In expensive multi-objective evolutionary algorithms

the evaluation of a large number of objective vectors spend a lot of time or experimental cost and lead to the cost of disaster.According to the fact that Pareto dominance relationships among candidate solutions are depended on the rank relationships of objective components

this paper proposes a predict method of rank equivalent to determine Pareto dominance.A decision vector and object vector rank matrix is established

and rank correlation analysis is used to calculate the correlation coefficient matrix R.Under the assumption of linear correlation

a prediction equation is established to predict rank relationships.Testing results on typical multi-objective optimization problems show that the proposed method only requires establishing a linear prediction model

which can remarkably improve the prediction accuracy and reduce the calculation of original expensive target function.Finally

the prediction method is integrated into the NSGA-II

it can avoid reconstruction the model in the process of evolution

then effectively decrease the number of evaluation for expensive objective vectors.