generation in the clustering.After experimenting 145 test problems for simulation,the results show that ADMaOEA-SC has greater advantages than other compared algorithms.Especially,when dealing with optimization problems with irregular Pareto fronts,ADMaOEA-SC has obvious advantages.To sum up,this paper proposes two different many-objective optimization algorithms for the convergence and diversity in many-objective space.They are verified the performance by the test problems.The emphasis on convergence and diversity balance in the many-objective space can alleviate the situation of individuals falling into local optimal solutions and improve the overall performance of the population.So that it can better adapt to complex Pareto frontier problems.