Knee Point Identification Based on Voronoi Diagram

Finding preferred solutions is important for DMs to take the next step in solving Multi-objective optimisation problems (MOPs). When no specific preferences are available, knee point(s) are typically considered to be the most preferred solutions in multi-criterion decision-making since their smallest trade-off loss at all objectives. Knee point(s), including concave, convex and edge knee point(s), can reflect some geometry characteristics of the given non-dominated solutions because of its unique location. However, most of contemporary research for knee point identification (KPI) is only designed for convex knee point(s). Based on Voronoi diagram which can effectively reflect the distribution of the given set, we propose a method to identify all three types of knee points from a geometry view. In order to validate our method, we compare the performance of our method with other three state of the art approaches on benchmark problems for knee point identification. Experimental results fully show the effectiveness and competitiveness of our proposed KPI method based on Voronoi diagram (KPIVD) for identifying three types of knee points.