AI::PSO - Module for running the Particle Swarm Optimization algorithm
use AI::PSO; my %params = ( numParticles => 4, # total number of particles involved in search numNeighbors => 3, # number of particles with which each particle will share its progress maxIterations => 1000, # maximum number of iterations before exiting with no solution found dimensions => 4, # number of parameters you want to optimize 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 means more individuality) meMin => 0.0, # 'individuality' minimum random weight meMax => 1.0, # 'individuality' maximum random weight themWeight => 2.0, # 'social' weighting constant (higher means trust group more) themMin => 0.0, # 'social' minimum random weight themMax => 1.0, # 'social' maximum random weight exitFitness => 0.9, # minimum fitness to achieve before exiting verbose => 0, # 0 prints solution # 1 prints (Y|N):particle:fitness at each iteration # 2 dumps each particle (+1) psoRandomRange => 4.0, # setting this enables the original PSO algorithm and # also subsequently ignores the me*/them* parameters ); 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();
I suggest that meWeight and themWeight add up up to 4.0, or that psoRandomRange = 4.0. Also, you should also be setting meMin and themMin to 0, and meMin and themMax to 1 unless you really know what you are doing.
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.
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. Also, I highly suggest you implement a simple fitness cache so you don't end up recomputing fitness values. This can easily be done with a perl hash that is keyed on the string concatenation of the array values passed to your fitness function. Note that these are floating point values, so determine how significant the values are and you can use sprintf to essentially limit the precision of the particle positions.
The number of particles increases cooperation and search space coverage at the expense of compute. Typical applications should suffice using 20-40 particles.
NOTE:
I force people to define all parameters, but guidelines 1-4 are standard and pretty safe.
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 marching of ants, to flocking of birds, to swarming of bees. PSO is a cooperative approach to optimization rather than an evolutionary approach which kills off unsuccessful members of the search team. In the swarm framework each particle, is a relatively unintelligent search agent. It is in the collective sharing of knowledge that solutions are found. Each particle simply 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 dimensionality of the problem hyperspace. So, if you want to optimize three variables, a particle will be three dimensional and will have 3 values that devine its position 3 values that define its velocity. The position of a particle determines how good it is by a user-defined fitness function. The velocity of a particle determines how quickly it changes location. Larger velocities provide more coverage of hyperspace at the cost of solution precision. With large velocities, a particle may come close to a maxima but over-shoot it because it is moving too quickly. With smaller velocities, particles can really hone in on a local solution and find the best position but they may be missing another, possibly even more optimal, solution because a full search of the hyperspace was not conducted. Techniques such as simulated annealing can be applied in certain areas so that the closer a partcle gets to a solution, the smaller its velocity will be so that in bad areas of the hyperspace, the particles move quickly, but in good areas, they spend some extra time looking around. In general, 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 position. As mentioned, 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. In this particluar perl module, the user is able to choose from two implementations of the algorithm. One is the original implementation from I<Swarm Intelligence> which requires the definition of a 'random range' to which the two stochastic weights are required to sum. The other implementation allows the user to define the weighting of how much a particle follows its own path versus following its peers. In both cases there is an element of randomness. 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. If the fitness function is expensive to compute, then it is often useful to start out with a small number of particles first and get a feel for how the algorithm converges. The algorithm implemented in this module is taken from the book I<Swarm Intelligence> by Russell Eberhart and James Kennedy. I highly suggest you read the book if you are interested in this sort of thing.
Sets the particle swarm configuration parameters to use for the search.
Sets the user defined fitness function to call. The fitness function should return a value between 0 and 1. Users may want to look into the sigmoid function [1 / (1+e^(-x))] and it's variants to implement this. Also, you may want to take a look at either t/PSO.t for the simple test or examples/NeuralNetwork/pso_ann.pl for an example on how to train a simple 3-layer feed forward neural network. (Note that a real training application would have a real dataset with many input-output pairs...pso_ann.pl is a _very_ simple example. Also note that the neural network exmaple requires g++. Type 'make run' in the examples/NeuralNetwork directory to run the example. Lastly, the neural network c++ code is in a very different coding style. I did indeed write this, but it was many years ago when I was striving to make my code nicely formatted and good looking :)).
Runs the particle swarm optimization algorithm. This consists of running iterations of search and many calls to the fitness function you registered with pso_register_fitness_function()
By default, pso_optimize() will print out to STDERR the first solution, or the best solution so far if the max iterations were reached. This function will simply return an array of the winning (or best so far) position of the entire swarm system. It is an array of floats to be used how you wish (like weights in a neural network!).
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 AI-PSO-0.86/extradocs/ReactivePower-PSO-wks.pdf http://webapps.calvin.edu/~pribeiro/courses/engr302/Samples/ReactivePower-PSO-wks.pdf
W. Kyle Schlansker kylesch@gmail.com
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
To install AI::PSO, copy and paste the appropriate command in to your terminal.
cpanm
cpanm AI::PSO
CPAN shell
perl -MCPAN -e shell install AI::PSO
For more information on module installation, please visit the detailed CPAN module installation guide.