NAME

PDL::Opt::ParticleSwarm - Particle Swarm Optimization (object oriented)

SYNOPSIS

use PDL::Opt::ParticleSwarm;

my $pso = PDL::Opt::ParticleSwarm->new (
    -fitFunc    => \&calcFit,
    -dimensions => 1,
    );

my $bestFit        = $pso->optimize();
my $bestPos        = $pso->getBestPos();

print "Fit $bestFit at $bestPos\n";

sub calcFit {
    my $vec = shift;
    my $x = $vec->slice('(0)');

    # The parabola (x+3)^2 - 5 has a minima at x=-3:
    return (($x+3)**2 - 5);
}

Description

The Particle Swarm Optimization technique uses communication of the current best position found between a number of particles moving over a hyper surface as a technique for locating the best location on the surface (where 'best' is the minimum of some fitness function). For a Wikipedia discussion of PSO see http://en.wikipedia.org/wiki/Particle_swarm_optimization.

This pure Perl module is an implementation of the Particle Swarm Optimization technique for finding minima of hyper surfaces using the PDL module for accelerated vector calculations. It presents an object oriented interface that facilitates easy configuration of the optimization parameters and (in principle) allows the creation of derived classes to reimplement all aspects of the optimization engine (a future version will describe the replaceable engine components).

This implementation allows communication of a local best point between a selected number of neighbours.

This module and its documentation is based on AI::ParticleSwarmOptimization by Peter Jaquiery to support PDL objects and additional features such as search space scaling and initial guess options.

Methods

PDL::Opt::ParticleSwarm provides the following public methods. The parameter lists shown for the methods denote optional parameters by showing them in [].

new(%parameters)

Create an optimization object. The following parameters may be used:

-initialGuess: a vector of initial "best" values to start with.

This must be a PDL object. As long as it is correctly broadcasts, this can take any PDL representation.

-searchSize: a scalar multiple to control the search distance from -initialGuess

For example, if your initialGuess is "5", posMin/posMax range is 0-10, and searchSize is 0.5 then it will initialize the particles to search in the region between 2.5 and 7.5.

If undefined, then search the entire space between posMin and posMax

Default value: undef

-dimensions: positive number, semi-required

The number of dimensions of the hypersurface being searched. This can be omitted if -intitialGuess is provided.

-exitFit: number, optional

If provided, -exitFit allows early termination of optimize if the fitness value becomes equal or less than -exitFit.

-fitFunc: required

-fitFunc is a reference to the fitness function used by the search. If extra parameters need to be passed to the fitness function an array ref may be used with the code ref as the first array element and parameters to be passed into the fitness function as following elements. User provided parameters are passed as the first parameters to the fitness function when it is called:

    my $pso = PDL::Opt::ParticleSwarm->new (
		fitFunc    => [\&calcFit, $context],
		dimensions => 3,
        );

    ...

    sub calcFit {
        my ($context, $pdl_vec_to_optimize) = @_;
		... do something with $pdl_vec_to_optimize
		return $fitness;
        }

In addition to any user provided parameters the list of values representing the current particle position in the hyperspace is passed in. There is one value per hyperspace dimension.

-logFunc: log function callback, optional

This function is called after each iteration with the current bestPos and bestFit values as follows:

$self->{logFunc}->($self->getBestPos(), $self->getBestFit());

-inertia: positive or zero number, optional

Determines what proportion of the previous velocity is carried forward to the next iteration. This can be a PDL object, so it should work in any dimension so long as it works in the broadcast sense.

Defaults to 0.9

See also -inertia and -themWeight.

-numNeighbors: positive number, optional

Number of local particles considered to be part of the neighbourhood of the current particle.

Defaults to the square root of the total number of particles.

Background: "The basic version of the algorithm uses the global topology as the swarm communication structure [when (numNeighbors=numParticles-1)]. This topology allows all particles to communicate with all the other particles, thus the whole swarm share the same best position from a single particle. However, this approach might lead the swarm to be trapped into a local minimum." [ https://en.wikipedia.org/wiki/Particle_swarm_optimization ]

Thus, as numNeighbors approaches numParticles-1, there is a greater risk of getting stuck in a local minima.

The neighbor selection algorithm in PDL::Opt::ParticleSwarm uses numNeighbors particles following the Nth particle index in the particle piddle being evaluated for its neighbors. The term "neighbor" is perhaps a misnomer in the sense that it is not a vector distance, but an index distance.

Future work could include adding other neighbor selection algorithms (ie, random, vector distance, ring, others).

-numParticles: positive number, optional

Number of particles in the swarm. Defaults to 10 times the number of dimensions.

-posMax: number, optional

Maximum coordinate value for any dimension in the hyper space. This can be a PDL object, so it should work in any dimension so long as it works in the broadcast sense. For example, different dimensions could have different posMax values by passing a vector of length dimension.

Defaults to 100.

-posMin: number, optional

Minimum coordinate value for any dimension in the hyper space. This can be a PDL object, so it should work in any dimension so long as it works in the broadcast sense. For example, different dimensions could have different posMax values by passing a vector of length dimension.

Defaults to --posMax (if -posMax is negative -posMin should be set more negative).

-randStartVelocity: boolean, optional

Set true to initialize particles with a random velocity. Otherwise particle velocity is set to 0 on initalization.

A range based on 1/100th of --posMax - -posMin is used for the initial speed in each dimension of the velocity vector if a random start velocity is used.

-stallSpeed: positive number, optional

Speed below which a particle is considered to be stalled and is repositioned to a new random location with a new initial speed. This can be a PDL object, so it should work in any dimension so long as it works in the broadcast sense.

By default -stallSpeed is undefined but particles with a speed of 1e-9 will be repositioned.

-stallSearchScale: positive number, optional

If a particle stalls, then jump to a random location that exists +/- searchSize% of the current location, but increase searchSize% for that particle by stallSearchScale after each stall:

$searchSize = $searchSize * ($stallSearchScale ** $numStalls)

Default: 1 (does not change searchSize).

A recommended value is that which will slightly increase searchSize over time. For example, if stallSearchScale = 1.1 and searchSize = 0.5 then searchSize will change for that particle as follows:

Stalls                  searchSize
------                  ----------
  0                        0.5        # initial configured value
  1                        0.55
  2                        0.605
  3                        0.6655
  5                        0.8053
  7                        0.9744

In this example, searchSize will be capped at a value of 1.0 after the particle stalls 8 times.

ACKNOWLEDGEMENTS

This PDL implementation is based on AI::ParticleSwarmOptimization by Peter Jaquiery (GRANDPA), which in turn was based on the AI::PSO originally created by Kyle Schlansker (KYLESCH).

AUTHORS

Copyright (C) 2011 by Peter Jaquiery (GRANDPA) as AI::ParticleSwarmOptimization

LICENSE

This module is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This module is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this module. If not, see <http://www.gnu.org/licenses/>.

To install PDL::Opt::Simplex::Simple, copy and paste the appropriate command in to your terminal.

cpanm

cpanm PDL::Opt::Simplex::Simple

CPAN shell

perl -MCPAN -e shell
install PDL::Opt::Simplex::Simple

For more information on module installation, please visit the detailed CPAN module installation guide.

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