Numerical Analysis of Pareto Set Modeling

Tianye Shu, Hisao Ishibuchi, Yang Nan, Lie Meng Pang

Abstract: Recently, neural network-based inverse models have been used for multi-objective optimization. The basic idea is to approximate the mapping from the Pareto front to the Pareto set. In general, inverse modeling from a low-dimensional objective space to a high-dimensional decision space is difficult. However, good results have been reported in the literature. In this paper, we numerically examine the performance of inverse modeling. For visual examination, we use 2- and 3-objective distance minimization problems with 2 to 1,000 decision variables. Our experimental results show that inverse modeling improves the quality of the final population, which is used as the training data. One interesting observation is that improving fitting accuracy by increasing the neural network complexity does not improve the quality of the model outputs. We also demonstrate that inverse modeling works well even for large-scale multi-objective problems with 1,000 decision variables when high-quality training data are available.