Nonlinear Dynamics

, Volume 77, Issue 1–2, pp 427–429 | Cite as

Comments on “Particle swarm optimization with fractional-order velocity”

Commentary

Abstract

In this paper, some comments on the paper Solteiro Pires et al. (Nonlinear Dyn. 67:893–901, 2010) are presented. We demonstrate that the authors of the above paper have deduced the incorrect formula about the velocity updating strategy of the fractional-order particle swarm optimization algorithm. This paper deduces the modified updating formula, and verified experiments are also conducted.

Keywords

Fractional-order calculus Particle swarm optimization 

Notes

Acknowledgments

This work was partially supported by the National Key Basic Research Program of China (973 Project) under Grant #2013CB035503 and #2014CB046401, the Natural Science Foundation of China (NSFC) under Grant # 61333004 and #61273054, the National Magnetic Confinement Fusion Research Program of China under Grant #2012GB102006, Top-Notch Young Talents Program of China, and Aeronautical Foundation of China under Grant #20135851042.

References

  1. 1.
    Solteiro Pires, E.J., Tenreiro Machado, J.A., Boaventura, Cunha J., Mendes, L.: Particle swarm optimization with fractional-order velocity. Nonlinear Dyn. 67(1–2), 893–901 (2010)Google Scholar
  2. 2.
    Ghamisi, P., Couceiro, M.S., Benediktsson, J.A., Ferreira, N.M.F.: An efficient method for segmentation of images based on fractional calculus and natural selection. Expert Syst. Appl. 39(16), 12407–12417 (2012)CrossRefGoogle Scholar
  3. 3.
    Couceiro, M.S., Rocha, R.P., Ferreira, N.M.F., Machado, J.A.T.: Introducing the fractional-order Darwinian PSO. SIViP 6(3), 343–350 (2012)CrossRefGoogle Scholar
  4. 4.
    Ghamisi, P., Couceiro, M. S., Martins, F. M. L., Benediktsson, J. A.: Multilevel image segmentation based on fractional-order Darwinian particle swarm optimization. IEEE Trans. Geosci. Remote. PP(99), 1–13 (2013). doi: 10.1109/TGRS.2013.2260552
  5. 5.
    Duan, H.B., Liu, S.Q.: Nonlinear dual-mode receding horizon control for multiple UAVs formation flight based on chaotic particle swarm optimization. IET Control Theory Appl. 4(11), 2565–2578 (2010)CrossRefGoogle Scholar
  6. 6.
    Duan, H.B., Luo, Q.N., Ma, G.J., Shi, Y.H.: Hybrid particle swarm optimization and genetic algorithm for multi-UAVs formation reconfiguration. IEEE Comput. Intell. Mag. 8(3), 16–27 (2013)CrossRefGoogle Scholar
  7. 7.
    Duan, H.B., Yu, Y.X., Zhao, Z.Y.: Parameters identification of UCAV flight control system based on predator–prey particle swarm optimization. SCIENCE CHINA Inf. Sci. 56(1), 012202 (2013)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.State Key Laboratory of Virtual Reality Technology and SystemsBeihang University (BUAA)BeijingPeople’s Republic of China

Personalised recommendations