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Fractional-Order Darwinian PSO

  • Micael CouceiroEmail author
  • Pedram Ghamisi
Chapter
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

As presented in Chap.  1, Darwinian particle swarm optimization (DPSO) presented by Tillett et al. (Darwinian particle swarm optimization, 2005) is an evolutionary algorithm that extends the PSO using natural selection, or survival of the fittest, to enhance the ability to escape from local optima. Despite its superior performance when compared to its nonevolutionary counterpart, the DPSO also exhibits a key drawback: its computational complexity. This chapter proposes a method for controlling the convergence rate of the DPSO using fractional calculus (FC) concepts (Pires et al., Journal on Nonlinear Dynamics, 61(1–2), 295–301, 2010). The fractional-order optimization algorithm, denoted fractional-order Darwinian particle swarm optimization (FODPSO), is then tested using several well-known functions and the relationship between the fractional-order velocity and the convergence of the algorithm is observed.

Keywords

FODPSO Swarm intelligence Optimization Benchmark 

References

  1. Couceiro, M. S., Martins, F. M., Rocha, R. P., & Ferreira, N. M. (2012). Introducing the fractional order robotic Darwinian PSO. Proceedings of the 9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences (ICNPAA2012) (pp. 242–251). Vienna, Austria.Google Scholar
  2. Machado, J. T., Silva, M. F., Barbosa, R. S., Jesus, I. S., Reis, C. M., Marcos, M. G., et al. (2010). Some applications of fractional calculus in engineering, Hindawi Publishing Corporation Mathematical Problems in Engineering, 1(34), 174–183.Google Scholar
  3. Ostalczyk, P. W. (2009). A note on the Grünwald-Letnikov fractional-order backward-difference. Physica Scripta, 136, 014036.CrossRefGoogle Scholar
  4. Pires, E. J., Machado, J. A., Cunha, P. B., & Mendes, L. (2010). Particle swarm optimization with fractional-order velocity. Journal on Nonlinear Dynamics, 61(1–2), 295–301.zbMATHCrossRefGoogle Scholar
  5. Sabatier, J., Agrawal, O. P., & Machado, J. A. (2007). Advances in fractional calculus—theoretical developments and applications in physics and engineering. Berlin: Springer.zbMATHGoogle Scholar
  6. Shi, Y., & Eberhart, R. (2001). Fuzzy adaptive particle swarm optimization. Proceedings of the IEEE Congress on Evolutionary Computation, 1, 101–106.Google Scholar
  7. Tillett, J., Rao, T. M., Sahin, F., Rao, R., & Brockport, S. (2005). Darwinian particle swarm optimization. In B. Prasad (Ed.), Proceedings of the 2nd Indian International Conference on Artificial Intelligence (pp. 1474–1487). Pune, India.Google Scholar
  8. Van Den Bergh, F., & Engelbrecht, A. P. (2006). A study of particle swarm optimization particle trajectories, 176(8), 937–971.zbMATHGoogle Scholar
  9. Wakasa, Y., Tanaka, K., & Nishimura, Y. (2010). Control-theoretic analysis of exploitation and exploration of the PSO algorithm. IEEE International Symposium on Computer-Aided Control System Design, IEEE Multi-Conference on Systems and Control (pp. 1807–1812). Yokohama, Japan.Google Scholar
  10. Yasuda, K., Iwasaki, N., Ueno, G., & Aiyoshi, E. (2008). Particle swarm optimization: A numerical stability analysis and parameter adjustment based on swarm activity. IEEJ Transactions on Electrical and Electronic Engineering, Wiley InterScience, 3, 642–659.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Ingeniarius, LtdMealhadaPortugal
  2. 2.Institute of Systems and Robotics (ISR)University of CoimbraCoimbraPortugal
  3. 3.Faculty of Electrical and Computer EngUniversity of IcelandReykjavikIceland

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