Pareto Front Estimation Using Unit Hyperplane

Abstract

This work proposes a method to estimate the Pareto front even in areas without objective vectors in the objective space. For the Pareto front approximation, we use a set of non-dominated points, objective vectors, in the objective space. To finely approximate the Pareto front, we need to increase the number of objective vectors. It is worth to estimate the Pareto front with a limited number of objective vectors. The proposed method uses the Kriging approximation and estimates the Pareto front using the unit hyperplane in the objective space. In the experiment using representative simple and complicated Pareto fronts derived from the DTLZ family, we visually show the estimation quality of the proposed method. Also, we show that the shape of the Pareto front and the distribution of sample objective vectors affect the estimation quality.