In many-objective optimization, the dimensionality of Pareto fronts becomes higher than three, and extracting preferable points for the decision maker is a key issue in the post-optimal analysis. The aim of this study is to develop a method to detect and visualize high-dimensional knee points. We propose a new definition of knee point and a graph-based approach to detect our knee points with a visualization of the geometry of the whole Pareto front. Our method is examined via Pareto front samples of synthetic problems and a real-world airplane design.
