Nadir point estimation for many-objective optimization problems based on emphasized critical regions

Nadir points play an important role in many-objective optimization problems, which describe the ranges of their Pareto fronts. Using nadir points as references, decision makers may obtain their preference information for many-objective optimization problems. As the number of objectives increases, nadir point estimation becomes a more difficult task. In this paper, we propose a novel nadir point estimation method based on emphasized critical regions for many-objective optimization problems. It maintains the non-dominated solutions near extreme points and critical regions after an individual number assignment to different critical regions. Furthermore, it eliminates similar individuals by a novel self-adaptive (Formula presented.)-clearing strategy. Our approach has been shown to perform better on many-objective optimization problems (between 10 objectives and 35 objectives) than two other state-of-the-art nadir point estimation approaches.