PSO

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1 September 2009 CITS7212 Computational
Intelligence School of Computer Science and
Software Engineering The University of Western
Australia Maria Bravo Rojas Evgeni Sergeev
PSO Particle Swarm Optimisation A nature-inspired
family of techniques for optimisation

• Outline
• The canonical PSO algorithm.
• Example program PSO in a 1 dimensional space.
• Properties of PSO.
• Topologies and neighbourhoods.
• PSO and evolutionary techniques.
• PSO and non-evolutionary techniques.
• Applications.

See slide notes (on some of the slides).
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Also Bare-bones PSO.
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Research and development in PSO
NEIGHBOURHOODS AND PARAMETERS
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PSO parameters

• Dynamic update of the particles velocity
• vid vid c1rand()(pid-xid)
  c2Rand()(pgd-xid)
• Momentum Cognitive part
  Social part
• Update of the flying particles position
• xid xid vid

• Inertia weight
• vid wvid c1rand()(pid-xid)
  c2Rand()(pgd-xid)
• xid xid vid
• Large inertia weights facilitates global search
• Small inertia weights facilitates local search
• Constriction coefficient Tries to insure
  convergence in the PSO
• vid k vid c1rand()(pid-xid)
  c2Rand()(pgd-xid)
• xid xid vid

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lbest neighbourhood (k 2)
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2
3
4
5
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8

• Each individuals neighbourhood contains itself
  and its two adjacent neighbours.
• The first and last are connected.

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lbest neighbourhood (k 2)
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2
4
3
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0.72
0.33
0.54

• Individual 3 has found the best position so far
  in 4s neighbourhood.
• 4s velocity will be adjusted toward 3s
  previous best position and 4s own previous best
  position.

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gbest neighbourhood

• Assuming that 3 has found the best fitness so
  far in the entire population, all others
  velocities will be attracted toward its previous
  best position.

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Research and development in PSO
TOPOLOGIES
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Circle topology
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Wheel topology
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Using Cluster centers as substitutes for the bests
Cluster B
Cluster A
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Research and development in PSO
HYBRID ALGORITHMS
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PSO and other Evolutionary Computation Techniques

• Selection -gt Particles with the best
  performance are copied into the next generation.
• Crossover -gt Information can be swapped between
  two individuals to have the ability to fly to
  the new search area.
• Mutation -gt Increases the diversity of the
  population and the ability to escape the local
  minima.

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PSO and other Evolutionary Algorithms

• PSO or Genetic Algorithms.
• Ant colony optimization PSO.
• Differential evolution PSO.

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PSO and non-Evolutionary Computation Techniques

• Cooperative PSO
• PSO deflection/stretching/repulsion techniques
• PSO negative entropy

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Research and development in PSO
APPLICATIONS
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The EED problem and other applications

• Multi-objective optimisation
• Constrained optimisation
• Min max
• Dynamic tracking
• Weight and structure evolution of neural
  networks / human tremor analysis / 3D-to-3D
  biomedical images registration.

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References (1)
J. Kennedy and R. Eberhart. Particle swarm
optimization. In Proceedings of the IEEE
International Conference on Neural Networks,
pages 1942-1948, IEEE Press, Piscataway, NJ,
1995. The original PSO paper. Description of
algorithm and discussion of its development. J.
Kennedy and R. Eberhart. Swarm Intelligence.
Morgan Kaufmann, San Francisco, CA, 2001. Book of
broad and PSO-specific discussion. Binary
(discrete) PSO, continuous PSO, hybrid PSO,
topologies. M. Clerc and J. Kennedy. The
particle swarm-explosion, stability and
convergence in a multidimensional complex space.
IEEE Transactions on Evolutionary Computation,
6(1)58-73, 2002. M. Dorigo., M. A. Montes de
Oca and A. Engelbrecht (2008) Particle swarm
optimization. Scholarpedia, 3(11)1486. URL
http//www.scholarpedia.org/article/Particle_swarm
_optimization More references are available on
this page.
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References (2)
Yuhui S. Particle swarm optimization. Feature
article, IEEE Neural Networks Society. February,
8-13, 2004. Parsopoulos, K. E. Plagianakos et
al. Improving the Particle Swarm Optimizer by
Function Stretching in Nonconvex optimization
and its applications, pages 445-458 Volume 54,
Kluwer Academic Publishers, Netherlands ,
2001. JiejinCai et al. A multi-objective
chaotic particle swarm optimization for
environmental/economic dispatch in Energy
Conversion and Management, pages 1318-1325 Volume
50, Issue 5, United Kingdom, May 2009. Xuanping
Zhang et al, A Modified Particle Swarm Optimizer
for Tracking Dynamic Systems In Advances in
Natural Computation, pages 592-601 Volume 3612,
Publisher Springer Berlin / Heidelberg ,
2005. Xiao-FengXie, Wen-Jun Zhang, Zhi-Lian
Yang. Dissipative particle swarm optimization
in Proceedings of the 2002 Congress on
Evolutionary Computation, pages 1456-1461 Volume
2, Honolulu, USA.
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References (3)
Parsopoulos, K.E., Vrahatis, M.N. On the
computation of all global minimizers through
particle swarm optimization in IEEE Transactions
on Evolutionary Computation, pages 211-224 Volume
8, Issue 3, USA, June 2004. El-Abd?Mohammed,?
Kamel?Mohamed S. A taxonomy of cooperative
particle swarm optimizers in International
Journal of Computational Intelligence Research,
pages 137-144 Volume 4, Issue 2-4, 2008. URL
http//www.ijcir.com/publishedPapers.php?volume4
number2volume_id5number_id16