The Study On Environmental Selection Of Many-objective Evolutionary Algorithms

It is known that Multi-objective Evolutionary Algorithms(MOEAs)commonly used for solving Multi-objective Optimization Problem(MOP)with more than two objectives.Since several decades research,many outstanding algorithms(e.g.NSGA-II,SPEA2,etc.)have been supposed,which can handle two or three objective problems and get a well-converged and well-distributed solution set.In practical application,however,the number of considered objectives can be larger(i.e.,over three),and these problems are known as many-objective optimization problems(MaOPs).Owing to the objectives often conflict with each other,traditional Pareto-based MOEAs do not easily get a set of trade-off solutions,which have “good” convergence and “good” diversity in MaOPs.The reason for the following two points: First of all,the dominant area of the individuals almost exponentially decreases with the increasing of the objective dimension,which will cause Pareto-based MOEAs failing to distinguish the stand or fall of individuals and unable to converge into the Pareto front;secondly,to enhance the extensive distribution of population,most diversity maintenance strategy prefer to extreme solutions,thus hinder evolutionary search in MaOPs.According to above analysis,two environment selection strategies,Angle Dominance Strategy(ADS)and Neighborhood Competition-based Strategy(NCS),have been proposed in this paper.Considering the first reason for the above mentioned,ADS amplify the dominance area of individual by comparing its angle vectors which consist of the angle of the individual on each axis.ADS can effectively distinguish between individuals in the high-dimensional space.In addition,an interesting property of the proposed dominance criterion lies in that it meets the relevant properties of the dominance relationship,for example,irreflexive relation,asymmetric relation,transitive relation and strict partial order.Considering the second reason for the above mentioned,NCS combines selection operation and elimination operation to reduce the impact of convergence.In the selection operation,NCS introduce convergence information(CI)to choose an individual with good convergence.What's more,we need diversity information(DI)to eliminate an individual with bad diversity in the elimination operation.In order to verify the validity of the above two strategies in solving MaOPs,several different contrast tests are given in this paper.For convenience,the ADS and NCS were respectively integrated into NSGA-II and constructed two different algorithms and their names were AD-NSGA-II and Neighborhood Competition-based Multi-objectiveEvolutionary Algorithms(NCEA).We carried out a competitive experiment with seven algorithms(e.g.,CDAS,AR+DMO,?-MOEA,GrEA,IBEA+HD,MSOPS,NSGA-III).The results have demonstrated that,the two strategies could achieve the best performance in most situations and obtain a set of non-dominated solutions with “good” convergence and “good” diversity in MaOPs.