基于相关分析的多目标优化Pareto优劣性预测

昂贵多目标进化算法中，目标向量评估所需计算时间或实验成本高昂，大量昂贵评估必然导致成本灾难.本文根据多目标优化Pareto优劣性取决于各目标分量的序关系这一关键性质，提出一种序拟合方法进行Pareto优劣性预测.在分析样本数据决策空间与目标空间序相关性的基础上，通过线性相关的假设条件，建立低成本的序关系预测方程，并用预测的序关系确定Pareto优劣性.然后对典型多目标优化问题进行Pareto优劣性预测对比实验，结果表明所提方法显著提高了Pareto优劣性的预测精度.最后，将该预测方法集成到NSGA-II算法中，可以避免进化过程中的模型重构，有效减少昂贵目标向量的评估次数.

Prediction of Pareto Dominance Based on Correlation Analysis

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.