The Research Of Convergence And Diversity In Many-objective Evolutionary Algorithms

EA is not restricted by problem properties(such as continuous and discontinuous,concave and convex,multi-objective and multiple constraints),and can effectively deal with the difficult problems which cannot be solved by traditional optimization problems.Multi-objective evolutionary algorithms(MOEAs)are able to obtain a set of trade-off solutions under the circumstance of having multiple conflicting objectives.Classical MOEAs(such as NSGA-II and SPEA2)are able to obtain a set of good Pareto optimal solutions when there are only two or three objectives.However,most real world optimization problems belong to many-objective optimization problems(MaOPs)that have more than three objectives.The past classical MOEAs are no more suitable for MaOPs.There mainly have two reasons.Firstly,with the increase of objective number,using Pareto dominance relationship cannot distinguish individuals and thus the number of nondominated individuals increases exponentially,which makes selection pressure of MOEAs decrease sharply.Secondly,once the Pareto dominance relationship losses effectiveness,the diversity maintenance mechanism-led selection criterion prefers well-distributed individuals,which can influence the convergence of MOEAs further.Based on the fully analysis of research status and existing advantages and disadvantages of many-objective evolutionary algorithms(MaOEAs),this paper proposed a Pareto-based MaOEAs and a weight vector generation approach used in the decomposition-based MaOEAs.Aimed at the phenomenon of selection pressure of the Pareto-based MOEAs in high-dimensional space decreases sharply,this paper proposed a Pareto-based many-objective evolutionary algorithm using space partitioning selection and angle-based truncation in order to improve convergence and diversity of the Pareto-based MOEAs in high-dimensional space.The space partitioning selection primarily divides the objective space into many layers of subspaces,and then selects the best converged individuals in each subspace.This mechanism can select well-converged individuals on the basis of good diversity.The angle-based truncation introduces the angle between any two individuals as the criterion to delete redundant individuals,and the angle not only includes the diversity information,but also includes the convergence information.Using the combination of the two mechanisms to improves the convergence of the algorithm,and meanwhile maintains diversity.Compared with 5 traditional MOEAs,the proposed algorithm can obtain a set of satisfied optimal solutions in high-dimensional space.Due to the raise of MOEA/D,the aggregation-based MaOEAs have gained very extensive research and attention.Moreover,the performance of this class of algorithms appears largely influenced by the distribution of weight vectors.Thus,the paper proposed a weight generation method to create well-distributed weights in high-dimensional space using multi-objective optimization algorithms.This method primarily initializes a huge population and employs NSGA-II to optimize the population,and then uses the truncation method in SPEA2 to truncate the population to a predefined number,and thus the final obtained population is set as weight vectors.The experiment results shown that the proposed method,compared with the normal boundary intersection method,can obviously improve convergence and diversity of the decomposition-based MaOEAs in dealing with degeneration and discontinuous problems.