Knee Point Identification Based on the Geometric Characteristic

The ultimate goal of multi-objective optimisation is to help decision makers (DMs) identify solution(s) of interest. However, providing the DMs with a large amount of the trade-off alternatives not only increase their workload, but also add irrelevant noise to the decision-making process. Without any prior knowledge, knee points, characterised as their smallest trade-off loss at all objectives, are attractive to decision makers in multi-criterion decision-making. In this paper, we propose a simple but effective knee point identification method based on Voronoi diagram. It divides the objective space into several Voronoi cells to capture the geometric characteristics of the underlying trade-off solution set. Thereafter, the knee points are identified as those having a local Voronoi distance. Empirical results demonstrate that our proposed method is able to identify knee points located in both convex and concave part of the corresponding Pareto-optimal front.