Soft Computing

, Volume 21, Issue 9, pp 2283–2295

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

Methodologies and Application


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 \(\varepsilon \)-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.


Multi-objective evolutionary algorithm Nadir point  Critical region Many-objective optimization problem Decision making 

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Key Lab of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center of Intelligent Perception and ComputationXidian UniversityXi’anChina
  2. 2.Department of Computer ScienceUniversity of SurreyGuildfordUK
  3. 3.CERCIA, School of Computer ScienceThe University of BirminghamBirminghamUK

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