Origin of bursts

The phenomenon of particle bursts, a well-known feature of PSO is investigated. Their origin is concluded to lie in multiplicative stochasticity, previously encountered in the study of first order stochastic difference equations. The work here demonstrates that bursts contribute to fattening of the tail of the particle position distribution and that these tails are well described by power laws. It is argued that recombinant PSO, a competitive PSO variant without multiplicative randomness, is burst-free.

[1]  George Kingsley Zipf,et al.  Human behavior and the principle of least effort , 1949 .

[2]  Frans van den Bergh,et al.  An analysis of particle swarm optimizers , 2002 .

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

[4]  J. Kennedy,et al.  Neighborhood topologies in fully informed and best-of-neighborhood particle swarms , 2003, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[5]  E. Ott.  Chaos in Dynamical Systems: Contents , 1993 .

[6]  D. Broomhead,et al.  Exact analysis of the sampling distribution for the canonical particle swarm optimiser and its convergence during stagnation , 2007, GECCO '07.

[7]  Rui Mendes,et al.  Neighborhood topologies in fully informed and best-of-neighborhood particle swarms , 2006 .

[8]  James Kennedy,et al.  Defining a Standard for Particle Swarm Optimization , 2007, 2007 IEEE Swarm Intelligence Symposium.

[9]  D. Sornette.  Multiplicative processes and power laws , 1997, cond-mat/9708231.

[10]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986, Encyclopedia of Big Data.

[11]  Andries Petrus Engelbrecht,et al.  Fundamentals of Computational Swarm Intelligence , 2005 .

[12]  Riccardo Poli,et al.  Continuous optimisation theory made easy? finite-element models of evolutionary strategies, genetic algorithms and particle swarm optimizers , 2007, FOGA'07.

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

[14]  Sidney Redner,et al.  Random Multiplicative Processes and Multifractals , 1988 .

[15]  D. Sornette.  MECHANISM FOR POWERLAWS WITHOUT SELF-ORGANIZATION , 2001, cond-mat/0110426.

[16]  E. Ozcan,et al.  Particle swarm optimization: surfing the waves , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[17]  Tim Blackwell,et al.  Understanding particle swarms through simplification: a study of recombinant PSO , 2007, GECCO '07.

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

[19]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[20]  Tim M. Blackwell,et al.  The Lévy Particle Swarm , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[21]  M. Newman.  Power laws, Pareto distributions and Zipf's law , 2005 .

[22]  Sidney Redner,et al.  Random multiplicative processes: An elementary tutorial , 1990 .

[23]  D. Sornette,et al.  Convergent Multiplicative Processes Repelled from Zero: Power Laws and Truncated Power Laws , 1996, cond-mat/9609074.

[24]  Andres Upegui,et al.  Particle Swarm Optimization with Discrete Recombination: An Online Optimizer for Evolvable Hardware , 2006, First NASA/ESA Conference on Adaptive Hardware and Systems (AHS'06).

[25]  Tang,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.