NAME
AI::Genetic::Pro - Efficient genetic algorithms for professional
purpose.
SYNOPSIS
use AI::Genetic::Pro;
sub fitness {
my ($ga, $chromosome) = @_;
return oct('0b' . $ga->as_string($chromosome));
}
sub terminate {
my ($ga) = @_;
my $result = oct('0b' . $ga->as_string($ga->getFittest));
return $result == 4294967295 ? 1 : 0;
}
my $ga = AI::Genetic::Pro->new(
-fitness => \&fitness, # fitness function
-terminate => \&terminate, # terminate function
-type => 'bitvector', # type of chromosomes
-population => 1000, # population
-crossover => 0.9, # probab. of crossover
-mutation => 0.01, # probab. of mutation
-parents => 2, # number of parents
-selection => [ 'Roulette' ], # selection strategy
-strategy => [ 'Points', 2 ], # crossover strategy
-cache => 0, # cache results
-history => 1, # remember best results
-preserve => 3, # remember the bests
-variable_length => 1, # turn variable length ON
);
# init population of 32-bit vectors
$ga->init(32);
# evolve 10 generations
$ga->evolve(10);
# best score
print "SCORE: ", $ga->as_value($ga->getFittest), ".\n";
# save evolution path as a chart
$ga->chart(-filename => 'evolution.png');
# save state of GA
$ga->save('genetic.sga');
# load state of GA
$ga->load('genetic.sga');
DESCRIPTION
This module provides efficient implementation of a genetic algorithm for
professional use. It was designed to operate as fast as possible even on
very large populations and big individuals/chromosomes.
"AI::Genetic::Pro" was inspired by "AI::Genetic", so it is in most cases
compatible (there are some changes). Additionally "AI::Genetic::Pro"
isn't a pure Perl solution, so it doesn't have limitations of its
ancestor (such as serious slow-down in the case of big populations (
>10000 ) or vectors with more than 33 fields).
If You are looking for a pure Perl solution, consider AI::Genetic.
Speed
To increase speed XS code is used, however with portability in mind.
This distribution was tested on Windows and Linux platforms (and
should work on any other).
Memory
This module was designed to use as little memory as possible. A
population of size 10000 consisting of 92-bit vectors uses only
~24MB ("AI::Genetic" would use about 78MB!).
Advanced options
To provide more flexibility "AI::Genetic::Pro" supports many
statistical distributions, such as "uniform", "natural",
"chi_square" and others. This feature can be used in selection
and/or crossover. See the documentation below.
METHODS
*$ga*->new( %options )
Constructor. It accepts options in hash-value style. See options and
an example below.
-fitness
This defines a *fitness* function. It expects a reference to
a subroutine.
-terminate
This defines a *terminate* function. It expects a reference
to a subroutine.
-type This defines the type of chromosomes. Currently,
"AI::Genetic::Pro" supports four types:
bitvector Individuals/chromosomes of this type have genes
that are bits. Each gene can be in one of two
possible states, on or off.
listvector Each gene of a "listvector"
individual/chromosome can assume one string
value from a specified list of possible string
values.
rangevector Each gene of a "rangevector"
individual/chromosome can assume one integer
value from a range of possible integer values.
Note that only integers are supported. The user
can always transform any desired fractional
values by multiplying and dividing by an
appropriate power of 10.
combination Each gene of a "combination"
individual/chromosome can assume one string
value from a specified list of possible string
values. All genes are unique.
-population
This defines the size of the population, i.e. how many
chromosomes simultaneously exist at each generation.
-crossover
This defines the crossover rate. The fairest results are
achieved with crossover rate ~0.95.
-mutation
This defines the mutation rate. The fairest results are
achieved with mutation rate ~0.01.
-preserve
This defines injection of the bests chromosomes into a next
generation. It causes a little slow down, however (very
often) much better results are achieved. You can specify,
how many chromosomes will be preserved, i.e.
-preserve => 1, # only one chromosome will be preserved
# or
-preserve => 9, # 9 chromosomes will be preserved
# and so on...
Attention! You cannot preserve more chromosomes than exist
in your population.
-variable_length
This defines whether variable-length chromosomes are turned
on (default off) and a which types of mutation are allowed.
