NAME
PSO - Perl module for running the Particle Swarm Optimization algorithm
SYNOPSIS
use AI::PSO;
my %params = (
numParticles => 4, # total number of particles involved in search (there is a trade-off between cooperation and time here if the fitness function takes a while...)
numNeighbors => 3, # number of particles that each particle will share its progress with (degree of cooperation)
maxIterations => 1000, # maximum number of iterations before exiting with no solution found
dimensions => 4, # this must be the number of parameters you want to optimize (it will also be the size of the array passed to your fitness function)
deltaMin => -4.0, # minimum change in velocity during PSO update
deltaMax => 4.0, # maximum change in velocity during PSO update
meWeight => 2.0, # 'individuality' weighting constant (higher weight (than group) means trust individual more, neighbors less)
meMin => 0.0, # 'individuality' minimum random weight (this should really be between 0, 1)
meMax => 1.0, # 'individuality' maximum random weight (this should really be between 0, 1)
themWeight => 2.0, # 'social' weighting constant (higher weight (than individual) means trust group more, self less)
themMin => 0.0, # 'social' minimum random weight (this should really be between 0, 1)
themMax => 1.0, # 'social' maximum random weight (this should really be between 0, 1)
exitFitness => 1.0, # minimum fitness to achieve before exiting (if maxIterations is reached before, then program will exit with no solution)
verbose => 0, # 0 prints solution, 1 prints particle:fitness at each iteration, 2 dumps each particle (+1)
);
sub custom_fitness_function(@input) {
# this is a callback function. @input will be passed to this, you do not need to worry about setting it...
# ... do something with @input which is an array of floats
# return a value in [0,1] with 0 being the worst and 1 being the best
}
pso_set_params(\%params);
pso_register_fitness_function('custom_fitness_function');
pso_optimize();
my @solutionArray = pso_get_solution_array();
--- general guidelines ---
1. I suggest that meWeight and themWeight add up up to 4.0
2. If you have a large search space, increasing deltaMin and deltaMax and delta max can help cover more area
Conversely, if you have a small search space, then decreasing them will fine tune the search.
3. You really should set meMin and themMin to 0, and meMin and themMin to 1 unless you know what you are doing.
4. I've personally found that using a global (fully connected) topology where each particle is neighbors with
all other particles (numNeighbors == numParticles - 1) converges more quickly. However, this will drastically
increase the number of calls to your fitness function. So, if your fitness function is the bottleneck, then
you should tune this value for the appropriate time/accuracy trade-off.
5. The number of particles also increases cooperation and search space coverage at the expense of compute.
Typical applications should suffice using 20-40 particles.
* I force people to define all parameters, but guidelines 1-3 are standard and pretty safe.
DESCRIPTION
Particle Swarm Optimization is an optimization algorithm designed by Russell Eberhart and James Kennedy from Purdue University. The algorithm itself is based off of the emergent behavior among societal groups ranging from ants, to flocking of birds, to swarming of bees.
It is a cooperative approach to optimization. Instead of an evolutionary approach which kills off unsuccessful members of the search team, each particle in PSO shares its information with its neighboring particles. So, if one particle is not doing to well (has a low fitness), then it looks to its neighbors for help and tries to be more like them while still maintaining a sense of individuality.
A particle is defined by its position and velocity. The parameters a user wants to optimize define the dimension of the problem hyperspace. So, if you want to optimize three variables, a particle will be three dimensional and will have 3 position values, 3 velocity values etc.
Particles fly around the problem hyperspace looking for local/global maxima. At each position, a particle computes its fitness. If it does not meet the exit criteria then it gets information from neighboring particles about how well they are doing. If a neighboring particle is doing better, then the current particle tries to move closer to its neighbor by adjusting its weights. The velocity controls how quickly a particle changes location in the problem hyperspace. There are also some stochastic weights involved in the positional updates so that each particle is truly independent and can take its own search path while still incorporating good information from other particles.
Solution convergence is quite fast once one particle becomes close to a local maxima. Having more particles active means there is more of a chance that you will not be stuck in a local maxima. Often times different neighborhoods (when not configured in a global neighborhood fashion) will converge to different maxima. It is quite interesting to watch graphically.
The algorithm implemented in this module is taken from the book Swarm Intelligence by Russell Eberhart and James Kennedy. I highly suggest you read the book if you are interested in this sort of thing. There are a few minor implementation changes I have made, but the heart of the algorithm is as stated in the book.
EXPORT
pso_set_params() pso_register_fitness_function() pso_optimize() pso_get_solution_array()
SEE ALSO
1. Swarm intelligence by James Kennedy and Russell C. Eberhart. ISBN 1-55860-595-9
2. A Hybrid Particle Swarm and Neural Network Approach for Reactive Power Control http://webapps.calvin.edu/~pribeiro/courses/engr302/Samples/ReactivePower-PSO-wks.pdf
AUTHOR
W. Kyle Schlansker kylesch@gmail.com
COPYRIGHT AND LICENSE
Copyright (C) 2006 by W. Kyle Schlansker
This code is released under the Mozilla Public License Version 1.1. A copy of this license may be found along with this module or at: http://www.mozilla.org/MPL/MPL-1.1.txt