Research On Population Distribution For High-dimensional Optimization And Its Application In Feature Selection

Multi-objective optimization is a common problem in scientific research and engineering applications,which consists of multiple conflicting optimization objectives.When the performance of one objective is improved,the performance of several other objectives will decline.When the dimension of the objective space exceeds 3,it is called many-objective optimization problem.When the dimension of decision space exceeds 100,it is called largescale multi-objective optimization problem.The above two kinds of high-dimensional optimization problems are hot topics in the field of intelligent computing and have important research significance.Multi-objective optimization is a NP problem,it is difficult to calculate the optimal solution in a limited time,so the multi-objective evolutionary algorithm is usually used to search the approximate optimal solution quickly.Multi-objective evolutionary algorithms have strong global search ability when dealing with low-dimensional problems.However,with the increase of the dimension of optimization problems,the search space explodes exponentially and the individual selection pressure loses rapidly,so it is difficult for ordinary multi-objective evolutionary algorithms to guarantee the convergence of the results for solving high-dimensional problems.The distribution of the evolutionary population not only profoundly affects the evolutionary direction of the population,but also is an important index to evaluate the final solution of the multi-objective optimization algorithm,which is an important direction to optimize the multi-objective evolutionary algorithm.Based on the discussion above,this paper in order to improve the performance of the multiobjective evolutionary algorithm processing high-dimensional optimization problem,from the objective space and decision space two perspective,explore the population distribution in the process of evolution,in the NSGA-III algorithm is put forward on the basis of two sets of improvement strategy,for solving many-objective optimization problem and large-scale sparse many-objective optimization problem.Specific work and innovation points are as follows:(1)Considering the irregularity of real Pareto front surface,AR-NSGA-III algorithm is proposed for many-objective optimization problem.Based on the NSGA-III algorithm,the new algorithm proposes a reference point selection strategy and a population evolution stage determination strategy.Firstly,according to the distribution characteristics of the population in the decision space,the entropy difference between the two generations of the adjacent population was calculated to determine the evolutionary stage of the population.Then,according to the distribution characteristics of the population in the objective space,the importance of the reference point was evaluated by the statistical information of the number of individuals associated with the reference point.Finally,in the middle and later stages of the population evolution,the redundant invalid reference points were eliminated according to the importance characteristics of the reference points,and the retained reference points were made to adapt to the population size and Pareto front,and the selected reference points were used to guide the population evolution direction,so as to accelerate the convergence and optimization efficiency of the algorithm.Through comparative experiments,the performance index of IGD and HV of the new algorithm on the standard test function set DTLZ and Ma F is obviously better than that of the other four algorithms.(2)Considering the Sparse decision variables of a kind of problem,Sparse-NSGA-III algorithm was proposed for large-scale many-objective optimization.Based on the NSGA-III algorithm,the new algorithm adds a hybrid coding strategy,a decision variable dynamic scoring strategy,a greedy-like initialization strategy and a greedy-like genetic operator.The hybrid coding strategy divides the decision variable into two parts: real vector and binary vector to compress the search space of the decision variable.First,score the decision variables of each dimension.In the initial stage of the population,the greedy-like strategy was adopted to initialize the population according to the score,so as to ensure the sparsity of the population decision variables.At the stage of population evolution,the greedy-like strategy was used to cross and mutate individuals according to the scores to guide the searching direction of the population and ensure the rapid convergence of the population.The scores of decision variables were updated dynamically for each generation of population evolution.Through comparative experiments,the convergence and distribution of the new algorithm on the standard test function set SMOP are all better than those of the other four algorithms.(3)Multi-objective feature selection is a large-scale problem.To verify the effectiveness of Sparse-NSGA-III algorithm in solving practical problems,it is applied to the multi-objective feature selection problem.The simulation experiment is carried out,and the HV index is compared and analyzed to further verify the solving performance of the new algorithm in practical application under high dimensional conditions.