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Introducing the fractional-order Darwinian PSO

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Abstract

One of the most well-known bio-inspired algorithms used in optimization problems is the particle swarm optimization (PSO), which basically consists on a machine-learning technique loosely inspired by birds flocking in search of food. More specifically, it consists of a number of particles that collectively move on the search space in search of the global optimum. The Darwinian particle swarm optimization (DPSO) 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. This paper firstly presents a survey on PSO algorithms mainly focusing on the DPSO. Afterward, a method for controlling the convergence rate of the DPSO using fractional calculus (FC) concepts is proposed. The fractional-order optimization algorithm, denoted as FO-DPSO, is tested using several well-known functions, and the relationship between the fractional-order velocity and the convergence of the algorithm is observed. Moreover, experimental results show that the FO-DPSO significantly outperforms the previously presented FO-PSO.

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References

  1. Floreano D., Mattiussi C.: Bio-Inspired Artificial Intelligence: Theories, Methods, and Technologies. MIT Press, Cambridge (2008)

    Google Scholar 

  2. Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the 6th International Symposium Micro Machine and Human Science (MHS), 1995, pp. 39–43 (1995)

  3. Tillett, T., Rao, T.M., Sahin, F., Rao, R.: Darwinian particle swarm optimization. In: Proceedings of the 2nd Indian international conference on artificial intelligence, Pune, Índia, pp. 1474–1487 (2005)

  4. Sabatier, J., Agrawal, O.P., Tenreiro Machado, J.A. (eds.): Advances in Fractional Calculus—Theoretical Developments and Applications in Physics and Engineering. Springer, Berlin. ISBN:978-1-4020-6-0. (2007)

  5. del Valle Y., Venayagamoorthy G.K., Mohagheghi S., Hernandez J.C., Harley R.: Particle swarm optimization: basic concepts, variants and applications in power systems. In: IEEE Trans. Evol. Comput. 12(2), 171–195 (2008)

    Article  Google Scholar 

  6. Tang, J., Zhu, J., Sun, Z.: A novel path panning approach based on appart and particle swarm optimization. In: Proceedings of the 2nd International Symposium on Neural Networks, LNCS 3498, pp. 253–258 (2005)

  7. Pires, E.J.S., Oliveira, P.B.M., Machado, J.A.T., Cunha, J.B.: Particle swarm optimization versus genetic algorithm in manipulator trajectory planning. In: 7th Portuguese Conference on Automatic Control, September 11–13 (2006)

  8. Couceiro, M.S., Mendes, R.M., Ferreira, N.M.F., Machado, J.A.T.: Control Optimization of a Robotic Bird. EWOMS ’09, Lisbon, Portugal, June 4–6 (2009)

  9. Couceiro, M.S., Luz, J.M.A., Figueiredo, C.M., Ferreira, N.M.F.: Modeling and control of biologically inspired flying robots. J. Robotica, Cambridge University Press (2011)

  10. Alrashidi M.R., El-Hawary M.E.: A survey of particle swarm optimization applications in power system operations. Electr. Power Compon. Syst. 34(12), 1349–1357 (2006)

    Article  Google Scholar 

  11. Couceiro, M.S., Luz, J.M.A., Figueiredo, C.M., Ferreira, N.M.F. Dias, G.: Parameter estimation for a mathematical model of the golf putting. In: Marques, V.M., Pereira, C.S., Madureira, A. (eds.) Proceedings of WACI-Workshop Applications of Computational Intelligence. ISEC. IPC. Coimbra. 2 de Dezembro, pp. 1–8. ISSN 978-989-8331-10-6 (2010)

  12. Shi, Y., Eberhart, R.: Fuzzy adaptive particle swarm optimization. In: Proceedings of the In: IEEE Congress Evolutionary Computation, vol. 1, pp. 101–106 (2001)

  13. Secrest, B., Lamont, G.: Visualizing particle swarm optimization—Gaussian particle swarm optimization. In: Proceedings of the In: IEEE Swarm Intelligence Symposium, pp. 198–204 (2003)

  14. Pires E.J.S., Machado J.A.T., Oliveira P.B.M., Cunha J.B., Mendes L.: Particle swarm optimization with fractional-order velocity. J. Nonlinear Dyn. 61, 295–301 (2010)

    Article  MATH  Google Scholar 

  15. Blackwell, T., Bentley, P.: Don’t push me! collision-avoiding swarms. In: Proceedings of the In: IEEE Congress on Evolutionary Computation, vol. 2, pp. 1691–1696 (2002)

  16. Krink, T., Vesterstrom, J., Riget, J.: Particle swarm optimization with spatial particle extension. In: Proceedings of the In: IEEE Congress on Evolutionary Computation, vol. 2, pp. 1474–1479 (2002)

