A performance indicator for reference-point-based multiobjective evolutionary optimization

Aiming at the difficulty in evaluating preference-based evolutionary multiobjective optimization, this paper proposes a new performance indicator. The main idea is to project the preferred solutions onto a constructed hyperplane which is perpendicular to the vector from the reference (aspiration) point to the origin. And then the distance from preferred solutions to the origin and the standard deviation of distance from each mapping point to the nearest point will be calculated. The former is used to measure the convergence of the obtained solutions. The latter is utilized to assess the diversity of preferred solutions in the region of interest. The indicator is conducted to assess different algorithms on a series of benchmark problems with various features. The results show that the proposed indicator is able to properly evaluate the performance of preference-based multiobjective evolutionary algorithms.