Research On Methods Of Predicting Pareto Dominance Based On Dimension Reduction Of Decision Space

Using pattern recognition to predict the Pareto dominance between candidate solutions can effectively reduce the computational cost and financial cost of expensive multi-objective optimization,and overcome the shortcomings of the surrogate model to some extent.However,due to the curse of dimensionality of the decision vector space,the high-dimensional small sample set brings a series of problems such as unreliable statistical results,low prediction accuracy and high computational complexity.In order to make better use of the information in the decision space,and improve the accuracy of the Pareto dominance prediction,we mainly research on methods of predicting Pareto dominance based on dimension reduction of decision space in this paper.Considering the influence of the decision component on the target component is different,a method of the equivalent dimension analysis and dimension reduction is put forward.The concept of satisfaction is introduced to determine the equivalent and redundant dimension of the decision vector,and the Sammon nonlinear mapping algorithm is used to reduce the dimension of the equivalent dimension.Then,the nearest neighbor method is used to predict the Pareto dominance between candidate solutions in the decision space data after dimensionality reduction.The experimental results of Pareto nearest neighbor dominance prediction for typical multi-objective optimization problems show that the proposed method can significantly improve the prediction accuracy.In order to solve the problem that decision vectors are nonlinear,the method of Pareto dominance prediction based on LLE decision vector dimension reduction is studied.Using principal component analysis(PCA)of a generalized range to determine the intrinsic dimension of the decision vector relative to each objective component.Then LLE algorithm is used to reduce the dimensionality of the decision vector to form a new low dimensional decision space for each objective component.Next,using the nearest neighbor method to predict the Pareto dominance of candidate solution in the new decision space.Simulation results show that the proposed method can significantly improve the prediction accuracy.Finally,the LLE decision space dimensionality reduction method based on Pareto dominance is applied to the multi-objective evolutionary algorithm.The experimental results show that for the two objective function ZDT series and three objective function DTLZ series,the dimension reduction method can get an acceptable Pareto front by embedding it into MOEAs.This result further proves the feasibility and effectiveness of dimensionality reduction method based on Pareto dominance prediction.