  17. Miranda, V., Fonseca, N.: New evolutionary particle swarm algorithm (EPSO) applied to voltage/VAR control. In: Proceedings 14th Power Systems Computational Conference (2002)

  18. Lovbjerg, M., Krink, T.: Extending particle swarms with self-organized criticality. In: Proceedings of the In: IEEE Congress on Evolutionary Computation, vol. 2, pp. 1588–1593 (2002)

  19. Chia-Feng J.: A hybrid of genetic algorithm and particle swarm optimization for recurrent network design. In: IEEE Trans. Syst. Man Cybern. Part B Cybern. 34(2), 997–1006 (2004)

    Article  Google Scholar 

  20. Angeline, P.: Using selection to improve particle swarm optimization. In: Proceedings of the In: IEEE International Conference Evolutionary Computation, pp. 84–89 (1998)

  21. Zhang, W., Xie, X.: DEPSO: hybrid particle swarm with differential evolution operator. In: Proceedings of the In: IEEE Internatinal Conference Systems, Man, Cybernetics, vol. 4, pp. 3816–3821 (2003)

  22. Kannan S., Slochanal S., Padhy N.: Application of particle swarm optimization technique and its variants to generation expansion problem. ELSERVIER Electr. Power Syst. Res. 70(3), 203–210 (2004)

    Article  Google Scholar 

  23. Couceiro, M.S., Rocha, R.P., Ferreira, N.M.F.: a novel multi-robot exploration approach based on particle swarm optimization algorithms. In: In: IEEE International Symposium on Safety, Security and Rescue Robotics, November 1–5, Kyoto, Japan (2011)

  24. Ortigueira M.D., Tenreiro Machado J.A.: Special issue on fractional signal processing. Signal Process. 83, 2285–2480 (2003)

    Article  Google Scholar 

  25. Machado, J.A.T., Silva, M.F., Barbosa, R.S., Jesus, I.S., Reis, C.M., Marcos, M.G., Galhano, A.F.: Some Applications of Fractional Calculus in Engineering. Hindawi Publishing Corporation Mathematical Problems in Engineering, 2010, 1–34 (2010)

  26. Podlubny I.: Fractional Differential Equations Mathematics in Science and Engineering 198. Academic Press, San Diego (1999)

    Google Scholar 

  27. Debnath L.: Recents applications of fractional calculus to science and engineering. Int. J. Math. Math. Sci. 54, 3413–3442 (2003)

    Article  MathSciNet  Google Scholar 

  28. Elshehawey E.F., Elbarbary E.M.E., Afifi N.A.S., El-Shahed M.: On the solution of the endolymph equation using fractional calculus. Appl. Math. Comput. 124, 337–341 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  29. Camargo R.F., Chiacchio A.O., Oliveira E.C.: Differentiation to fractional orders and the fractional telegraph equation. J. Math. Phys. 49, 033–505 (2008)

    Google Scholar 

  30. Yasuda, K., Iwasaki, N., Ueno, G., Aiyoshi, E.: Particle swarm optimization: a numerical stability analysis and parameter adjustment based on swarm activity. In: IEEJ Transactions on Electrical and Electronic Engineering, vol. 3, pp. 642–659, Wiley InterScience (2008)

  31. Wakasa, Y., Tanaka, K., Nishimura, Y.: Control-theoretic analysis of exploitation and exploration of the PSO algorithm. In: In: IEEE International Symposium on Computer-Aided Control System Design, In: IEEE Multi-Conference on Systems and Control, Yokohama, Japan (2010)

  32. Bergh F.V.den, Engelbrecht A.P.: A study of particle swarm optimization particle trajectories. Inf. Sci. 176(8), 937–971 (2006)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. RoboCorp, Department of Electrotechnics Engineering, Engineering Institute of Coimbra, Coimbra, Portugal

    Micael S. Couceiro & N. M. Fonseca Ferreira

  2. Mobile Robotics Laboratory, Institute of Systems and Robotics, University of Coimbra, Pólo 2, Portugal

    Micael S. Couceiro & Rui P. Rocha

  3. Department of Electrotechnics Engineering, Engineering Institute of Porto, Porto, Portugal

    J. A. Tenreiro Machado

Authors
  1. Micael S. Couceiro
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  2. Rui P. Rocha
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  3. N. M. Fonseca Ferreira
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  4. J. A. Tenreiro Machado
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Correspondence to Micael S. Couceiro.

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Couceiro, M.S., Rocha, R.P., Ferreira, N.M.F. et al. Introducing the fractional-order Darwinian PSO. SIViP 6, 343–350 (2012). https://doi.org/10.1007/s11760-012-0316-2

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  • DOI: https://doi.org/10.1007/s11760-012-0316-2

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