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

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Abstract

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.

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Acknowledgments

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.

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Authors and Affiliations

  1. Key Lab of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center of Intelligent Perception and Computation, Xidian University, Xi’an, 710071, China

    Handing Wang

  2. Department of Computer Science, University of Surrey, Guildford, GU2 7XH, UK

    Handing Wang

  3. CERCIA, School of Computer Science, The University of Birmingham, Birmingham, B15 2TT, UK

    Shan He & Xin Yao

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  1. Handing Wang
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  2. Shan He
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  3. Xin Yao
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Correspondence to Handing Wang.

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Communicated by V. Loia.

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Wang, H., He, S. & Yao, X. Nadir point estimation for many-objective optimization problems based on emphasized critical regions. Soft Comput 21, 2283–2295 (2017). https://doi.org/10.1007/s00500-015-1940-x

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