26 | | '''References:''' |
| 29 | So far, the following topologies have been implemented: |
| 30 | * `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 | * `RingTopologyInitializer`: Every particle is connected with its preceeding and its following particle. |
| 32 | * `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 | |
| 34 | If you want to implement your own topology, you must inherit from `ITopologyInitializer` or derive from the base class `TopologyInitializer`. |
| 35 | |
| 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 results |
| 38 | * Circular Topology: moderate results |
| 39 | * Wheel Topology: moderate results |
| 40 | * Von Neumann Topology: best results |
| 41 | |
| 42 | === Parameter Adjustment === |
| 43 | |
| 44 | 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. |
| 45 | |
| 46 | '''Parameter Tuning ''' |
| 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. |
| 49 | |
| 50 | '''Velocity Bounds''' |
| 51 | 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. |
| 52 | * large velocity --> global exploration |
| 53 | * small velocity --> local exploitation |
| 54 | |
| 55 | '''Inertia Weight''' |
| 56 | 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). |
| 57 | |
| 58 | It is possible to let the algorithm adjust some parameters dynamically during runtime. |
| 59 | * 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. |
| 60 | * 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. |
| 61 | |
| 62 | '''Topology Updaters''' |
| 63 | * `MultiPSOTopologyUpdater`: The whole population is divided into `NrOfSwarms` non-overlapping sub-swarms. Neighborhood topology is dynamic and randomly assigned. Swarms are re-grouped every regroupingPeriod iteration. The operator is implemented as described in (Liang and Suganthan 2005). |
| 64 | |
| 65 | === Is there a sample/tutorial? === |
| 66 | |
| 67 | We are currently preparing one. Please stay tuned. |
| 68 | |
| 69 | === References: === |