See below.
level 0 Feature is inactive (default). Example:
-variable_length => 0
# chromosomes (i.e. bitvectors)
0 1 0 0 1 1 0 1 1 1 0 1 0 1
0 0 1 1 0 1 1 1 1 0 0 1 1 0
0 1 1 1 0 1 0 0 1 1 0 1 1 1
0 1 0 0 1 1 0 1 1 1 1 0 1 0
# ...and so on
level 1 Feature is active, but chromosomes can varies only
on the right side, Example:
-variable_length => 1
# chromosomes (i.e. bitvectors)
0 1 0 0 1 1 0 1 1 1
0 0 1 1 0 1 1 1 1
0 1 1 1 0 1 0 0 1 1 0 1 1 1
0 1 0 0 1 1 0 1 1 1
# ...and so on
level 2 Feature is active and chromosomes can varies on the
left side and on the right side; unwanted
values/genes on the left side are replaced with
"undef", ie.
-variable_length => 2
# chromosomes (i.e. bitvectors)
x x x 0 1 1 0 1 1 1
x x x x 0 1 1 1 1
x 1 1 1 0 1 0 0 1 1 0 1 1 1
0 1 0 0 1 1 0 1 1 1
# where 'x' means 'undef'
# ...and so on
In this situation returned chromosomes in an array
context ($ga->as_array($chromosome)) can have undef
values on the left side (only). In a scalar context
each undefined value is replaced with a single
space. If You don't want to see any "undef" or
space, just use "as_array_def_only" and
"as_string_def_only" instead of "as_array" and
"as_string".
-parents
This defines how many parents should be used in a crossover.
-selection
This defines how individuals/chromosomes are selected to
crossover. It expects an array reference listed below:
-selection => [ $type, @params ]
where type is one of:
RouletteBasic
Each individual/chromosome can be selected with
probability proportional to its fitness.
Roulette
First the best individuals/chromosomes are selected.
From this collection parents are selected with
probability poportional to their fitness.
RouletteDistribution
Each individual/chromosome has a portion of roulette
wheel proportional to its fitness. Selection is done
with the specified distribution. Supported
distributions and parameters are listed below.
"-selection => [ 'RouletteDistribution', 'uniform'
]"
Standard uniform distribution. No
additional parameters are needed.
"-selection => [ 'RouletteDistribution', 'normal',
$av, $sd ]"
Normal distribution, where $av is
average (default: size of population /2)
and $$sd is standard deviation (default:
size of population).
"-selection => [ 'RouletteDistribution', 'beta',
$aa, $bb ]"
*Beta* distribution. The density of the
beta is:
X^($aa - 1) * (1 - X)^($bb - 1) / B($aa , $bb) for 0 < X < 1.
$aa and $bb are set by default to number
of parents.
Argument restrictions: Both $aa and $bb
must not be less than 1.0E-37.
"-selection => [ 'RouletteDistribution', 'binomial'
]"
Binomial distribution. No additional
parameters are needed.
"-selection => [ 'RouletteDistribution',
'chi_square', $df ]"
Chi-square distribution with $df degrees
of freedom. $df by default is set to
size of population.
"-selection => [ 'RouletteDistribution',
'exponential', $av ]"
Exponential distribution, where $av is
average . $av by default is set to size
of population.
"-selection => [ 'RouletteDistribution', 'poisson',
$mu ]"
Poisson distribution, where $mu is mean.
$mu by default is set to size of
population.
Distribution
Chromosomes/individuals are selected with specified
distribution. See below.
"-selection => [ 'Distribution', 'uniform' ]"
Standard uniform distribution. No
additional parameters are needed.
"-selection => [ 'Distribution', 'normal', $av, $sd
]"
Normal distribution, where $av is
average (default: size of population /2)
and $$sd is standard deviation (default:
size of population).
"-selection => [ 'Distribution', 'beta', $aa, $bb ]"
*Beta* distribution. The density of the
beta is:
X^($aa - 1) * (1 - X)^($bb - 1) / B($aa , $bb) for 0 < X < 1.
$aa and $bb are set by default to number
of parents.
Argument restrictions: Both $aa and $bb
must not be less than 1.0E-37.
"-selection => [ 'Distribution', 'binomial' ]"
Binomial distribution. No additional
parameters are needed.
