The Generalized PSO: A New Door to PSO
Evolution

Fernández Martínez, J. L.; García Gonzalo, E.

doi:https://doi.org/10.1155/2008/861275

Journal of Artificial Evolution and Applications

On this page

Abstract References Copyright Related Articles

Special Issue

Particle Swarms: The Second Decade

View this Special Issue

Research Article | Open Access

Volume 2008 | Article ID 861275 | https://doi.org/10.1155/2008/861275

The Generalized PSO: A New Door to PSO Evolution

J. L. Fernández Martínez¹and E. García Gonzalo¹

Academic Editor: Riccardo Poli

Received20 Jul 2007

Revised15 Jan 2008

Accepted24 Feb 2008

Published12 May 2008

Abstract

A generalized form of the particle swarm optimization (PSO) algorithm is presented. Generalized PSO (GPSO) is derived from a continuous version of PSO adopting a time step different than the unit. Generalized continuous particle swarm optimizations are compared in terms of attenuation and oscillation. The deterministic and stochastic stability regions and their respective asymptotic velocities of convergence are analyzed as a function of the time step and the GPSO parameters. The sampling distribution of the GPSO algorithm helps to study the effect of stochasticity on the stability of trajectories. The stability regions for the second-, third-, and fourth-order moments depend on inertia, local, and global accelerations and the time step and are inside of the deterministic stability region for the same time step. We prove that stability regions are the same under stagnation and with a moving center of attraction. Properties of the second-order moments variance and covariance serve to propose some promising parameter sets. High variance and temporal uncorrelation improve the exploration task while solving ill-posed inverse problems. Finally, a comparison is made between PSO and GPSO by means of numerical experiments using well-known benchmark functions with two types of ill-posedness commonly found in inverse problems: the Rosenbrock and the “elongated” DeJong functions (global minimum located in a very flat area), and the Griewank function (global minimum surrounded by multiple minima). Numerical simulations support the results provided by theoretical analysis. Based on these results, two variants of Generalized PSO algorithm are proposed, improving the convergence and the exploration task while solving real applications of inverse problems.

References

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks (ICNN '95), vol. 4, pp. 1942–1948, Perth, WA, Australia, November-December 1995.
View at: Publisher Site | Google Scholar
M. Clerc and J. Kennedy, “The particle swarm—explosion, stability, and convergence in a multidimensional complex space,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 1, pp. 58–73, 2002.
View at: Publisher Site | Google Scholar
E. Ozcan and C. K. Mohan, “Particle swarm optimization: surfing the waves,” in Proceedings of the Congress on Evolutionary Computation (CEC '99), vol. 3, pp. 1939–1944, Washington, DC, USA, July 1999.
View at: Publisher Site | Google Scholar
I. C. Trelea, “The particle swarm optimization algorithm: convergence analysis and parameter selection,” Information Processing Letters, vol. 85, no. 6, pp. 317–325, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
Y.-L. Zheng, L.-H. Ma, L.-Y. Zhang, and J.-X. Qian, “On the convergence analysis and parameter selection in particle swarm optimisation,” in Proceedings of the 2nd International Conference on Machine Learning and Cybernetics (ICMLC '03), vol. 3, pp. 1802–1807, Xi'an, China, November 2003.
View at: Publisher Site | Google Scholar
F. van den Bergh and A. P. Engelbrecht, “A study of particle swarm optimization particle trajectories,” Information Sciences, vol. 176, no. 8, pp. 937–971, 2006.
View at: Publisher Site | Google Scholar | MathSciNet
V. Kadirkamanathan, K. Selvarajah, and P. J. Fleming, “Stability analysis of the particle dynamics in particle swarm optimizer,” IEEE Transactions on Evolutionary Computation, vol. 10, no. 3, pp. 245–255, 2006.
View at: Publisher Site | Google Scholar
B. Brandstätter and U. Baumgartner, “Particle swarm optimization—mass-spring system analogon,” IEEE Transactions on Magnetics, vol. 38, no. 2, pp. 997–1000, 2002.
View at: Publisher Site | Google Scholar
J. L. Fernández Martínez, E. García Gonzalo, and J. P. Fernández Alvarez, “Theoretical analysis of particle swarm trajectories through a mechanical analogy,” International Journal of Computational Intelligence Research, vol. 4, no. 2, 2008.
View at: Google Scholar
S. M. Mikki and A. A. Kishk, “Physical theory for particle swarm optimisation,” Progress in Electromagnetics Research, vol. 75, pp. 171–207, 2007.
View at: Publisher Site | Google Scholar
M. Clerc, “Stagnation analysis in particle swarm optimization or what happens when nothing happens,” Department of Computer Science, University of Essex, Colchester, UK, 2006, http://clerc.maurice.free.fr/pso/.
View at: Google Scholar
R. Poli, “The sampling distribution of particle swarm optimisers and their stability,” Department of Computer Science, University of Essex, Colchester, UK, 2007, http://cswww.essex.ac.uk/technical-reports/2007/csm-465.pdf.
View at: Google Scholar
J. P. Fernández Alvarez, J. L. Fernández Martínez, E. García Gonzalo, and C. O. Menéndez Pérez, “Application of the particle swarm optimization algorithm to the solution and appraisal of the vertical electrical sounding inverse problem,” in Proceedings of the 11th Annual Conference of the International Association of Mathematical Geology (IAMG '06), Liège, Belgium, September 2006.
View at: Google Scholar
J. P. Fernández Alvarez, J. L. Fernández Martínez, and C. O. Menéndez Pérez, “Feasibility analysis of the use of binary genetic algorithms as importance samplers application to a geo-electrical VES inverse problem,” Mathematical Geosciences, 2008.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2008 J. L. Fernández Martínez and E. García Gonzalo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies

Views

1704

Downloads

0

Citations