High-dimensional Multi-objective Evolutionary Algorithm Based On Angle Selection And Dynamic Penalty

The many-objective optimization problems have gradually been regarded as a crucial and popular research topic.Although the concept of “division” of the Multi-Objective Evolutionary Algorithm based on Decomposition(MOEA/D)makes it one of the key technologies for solving high-dimensional multi-objective optimization problems,there are still defects and deficiencies in regard to balancing the convergence and diversity in the objective space.This study carries out a systematic investigation on the issue above and has got the results as follows: First,aiming at the problem of insufficient convergence in the high-dimensional multi-objective optimization problems,it is proposed an Angle Selection Strategy(AS)to select a minimum angle between the new solution and different weight vectors in the objective space in every iteration.Besides,it's also helpful to guide a rapid convergence of the population explicitly.The new solution could only replace one inferior solution at a time,in order to maintain the diversity of the solution set as much as possible while promoting the convergence of it.Second,there is a problem that the diversity of the solution set generated by the algorithm is damaged in the high-dimensional objective space.It is found that the solution accuracy of MOEA/D algorithm is directly related to the aggregation methods.The Penalty-based Boundary Intersection Approach(PBI)is much influenced by a penalty parameter ?,and meanwhile a fixed penalty parameter fails to match the sub-problems in different positions.In particular,the extreme solutions on the boundary sub-problems are easily replaced by the non-dominated solutions in the neighborhood.In terms of all these problems,it is suggested a Dynamic Penalty Strategy(DPS)that the selection region size of candidate solutions be changed by dynamically adjusting the penalty parameter ?,which provides more suitable selection areas for the sub-problems in different locations.It's also promising that and the loss of elite solutions on boundary sub-problems can be reduced,and the diversity of solutions be better maintained.Meanwhile,the penalty parameter ? is set to be changed from a small value to a larger one with the iteration of the algorithm,so as to ensure the convergence of the population would not be damaged.Finally,this paper demonstrates the efficiency of the two improved methods through simulation experiments.Compared with the related advanced algorithms,the results show that the quality of the solutions obtained by the improved algorithms is better.