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

Handing WANG, Shan HE, Xin YAO

Research output: Journal PublicationsJournal Article (refereed)peer-review

28 Citations (Scopus)


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 ε-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. © 2015, Springer-Verlag Berlin Heidelberg.
Original languageEnglish
Pages (from-to)2283-2295
Number of pages13
JournalSoft Computing
Issue number9
Early online date17 Nov 2015
Publication statusPublished - May 2017
Externally publishedYes

Bibliographical note

This work was supported by the National Basic Research Program (973 Program) of China (No.2013CB329402), an EPSRC Grant (No. EP/J017515/1) on “DAASE: Dynamic Adaptive Automated Software Engineering”, the Program for Cheung Kong Scholars and Innovative Research Team in University (No. IRT1170), the National Natural Science Foundation of China (No. 61329302), National Science Foundation of China (Nos. 91438103 and 91438201), and the Fund for Foreign Scholars in University Research and Teaching Programs (the 111 Project) (No. B07048). Xin Yao was supported by a Royal Society Wolfson Research Merit Award.


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


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