"-selection => [ 'Distribution', 'chi_square', $df
]"
Chi-square distribution with $df degrees
of freedom. $df by default is set to
size of population.
"-selection => [ 'Distribution', 'exponential', $av
]"
Exponential distribution, where $av is
average . $av by default is set to size
of population.
"-selection => [ 'Distribution', 'poisson', $mu ]"
Poisson distribution, where $mu is mean.
$mu by default is set to size of
population.
-strategy
This defines the astrategy of crossover operation. It
expects an array reference listed below:
-strategy => [ $type, @params ]
where type is one of:
PointsSimple
Simple crossover in one or many points. The best
chromosomes/individuals are selected for the new
generation. For example:
-strategy => [ 'PointsSimple', $n ]
where $n is the number of points for crossing.
PointsBasic
Crossover in one or many points. In basic crossover
selected parents are crossed and one (randomly-chosen)
child is moved to the new generation. For example:
-strategy => [ 'PointsBasic', $n ]
where $n is the number of points for crossing.
Points
Crossover in one or many points. In normal crossover
selected parents are crossed and the best child is moved
to the new generation. For example:
-strategy => [ 'Points', $n ]
where $n is number of points for crossing.
PointsAdvenced
Crossover in one or many points. After crossover the
best chromosomes/individuals from all parents and
chidren are selected for the new generation. For
example:
-strategy => [ 'PointsAdvanced', $n ]
where $n is the number of points for crossing.
Distribution
In *distribution* crossover parents are crossed in
points selected with the specified distribution. See
below.
"-strategy => [ 'Distribution', 'uniform' ]"
Standard uniform distribution. No additional
parameters are needed.
"-strategy => [ 'Distribution', 'normal', $av, $sd ]"
Normal distribution, where $av is average
(default: number of parents/2) and $sd is
standard deviation (default: number of parents).
"-strategy => [ 'Distribution', 'beta', $aa, $bb ]"
*Beta* distribution. The density of the beta is:
X^($aa - 1) * (1 - X)^($bb - 1) / B($aa , $bb) for 0 < X < 1.
$aa and $bb are set by default to the number of
parents.
Argument restrictions: Both $aa and $bb must not
be less than 1.0E-37.
"-strategy => [ 'Distribution', 'binomial' ]"
Binomial distribution. No additional parameters
are needed.
"-strategy => [ 'Distribution', 'chi_square', $df ]"
Chi-squared distribution with $df degrees of
freedom. $df by default is set to the number of
parents.
"-strategy => [ 'Distribution', 'exponential', $av ]"
Exponential distribution, where $av is average .
$av by default is set to the number of parents.
"-strategy => [ 'Distribution', 'poisson', $mu ]"
Poisson distribution, where $mu is mean. $mu by
default is set to the number of parents.
PMX PMX method defined by Goldberg and Lingle in 1985.
Parameters: *none*.
OX OX method defined by Davis (?) in 1985. Parameters:
*none*.
-cache This defines whether a cache should be used. Allowed values
are 1 or 0 (default: *0*).
-history
This defines whether history should be collected. Allowed
values are 1 or 0 (default: *0*).
-strict This defines if the check for modifying chromosomes in a
user-defined fitness function is active. Directly modifying
chromosomes is not allowed and it is a highway to big
trouble. This mode should be used only for testing, because
it is slow.
*$ga*->inject($chromosomes)
Inject new, user defined, chromosomes into the current population.
See example below:
# example for bitvector
my $chromosomes = [
[ 1, 1, 0, 1, 0, 1 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 1, 0, 1, 0, 0 ],
...
];
# inject
$ga->inject($chromosomes);
If You want to delete some chromosomes from population, just
"splice" them:
my @remove = qw(1 2 3 9 12);
for my $idx (sort { $b <=> $a } @remove){
splice @{$ga->chromosomes}, $idx, 1;
}
*$ga*->population($population)
Set/get size of the population. This defines the size of the
population, i.e. how many chromosomes to simultaneously exist at
each generation.
*$ga*->indType()
Get type of individuals/chromosomes. Currently supported types are:
"bitvector"
Chromosomes will be just bitvectors. See documentation of "new"
method.
"listvector"
Chromosomes will be lists of specified values. See documentation
of "new" method.
