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

The expensive multi-objective optimization problem generally refers to a class of multiobjective optimization problems where the performance evaluation of the objective function nonanalytical model or candidate solution is very time-consuming and costly.When evaluating the performance of its candidate solutions,if the multi-objective evolutionary algorithm completely relies on costly real experiments,or time-consuming computer simulation analysis,or interactive manual evaluation methods,it will inevitably lead to serious calculation cost disasters.Therefore,it must be solved with a data-driven modeling approach.A common modeling method in the literature is to establish a proxy model for each black box function of an expensive multi-objective optimization problem by learning sample data of the candidate solution,and to use the prediction output of the proxy model to assist multi-objective optimization.Another kind of modeling method is to establish the Pareto dominance training sample set of the candidate solution,and predict the Pareto dominance relationship between the candidate solutions directly.Then,use the predicted Pareto dominance relationship to assist the multi-objective optimization.Although both methods can reduce the number of evaluations of the target vector and overcome the computational cost catastrophe problem to a certain extent,the high dimensionality of the decision space can lead to dimensionality catastrophe of proxy model modeling or prediction of Pareto dominance relationship.For the multi-objective optimization problem of non-analytical model,this paper focuses on data-driven decision-making space equivalent dimension recognition method.In this paper,the sample points consisting of the decision vector and the target vector are first projected onto a two-dimensional plane composed of the decision component and the target component.The grid point method is used to filter the projection point set to obtain the projected feature points that reflects the mapping relationship between the corresponding decision component and the target component.Aiming at the possible sparse and inhomogeneous situations of projection feature points distribution,a fitting method based on fitting for projected feature points is proposed to reconstruct the filtered projection feature points.Then,based on the reconstructed feature points,a decision space equivalent dimension criterion is proposed.Experiments on simulation testing problems show that the proposed method can effectively identify the equivalent dimensions in the decision space.Secondly,according to the recognition result of the equivalent dimension,the paper uses Sammon mapping method to group the dimensionality of the equivalent dimension in the decision space,predicts the Pareto dominance in the reduced dimension of the mapping space,and applies the results of the prediction to multi-objective evolutionary algorithm.Simulation experiments show that the proposed method can significantly improve the accuracy of prediction of Pareto dominance.The predicted Pareto advantage can guide multi-objective evolutionary algorithm to approach Pareto optimal surface.