Prediction of Pareto dominance by reducing equivalent and redundent dimensions in decision vectors

Abstract

In order to increase accuracy predicting Pareto dominance in optimizing expensive multi-objective problems with high dimensional decision vector space, a method to identifying the equivalent and redundant dimensions in decision vector space is proposed. A kind of satisfaction degree based on the contribution of each decision component to each objective function is defined and used to determine the equivalent and redundant dimensions. In calculating the similarity of two candidate solutions based on distance measurement, equivalent components in decision vectors are mapped into a single component by using Sammon nonlinear mapping, and the redundant components are directly ignored. The reduced decision vector space of the observed data is used in the nearest neighbor method of predicting Pareto dominance. The experiment results on 6 typical unconstrained multi-objective optimization problems show that the proposed method is capable of increasing the accuracy of predicting Pareto dominance significantly.