"rangevector"
Chromosomes will be lists of values from specified range. See
documentation of "new" method.
"combination"
Chromosomes will be unique lists of specified values. This is
used for example in the *Traveling Salesman Problem*. See the
documentation of the "new" method.
In example:
my $type = $ga->type();
*$ga*->type()
Alias for "indType".
*$ga*->crossProb()
This method is used to query and set the crossover rate.
*$ga*->crossover()
Alias for "crossProb".
*$ga*->mutProb()
This method is used to query and set the mutation rate.
*$ga*->mutation()
Alias for "mutProb".
*$ga*->parents($parents)
Set/get number of parents in a crossover.
*$ga*->init($args)
This method initializes the population with random
individuals/chromosomes. It MUST be called before any call to
"evolve()". It expects one argument, which depends on the type of
individuals/chromosomes:
bitvector
For bitvectors, the argument is simply the length of the
bitvector.
$ga->init(10);
This initializes a population where each individual/chromosome
has 10 genes.
listvector
For listvectors, the argument is an anonymous list of lists. The
number of sub-lists is equal to the number of genes of each
individual/chromosome. Each sub-list defines the possible string
values that the corresponding gene can assume.
$ga->init([
[qw/red blue green/],
[qw/big medium small/],
[qw/very_fat fat fit thin very_thin/],
]);
This initializes a population where each individual/chromosome
has 3 genes and each gene can assume one of the given values.
rangevector
For rangevectors, the argument is an anonymous list of lists.
The number of sub-lists is equal to the number of genes of each
individual/chromosome. Each sub-list defines the minimum and
maximum integer values that the corresponding gene can assume.
$ga->init([
[1, 5],
[0, 20],
[4, 9],
]);
This initializes a population where each individual/chromosome
has 3 genes and each gene can assume an integer within the
corresponding range.
combination
For combination, the argument is an anonymous list of possible
values of gene.
$ga->init( [ 'a', 'b', 'c' ] );
This initializes a population where each chromosome has 3 genes
and each gene is a unique combination of 'a', 'b' and 'c'. For
example genes looks something like that:
[ 'a', 'b', 'c' ] # gene 1
[ 'c', 'a', 'b' ] # gene 2
[ 'b', 'c', 'a' ] # gene 3
# ...and so on...
*$ga*->evolve($n)
This method causes the GA to evolve the population for the specified
number of generations. If its argument is 0 or "undef" GA will
evolve the population to infinity unless a "terminate" function is
specified.
*$ga*->getHistory()
Get history of the evolution. It is in a format listed below:
[
# gen0 gen1 gen2 ... # generations
[ max0, max1, max2, ... ], # max values
[ mean, mean1, mean2, ... ], # mean values
[ min0, min1, min2, ... ], # min values
]
*$ga*->getAvgFitness()
Get *max*, *mean* and *min* score of the current generation. In
example:
my ($max, $mean, $min) = $ga->getAvgFitness();
*$ga*->getFittest($n, $unique)
This function returns a list of the fittest chromosomes from the
current population. You can specify how many chromosomes should be
returned and if the returned chromosomes should be unique. See
example below.
# only one - the best
my ($best) = $ga->getFittest;
# or 5 bests chromosomes, NOT unique
my @bests = $ga->getFittest(5);
# or 7 bests and UNIQUE chromosomes
my @bests = $ga->getFittest(7, 1);
If you want to get a large number of chromosomes, try to use the
"getFittest_as_arrayref" function instead (for efficiency).
*$ga*->getFittest_as_arrayref($n, $unique)
This function is very similar to "getFittest", but it returns a
reference to an array instead of a list.
*$ga*->generation()
Get the number of the current generation.
*$ga*->people()
Returns an anonymous list of individuals/chromosomes of the current
population.
IMPORTANT: the actual array reference used by the "AI::Genetic::Pro"
object is returned, so any changes to it will be reflected in *$ga*.
*$ga*->chromosomes()
Alias for "people".
*$ga*->chart(%options)
Generate a chart describing changes of min, mean, and max scores in
your population. To satisfy your needs, you can pass the following
options:
-filename
File to save a chart in (obligatory).
-title
Title of a chart (default: *Evolution*).
-x_label
X label (default: *Generations*).
