A quantum-behaved particle swarm optimization algorithm with the flexible single-/multi-population strategy and multi-stage perturbation strategy based on the characteristics of objective function

  • Yunhua GuoEmail author
  • Nian-Zhong ChenEmail author
  • Junmin Mou
  • Ben Zhang
Methodologies and Application


The characteristics of objective functions have important impacts on the search process of the optimization algorithm. Many multimodal functions tend to make the algorithm fall into local optima, and the local search accuracy is usually affected by the coupling of the objective functions in different dimensions. A novel quantum-behaved particle swarm optimization algorithm with the flexible single-/multi-population strategy and the multi-stage perturbation strategy (QPSO_FM) is proposed in the present paper. This algorithm aims to adjust the optimization strategies based on the characteristics of the objective functions. The number of sub-populations is determined by the monotonicity variations of the objective functions, and two mechanisms are introduced to balance the diversity and the convergent speed for the multi-population case. The strategy of multi-stage perturbation is applied to enhance the search ability. At the first stage, the main target of the perturbation is to broaden the search range. The second stage applies the univariate perturbation (relying on the coupling degree of the objective function) to raise the local search accuracy. Performance comparisons between the proposed and existing algorithms are carried out through the experiments on the standard functions. The results show that the proposed algorithm can generally provide excellent global search ability and high local search accuracy.


Quantum-behaved particle swarm Characteristics of function Single-/multi-population Multi-stage perturbation 



The authors would like to thank all the reviewers for their constructive comments. This work was supported by National Natural Science Foundation of China (Project No.: 51579201) and the High Technology Ship Foundation of Ministry of Industry and Information Technology of China (Project No.: MC-201710-H01).


This study was funded by National Natural Science Foundation of China (51579201).

Compliance with ethical standards

Conflict of interest

The authors declare that they have 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 GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of High Performance Ship Technology (Wuhan University of Technology)Ministry of EducationWuhanChina
  2. 2.School of Energy and Power EngineeringWuhan University of TechnologyWuhanChina
  3. 3.School of Civil EngineeringTianjin UniversityTianjinChina
  4. 4.School of NavigationWuhan University of TechnologyWuhanChina

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