Changes between Version 3 and Version 4 of Documentation/Reference/Particle Swarm Optimization
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 03/31/11 13:42:09 (11 years ago)
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Documentation/Reference/Particle Swarm Optimization
v3 v4 1 1 = Particle Swarm Optimization = 2 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.2 Particle swarm optimization (PSO) is a stochastic populationbased optimization algorithm that was first introduced by Kennedy and Eberhart. Members of the population (= swarm) are called particles. Each particle moves around in the search space, taking advantage of the particle’s own experience and the experience of the particle’s neighbours or of the whole swarm to guide the search. A great introduction to PSOs can be found in [#References (Kennedy and Eberhart, 2001)]. 3 3 4 4 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]]. … … 25 25 26 26 === Local vs. Global PSO === 27 Topology initializers group the particles into neighborhoods according to a certain strategy.27 In the (standard) global PSO, all the particles are neighbors of each other. Therefore the position of the global best particle is propagated to the whole swarm and affects the velocity update. If the current global optimum is not close to the best solution, it may become impossible for the swarm to explore other areas of the search space. Generally speaking, global PSOs usually converge faster and get trapped in local optima more easily. 28 28 29 So far, the following topologies have been implemented: 29 In local PSO variants, particles are grouped into neighborhoods according to a certain strategy. In this variant only the neighbor particles of a given particle can influence its velocity update. Consequently, local PSOs (with topologies) converge slower than global PSOs but are less likely to be captured in local minima due to greater population diversity. 30 31 So far, the following neighborhood topologies have been implemented: 30 32 * `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. 31 33 * `RingTopologyInitializer`: Every particle is connected with its preceeding and its following particle. 32 34 * `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. 33 35 34 If you want to implement your own topology, you must inherit from `ITopologyInitializer` or derive from the base class `TopologyInitializer`. 36 [#References (Kennedy and Mendes, 2002)] investigated the impact of different topologies on algorithm performance. They found that the global PSO was quick to converge but yielded the worst results. Circular and weel topologies improved the results moderately and using the Von Neumann topology produed the best results. 37 38 39 The topologies are static and do not change during algorithm execution, once they have been initialized. If you want to implement your own topology, you must inherit from `ITopologyInitializer` or derive from the base class `TopologyInitializer`. 35 40 36 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:37 * Global PSO: quick to converge, worst results38 * Circular Topology: moderate results39 * Wheel Topology: moderate results40 * Von Neumann Topology: best results41 41 42 42 === Parameter Adjustment === … … 46 46 '''Parameter Tuning ''' 47 47 48 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.48 A recent paper by [#References (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. 49 49 50 50 '''Velocity Bounds''' … … 61 61 62 62 '''Topology Updaters''' 63 * `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).63 * `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 [#References (Liang and Suganthan 2005)]. 64 64 65 65 === Is there a sample/tutorial? === 66 66 67 We are currently preparing one. Please stay tuned.67 A global PSO with dynamically updated inertia and velocity bounds has been implemented for the Schwefel test function. Details and parameter settings: 68 68 69 70 [UsersSamples#GPAA Particle Swarm Optimization + Schwefel Test Function] 71 72 [=#References] 69 73 === References: === 70 74 * Kennedy, J. and Eberhart, R.C., 2001. Swarm Intelligence. Morgan Kaufmann. ISBN 1558605959.