Soft Computing

, Volume 21, Issue 24, pp 7435–7445 | Cite as

Many-objective optimization with dynamic constraint handling for constrained optimization problems

  • Xi Li
  • Sanyou ZengEmail author
  • Changhe LiEmail author
  • Jiantao Ma
Methodologies and Application


In real-world applications, the optimization problems are usually subject to various constraints. To solve constrained optimization problems (COPs), this paper presents a new methodology, which incorporates a dynamic constraint handling mechanism into many-objective evolutionary optimization. Firstly we convert a COP into a dynamic constrained many-objective optimization problem (DCMaOP), which is equivalent to the COP, then the proposed many-objective optimization evolutionary algorithm with dynamic constraint handling, called MaDC, is realized to solve the DCMaOP. MaDC uses the differential evolution (DE) to generate individuals, and a reference-point-based nondominated sorting approach to select individuals. The effectiveness of MaDC is verified on 22 test instances. The experimental results show that MaDC is competitive to several state-of-the-art algorithms, and it has better global search ability than its peer algorithms.


Constrained optimization Many-objective optimization Dynamic constraint optimization Reference-point-based nondominated sorting 



The research in this paper was supported by the National Natural Science Foundation of China (Nos.: 61203306, 61271140 and 61305086).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical standard

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. This article does not contain any studies with animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Computer ScienceChina University of GeosciencesWuhanPeople’s Republic of China
  2. 2.School of Information EngineeringShijiazhuang University of EconomicsShijiazhuangPeople’s Republic of China

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