The Lévy Particle Swarm

Many foragers and wandering animals have been shown to follow a Levy distribution of steps and it is conjectured here that this distribution may be useful for optimization algorithms too. This paper investigates the effectiveness of replacing the particle dynamics within particle swarm optimization (PSO) by random sampling from a Levy distribution. The resulting Levy PSO is demonstrated to perform as well, or better, than a standard PSO or equivalent Gaussian models over a range of benchmark problems.

[1]  M. Levandowsky,et al.  Swimming behavior and chemosensory responses in the protistan microzooplankton as a function of the hydrodynamic regime , 1988 .

[2]  R. Mantegna,et al.  Fast, accurate algorithm for numerical simulation of Lévy stable stochastic processes. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  B. Cole.  Fractal time in animal behaviour: the movement activity of Drosophila , 1995, Animal Behaviour.

[4]  P. A. Prince,et al.  Lévy flight search patterns of wandering albatrosses , 1996, Nature.

[5]  M. Levandowsky,et al.  Chemosensory Responses of Acanthamoeba castellanii: Visual Analysis of Random Movement and Responses to Chemical Signals , 1996, The Journal of eukaryotic microbiology.

[6]  O. Kallenberg.  Foundations of Modern Probability , 2021, Probability Theory and Stochastic Modelling.

[7]  H. Stanley,et al.  Optimizing the success of random searches , 1999, Nature.

[8]  M. Clerc,et al.  The swarm and the queen: towards a deterministic and adaptive particle swarm optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[9]  H. Stanley,et al.  Statistical physics of random searches , 2001 .

[10]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[11]  James Kennedy,et al.  Bare bones particle swarms , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[12]  Gary B. Lamont,et al.  Visualizing particle swarm optimization - Gaussian particle swarm optimization , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[13]  James Kennedy,et al.  Probability and dynamics in the particle swarm , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[14]  Xin Yao,et al.  Evolutionary programming using mutations based on the Levy probability distribution , 2004, IEEE Transactions on Evolutionary Computation.

[15]  O Bénichou,et al.  Optimal search strategies for hidden targets. , 2005, Physical review letters.