Research On High-dimensional Multi-objective Optimization Problems Based On Evolutionary Algorithms

Multi-objective optimizations are widely used in engineering,industrial,and scientific.For example,multipoint aerodynamic optimization of a wing shape for supersonic aircraft can be regarded as a multi-objective optimization problem.Designers should account for tradeoffs among aerodynamic performance,structural strength and weight,fuel storage,and so on.There are two main aspects of the so-called high-dimensional multi-objective optimization problems.First,many-objective optimization problems: from the problems with two or three objectives,to the many-objective optimization problem with more than three objectives,the dimensions of the objectives to be optimized increase gradually.Second,large-scale multi-objective optimization problems: the dimensions of decision variables of multi-objective optimization problems have been increasing from simple one to hundreds nowadays.Multi-objective optimization problems have the tendency of being more and more complex,which also have higher requirements for the corresponding algorithms.As heuristic search methods,evolutionary algorithms have been successfully applied in the field of multi-objective optimization problems and have good effects.However,with the increase of the dimensions of objectives and the dimensions of decision variables,the effectiveness of multi-objective evolutionary algorithms decreases significantly.In this paper,two algorithms are proposed for these two kinds of high-dimensional multi-objective optimization problems.The main contributions of this paper are: 1.For many-objective optimization problems,nowadays a research idea is removing the redundant objectives: the dimension of the high-dimensional multi-objective optimization problem is reduced by removing objectives,so the performances of evolutionary algorithms can be improved.However,most of the proposed algorithms for removing redundant objectives rely on analyzing non-dominated solutions,which are obtained by various multi-objective evolutionary algorithms with high computational complexity.In this paper,a new algorithm for removing redundant objectives is proposed.Firstly,a sampling method is used to sample the objective functions to obtain points that represent the objectives.Secondly,affinity propagation clustering algorithm is used to cluster the objectives,then the redundant objectives are removed.The innovation of this algorithm is that it does not require using an evolutionary algorithm to get the non-dominated solutions,but directly analyzes the relationships between objective functions to determine the redundancies of the objective functions.The experimental results show that the proposed algorithm is effective and accurate.2.For the large-scale multi-objective optimization problems,which have high dimensions of decision variables,there are few research achievements at present,and the focus is still on large-scale single-objective optimization problems.This paper adopts a fast interdependency identification algorithm to group decision variables.Then a cooperative coevolution algorithm is used to solve multi-objective optimization problems with the grouped variables.Experiments are conducted on multi-objective test problems with more than 100 decision variables,and the results show that the proposed algorithm can accurately obtain the optimal solution of large-scale multi-objective optimization problems.