Soft Computing

, Volume 22, Issue 4, pp 1159–1173 | Cite as

Objective reduction for many-objective optimization problems using objective subspace extraction

Foundations
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Abstract

Multi-objective evolutionary algorithms (MOEAs) have shown their effectiveness in exploring a well converged and diversified approximation set for multi-objective optimization problems (MOPs) with 2 and 3 objectives. However, most of them perform poorly when tackling MOPs with more than 3 objectives [often called many-objective optimization problems (MaOPs)]. This is mainly due to the fact that the number of non-dominated individuals increases rapidly in MaOPs, leading to the loss of selection pressure in population update. Objective reduction can be used to lower the difficulties of some MaOPs, which helps to alleviate the above problem. This paper proposes a novel objective reduction framework for MaOPs using objective subspace extraction, named OSEOR. A new conflict information measurement among different objectives is defined to sort the relative importance of each objective, and then an effective approach is designed to extract several overlapped subspaces with reduced dimensionality during the execution of MOEAs. To validate the effectiveness of the proposed approach, it is embedded into a well-known and frequently used MOEA (NSGA-II). Several test MaOPs, including four irreducible problems (i.e. DTLZ1–DTLZ4) and a reducible problem (i.e. DTLZ5), are used to assess the optimization performance. The experimental results indicate that the performance of NSGA-II can be significantly enhanced using OSEOR on both irreducible and reducible MaOPs.

Keywords

Many-objective optimization Objective reduction Objective subspace extraction Conflict information 

Notes

Acknowledgements

This work was supported by the National Nature Science Foundation of China under Grants 61402291, 61171124, 61301298, Seed Funding from Scientific and Technical Innovation Council of Shenzhen Government under Grant 0000012528, Foundation for Distinguished Young Talents in Higher Education of Guangdong under Grant 2014KQNCX129, Natural Science Foundation of SZU under Grants 201531, JCYJ20160422112909302, GJHS20160328145558586, and Science and Technology Planning Project of Guangdong under Grant 2013B021500017.

Compliance with ethical standards

Conflict of interest

Author Naili Luo declares that she has no conflict of interest. Author Xia Li declares that she has no conflict of interest. Author Qiuzhen Lin declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.College of Information EngineeringShenzhen UniversityShenzhenPeople’s Republic of China
  2. 2.Shenzhen Key Lab of Communication and Information ProcessingShenzhenPeople’s Republic of China
  3. 3.College of Computer Science and Software EngineeringShenzhen UniversityShenzhenPeople’s Republic of China
  4. 4.The Chinese University of Hong KongLonggang DistrictPeople’s Republic of China

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