-y_label
Y label (default: *Value*).
-format
Format of values, like "sprintf" (default: *'%.2f'*).
-legend1
Description of min line (default: *Min value*).
-legend2
Description of min line (default: *Mean value*).
-legend3
Description of min line (default: *Max value*).
-width
Width of a chart (default: *640*).
-height
Height of a chart (default: *480*).
-font
Path to font (in *.ttf format) to be used (default: none).
-logo
Path to logo (png/jpg image) to embed in a chart (default:
none).
For example:
$ga->chart(-width => 480, height => 320, -filename => 'chart.png');
*$ga*->save($file)
Save the current state of the genetic algorithm to the specified
file.
*$ga*->load($file)
Load a state of the genetic algorithm from the specified file.
*$ga*->as_array($chromosome)
In list context return an array representing the specified
chromosome. In scalar context return an reference to an array
representing the specified chromosome. If *variable_length* is
turned on and is set to level 2, an array can have some "undef"
values. To get only "not undef" values use "as_array_def_only"
instead of "as_array".
*$ga*->as_array_def_only($chromosome)
In list context return an array representing the specified
chromosome. In scalar context return an reference to an array
representing the specified chromosome. If *variable_length* is
turned off, this function is just an alias for "as_array". If
*variable_length* is turned on and is set to level 2, this function
will return only "not undef" values from chromosome. See example
below:
# -variable_length => 2, -type => 'bitvector'
my @chromosome = $ga->as_array($chromosome)
# @chromosome looks something like that
# ( undef, undef, undef, 1, 0, 1, 1, 1, 0 )
@chromosome = $ga->as_array_def_only($chromosome)
# @chromosome looks something like that
# ( 1, 0, 1, 1, 1, 0 )
*$ga*->as_string($chromosome)
Return a string representation of the specified chromosome. See
example below:
# -type => 'bitvector'
my $string = $ga->as_string($chromosome);
# $string looks something like that
# 1___0___1___1___1___0
# or
# -type => 'listvector'
$string = $ga->as_string($chromosome);
# $string looks something like that
# element0___element1___element2___element3...
Attention! If *variable_length* is turned on and is set to level 2,
it is possible to get "undef" values on the left side of the vector.
In the returned string "undef" values will be replaced with spaces.
If you don't want to see any *spaces*, use "as_string_def_only"
instead of "as_string".
*$ga*->as_string_def_only($chromosome)
Return a string representation of specified chromosome. If
*variable_length* is turned off, this function is just alias for
"as_string". If *variable_length* is turned on and is set to level
2, this function will return a string without "undef" values. See
example below:
# -variable_length => 2, -type => 'bitvector'
my $string = $ga->as_string($chromosome);
# $string looks something like that
# ___ ___ ___1___1___0
$string = $ga->as_string_def_only($chromosome);
# $string looks something like that
# 1___1___0
*$ga*->as_value($chromosome)
Return the score of the specified chromosome. The value of
*chromosome* is calculated by the fitness function.
SUPPORT
"AI::Genetic::Pro" is still under development; however, it is used in
many production environments.
TODO
Examples.
More tests.
More warnings about incorrect parameters.
REPORTING BUGS
When reporting bugs/problems please include as much information as
possible. It may be difficult for me to reproduce the problem as almost
every setup is different.
A small script which yields the problem will probably be of help.
THANKS
Miles Gould for suggestions and some fixes (even in this documentation!
:-).
Alun Jones for fixing memory leaks.
Tod Hagan for reporting a bug (rangevector values truncated to signed
8-bit quantities) and supplying a patch.
Randal L. Schwartz for reporting a bug in this documentation.
Maciej Misiak for reporting problems with "combination" (and a bug in a
PMX strategy).
LEONID ZAMDBORG for recommending the addition of variable-length
chromosomes as well as supplying relevant code samples, for testing and
at the end reporting some bugs.
Christoph Meissner for reporting a bug.
Alec Chen for reporting some bugs.
AUTHOR
Strzelecki Lukasz <
[email protected]>
SEE ALSO
AI::Genetic Algorithm::Evolutionary
COPYRIGHT
Copyright (c) Strzelecki Lukasz. All rights reserved. This program is
free software; you can redistribute it and/or modify it under the same
terms as Perl itself.
