Research On Enhanced Convergence Of Evolutionary Operators In Evolutionary Solution For High-dimensional Optimization Problems

In the actual production and life,problems encountered often need to be optimized,which optimization objectives are often more than one,and the objectives are conflict with each other,such problems are called multi-objective optimization problems(MOPs).When the objectives more than three,called many-objective optimization problems.Due to problems encountered in life are not only many-objective,but also high-dimensional decision-making,it is great significance to research on MOPs of high-dimensional characteristics.Evolutionary Algorithms(EA)is one of the main algorithms for solving MOPs and has a strong global search capability.However,when the MOPs is extended to high dimensions,most evolutionary algorithms cannot ensure convergence in solving high dimensional optimization problems because the difficulty of optimization increases and loss of dominance relationship.The evolution operator is the power source of the evolutionary algorithm.It guides population evolution with different degrees and speeds to affects the convergence performance.For the convergence of evolutionary operators in high-dimensional optimization problems,two new evolution operators are proposed to enhance the convergence of MOPs in high-dimensional decision space and many-objective space,respectively.The specific work of the two new evolution operators is as follows:1.A convergence-enhanced evolution operator based on high-dimensional decision space is proposed in MOPs of high-dimensional decision space.In the new evolution operators,two strategies are designed to the problem of low accuracy and low speed of convergence in the high-dimensional decision space.In the convergence speed enhancement strategy based on Controlling Dominance Area of Solutions(CDAS),firstly,sort the populations or neighborhoods by the non-dominated sorting based on CD AS,and generates vector differences that match different evolutionary periods according to the ranking results,and the dynamics scaling factor strategy based on high-dimensional decision information mining,it uses Principal Component Analysis(PCA)to analyze the high-dimensional decision space and dynamically adjust the scaling factor of Differential Evolution(DE).Finally,the vector difference is combined with the scaling factor to generate the individual.Experiments show that the proposed convergence-enhanced evolution operator can effectively enhance the convergence of the algorithm in MOPs in high-dimensional decision space.2.An evolution operator based on the convergence strategy of many-objective space is proposed in MOPs of many-objective space.In the new evolutionary operator,the combination of Locally Linear Embedding(LLE)and DE improve the convergence of many-objective space.LLE still maintains the characteristics of local features in dimensionality reduction,reduces dimensionality in many-objective space to enhance selection pressure,and then uses fast non-dominated sorting to stratify,and performs differential evolution operations based on hierarchical information,improving convergence speed of populations.The experimental results show that the new evolution operator has better selection pressure and convergence speed when ensuring diversity.3.In order to test the effectiveness of the two new evolution operators in solving MOPs in high-dimensional decision,many-objectives and practical applications,a multi-objective 0-1 knapsack problem simulation experiment was designed in high dimensional conditions.Further verify the solution performance of the new evolution operator in practical applications of high dimensional conditions.