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=item * NOTE: 

    I force people to define all parameters, but guidelines 1-4 are 
    standard and pretty safe.

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=head1 DESCRIPTION OF ALGORITHM

  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.  


=head1 EXPORTED FUNCTIONS

=over 4

=item pso_set_params()

  Sets the particle swarm configuration parameters to use for the search.

=item pso_register_fitness_function()

  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 :)).

=item pso_optimize()

  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()

=item pso_get_solution_array()

  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!).

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