particle-swarm-optimization
Particle Swarm Optimization
The purpose of this project is to show the use of PSO (Particle Swarm Optimization) methods in minimization problems. This particular example is focused on finding the minimal value of a function. It is applied only for two dimensional functions (which made possible to graphically represent algorithm’s execution) but can be extended to any number of dimensions. Used functions:
- Sphere
- Griewangk
- Rastrigin
- Rosenbock
For more details (formula/representation) on optimisation functions (including the used ones) consult this Wiki page.
Another swarm intelligence based algorithm can be found here - Ant Colony Optimization.
Solution
By running the application it can be seen that the system is initialized with a randomly placed particles - which represents the initial solution in the function’s visible domain. It tries to improve the solution gradually moving each particle closer to a possible solution. Eventually all particles will gather in a single point representing the minimal value.
Interface
There is a graphical representation of the problem on the left side and control panel on the right.
Graphic
The functions origin is in the middle of the image, the color represents function value taking each points coordinates as input values, the dots represent the particles.
Control
Parameters:
- Population size - particles number
- Delay - small freeze time used in simulation
- Optimization function - mentioned above
- Algorithm
- Base - particle’s position shifting is determined equaly by all other particles
- Initial weight - in addition to base case it adds a coefficient to the previous shifting (other way said it sets previous step position importance)
- Constriction factor - the entire formula from base case is scaled by a factor
- Topology
- Full - each particle is affected by the entire population
- Ring - each particle is affected only by two neigbours
- 4-neighbours - each particle is affected by 4 neighbours
- Coeficients
- φ1 - individual influence (how much te movement is affected by individual position)
- φ2 - social infuence (how much te movement is affected by other’s particles position)
- w/ψ - initial weight or constriction factor (depending on selected algorithm)
Best result is displayed on the bottom.