Version 3 (modified by mkofler, 11 years ago) (diff) 

Particle Swarm Optimization
Particle swarm optimization (PSO) is a stochastic populationbased optimization algorithm that was first introduced by Kennedy and Eberhart. Members of the population are called particles. Each particle moves in search space, taking advantage of the particle’s own experience and the experience of the particle’s neighbours or the experience of the whole swarm.
Our particle swarm optimization algorithm has been designed to work with arbitrary solution encodings. However, so far a concrete implementation is only available for real vector encoded problems, i.e. Single Objective Test Function.
Algorithm Parameters:
Parameter  Description 

Analyzer  The operator used to analyze each generation. 
Inertia  Inertia weight on a particle's movement (omega). Default: 0.2 
InertiaUpdater  Updates the omega parameter. 
MaxIterations  The maximum number of iterations which should be processed. Default: 1000 
MutationProbability  The probability that the mutation operator is applied on a solution. 
Mutator  The operator used to mutate solutions. 
NeighborBestAttraction  Weight for pull towards the neighborhood best solution or global best solution in case of a totally connected topology (phi_g). Default: 3.7 
ParticleCreator  Operator creates a new particle. 
ParticleUpdater  Operator that updates a particle. 
PersonalBestAttraction  Weight for particle's pull towards its personal best soution (phi_p). Default: 0.01 
Population Size  The size of the population of solutions. 
Seed  The random seed used to initialize the new pseudo random number generator. Default: 0 
SetSeedRandomly  True if the random seed should be set to a random value, otherwise false. Default: true 
SwarmSize  Size of the particle swarm. Default: 10 
SwarmUpdater  Encodingspecific parameter which is provided by the problem. May provide additional encodingspecific parameters, such as velocity bounds for real valued problems. 
TopologyInitializer  Creates neighborhood description vectors. 
TopologyUpdater  Updates the neighborhood description vectors. 
Local vs. Global PSO
Topology initializers group the particles into neighborhoods according to a certain strategy.
So far, the following topologies have been implemented:
 RandomTopologyInitializer: Randomly connectes every particle with NroOfParticles other particles. Neighborhood connections are not symmetric, meaning if particle A is a neighbor of particle B, particle B does not necessarily have to be a neighbor of particle A. The default NroOfParticles is 3.
 RingTopologyInitializer: Every particle is connected with its preceeding and its following particle.
 VonNeumannTopologyInitializer: Every particle is connected with the two following and the two previous particles, wrapping around at the beginning and the end of the population.
If you want to implement your own topology, you must inherit from ITopologyInitializer or derive from the base class TopologyInitializer. In general local PSOs (with topologies) converge slower than global PSOs but are less likely to be captured in local minima due to greater population diversity. (Kennedy and Mendes, 2002) investigated the impact of different topologies on algorithm performance. The found that:
 Global PSO: quick to converge, worst results
 Circular Topology: moderate results
 Wheel Topology: moderate results
 Von Neumann Topology: best results
Parameter Adjustment
Like many other metheuristics, the PSO algorithm frequently faces the problems of being trapped in local optima. Balancing the global exploration and local exploitation abilities of PSO is therefore very important.
Parameter Tuning
A recent paper by (Pedersen 2010) provides a most helpful table of PSO parameters that have been tuned for different optimization scenarios. We recommend them as a first starting point when optimizing new problems. Some of the settings (like using a negative inertia weight) may seem quirky, but we also got some very good results with those settings.
Velocity Bounds Another is to adjust the minimum/maximum velocity bounds vector. Particle velocities on each dimension are clamped to a certain velocity range. The parameter VelocityBounds controls the maximum global exploration ability of PSO.
 large velocity > global exploration
 small velocity > local exploitation
Inertia Weight The inertia weight parameter was introduced in 1998 by Shi and Eberhart. The idea was to use a maximum velocity ad set the velocity bounds to One common strategy is to adjust the inertia weight dynamically during the optimization run (via fuzzy optimization, by linear decreasing or increasing or randomizing the parameter).
It is possible to let the algorithm adjust some parameters dynamically during runtime.
 Inertia Weight: Configure the InertiaUpdater to adjust the inertia weight. You can select any operator that implements IDiscreteDoubleValueModifier. The standard Simulated Annealing annealing operators (exponential, square root, linear, quadratic increase/decrease) can be used.
 Velocity Vector: In the SwarmUpdater the velocity vector can be likewise adjusted. Please note that do so far only use one IDiscreteDoubleValueModifier for all vector dimensions, therefore the value (but not the sign) of all dimensions will be equal.
Topology Updaters
 MultiPSOTopologyUpdater: The whole population is divided into NrOfSwarms nonoverlapping subswarms. Neighborhood topology is dynamic and randomly assigned. Swarms are regrouped every regroupingPeriod iteration. The operator is implemented as described in (Liang and Suganthan 2005).
Is there a sample/tutorial?
We are currently preparing one. Please stay tuned.
References:
 Kennedy, J. and Eberhart, R.C., 2001. Swarm Intelligence. Morgan Kaufmann. ISBN 1558605959.
 Kennedy, J. and Mendes, 2002. R. Population structure and particle swarm performance. Congress on Evolutionary Computation, pp. 16711676.
 Liang, J.J. and Suganthan, P.N., 2005. Dynamic multiswarm particle swarm optimizer. IEEE Swarm Intelligence Symposium, pp. 124129.
 Pedersen, M.E.H., 2010.  Good parameters for particle swarm optimization. Technical Report HL1001 (Hvass Laboratories)
Attachments (4)

PSO_InertiaUpdater.png
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Screenshot of the inertia updater
 PSO_SwarmUpdater.png (35.6 KB)  added by mkofler 11 years ago.

PSO_Topologies.png
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added by mkofler 11 years ago.
Added illustration of PSO topologies

PSO_Regrouping.png
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added by mkofler 11 years ago.
MultiPSO  Regrouping of subswarms
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