AI-Genetic-Pro
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lib/AI/Genetic/Pro.pm view on Meta::CPAN
package AI::Genetic::Pro;
$AI::Genetic::Pro::VERSION = '1.009';
#---------------
use warnings;
use strict;
use base qw( Class::Accessor::Fast::XS );
#-----------------------------------------------------------------------
use Carp;
use Clone qw( clone );
use Struct::Compare;
use Digest::MD5 qw( md5_hex );
use List::Util qw( sum );
use List::MoreUtils qw( minmax first_index apply );
#use Data::Dumper; $Data::Dumper::Sortkeys = 1;
use Tie::Array::Packed;
use UNIVERSAL::require;
#-----------------------------------------------------------------------
use AI::Genetic::Pro::Array::Type qw( get_package_by_element_size );
use AI::Genetic::Pro::Chromosome;
#-----------------------------------------------------------------------
__PACKAGE__->mk_accessors(qw(
mce
type
population
terminate
chromosomes
crossover
native
parents _parents
history _history
fitness _fitness _fitness_real
cache
mutation _mutator
strategy _strategist
selection _selector
_translations
generation
preserve
variable_length
_fix_range
_package
_length
strict _strict
workers
size
_init
));
#=======================================================================
# Additional modules
use constant STORABLE => 'Storable';
use constant GD => 'GD::Graph::linespoints';
#=======================================================================
my $_Cache = { };
my $_temp_chromosome;
#=======================================================================
sub new {
my ( $class, %args ) = ( shift, @_ );
#-------------------------------------------------------------------
my %opts = map { if(ref $_){$_}else{ /^-?(.*)$/o; $1 }} @_;
my $self = bless \%opts, $class;
#-------------------------------------------------------------------
$AI::Genetic::Pro::Array::Type::Native = 1 if $self->native;
#-------------------------------------------------------------------
croak(q/Type of chromosomes cannot be "combination" if "variable length" feature is active!/)
if $self->type eq q/combination/ and $self->variable_length;
croak(q/You must specify a crossover strategy with -strategy!/)
unless defined ($self->strategy);
croak(q/Type of chromosomes cannot be "combination" if strategy is not one of: OX, PMX!/)
if $self->type eq q/combination/ and ($self->strategy->[0] ne q/OX/ and $self->strategy->[0] ne q/PMX/);
croak(q/Strategy cannot be "/,$self->strategy->[0],q/" if "variable length" feature is active!/ )
if ($self->strategy->[0] eq 'PMX' or $self->strategy->[0] eq 'OX') and $self->variable_length;
#-------------------------------------------------------------------
$self->_set_strict if $self->strict;
#-------------------------------------------------------------------
return $self unless $self->mce;
#-------------------------------------------------------------------
delete $self->{ mce };
'AI::Genetic::Pro::MCE'->use or die q[Cannot raise multicore support: ] . $@;
return AI::Genetic::Pro::MCE->new( $self, \%args );
}
#=======================================================================
sub _Cache { $_Cache; }
#=======================================================================
# INIT #################################################################
#=======================================================================
sub _set_strict {
my ($self) = @_;
lib/AI/Genetic/Pro.pm view on Meta::CPAN
$self->_init( $data );
$self->_fitness( { } );
$self->_fix_range( [ ] );
$self->_history( [ [ ], [ ], [ ] ] );
$self->_init_cache if $self->cache;
#-------------------------------------------------------------------
if($self->type eq q/listvector/){
croak(q/You have to pass array reference if "type" is set to "listvector"/) unless ref $data eq 'ARRAY';
$self->_translations( $self->_check_data_ref($data) );
}elsif($self->type eq q/bitvector/){
croak(q/You have to pass integer if "type" is set to "bitvector"/) if $data !~ /^\d+$/o;
$self->_translations( [ [ 0, 1 ] ] );
$self->_translations->[$_] = $self->_translations->[0] for 1..$data-1;
}elsif($self->type eq q/combination/){
croak(q/You have to pass array reference if "type" is set to "combination"/) unless ref $data eq 'ARRAY';
$self->_translations( [ clone($data) ] );
$self->_translations->[$_] = $self->_translations->[0] for 1..$#$data;
}elsif($self->type eq q/rangevector/){
croak(q/You have to pass array reference if "type" is set to "rangevector"/) unless ref $data eq 'ARRAY';
$self->_translations( $self->_find_fix_range( $self->_check_data_ref($data) ));
}else{
croak(q/You have to specify first "type" of vector!/);
}
my $size = 0;
if($self->type ne q/rangevector/){ for(@{$self->_translations}){ $size = $#$_ if $#$_ > $size; } }
# else{ for(@{$self->_translations}){ $size = $_->[1] if $_->[1] > $size; } }
else{ for(@{$self->_translations}){ $size = $_->[2] if $_->[2] > $size; } } # Provisional patch for rangevector values truncated to signed 8-bit quantities. Thx to Tod Hagan
my $package = get_package_by_element_size($size);
$self->_package($package);
my $length = ref $data ? sub { $#$data; } : sub { $data - 1 };
if($self->variable_length){
$length = ref $data ? sub { 1 + int( rand( $#{ $self->_init } ) ); } : sub { 1 + int( rand( $self->_init - 1) ); };
}
$self->_length( $length );
$self->chromosomes( [ ] );
push @{$self->chromosomes},
AI::Genetic::Pro::Chromosome->new($self->_translations, $self->type, $package, $length->())
for 1..$self->population;
$self->_calculate_fitness_all();
}
#=======================================================================
# SAVE / LOAD ##########################################################
#=======================================================================
sub spew {
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
STORABLE->use( qw( store retrieve freeze thaw ) ) or croak(q/You need "/.STORABLE.q/" module to save a state of "/.__PACKAGE__.q/"!/);
$Storable::Deparse = 1;
$Storable::Eval = 1;
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
my ( $self ) = @_;
my $clone = {
_selector => undef,
_strategist => undef,
_mutator => undef,
};
$clone->{ chromosomes } = [ map { ${ tied( @$_ ) } } @{ $self->chromosomes } ]
if $self->_package;
foreach my $key(keys %$self){
next if exists $clone->{$key};
$clone->{$key} = $self->{$key};
}
return $clone;
}
#=======================================================================
sub slurp {
my ( $self, $dump ) = @_;
if( my $typ = $self->_package ){
@{ $dump->{ chromosomes } } = map {
my $arr = $typ->make_with_packed( $_ );
bless $arr, q[AI::Genetic::Pro::Chromosome];
} @{ $dump->{ chromosomes } };
}
%$self = %$dump;
return 1;
}
#=======================================================================
sub save {
my ( $self, $file ) = @_;
croak(q/You have to specify file!/) unless defined $file;
store( $self->spew, $file );
}
#=======================================================================
sub load {
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
STORABLE->use( qw( store retrieve freeze thaw ) ) or croak(q/You need "/.STORABLE.q/" module to load a state of "/.__PACKAGE__.q/"!/);
$Storable::Deparse = 1;
$Storable::Eval = 1;
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
my ($self, $file) = @_;
croak(q/You have to specify file!/) unless defined $file;
my $clone = retrieve($file);
return carp('Incorrect file!') unless $clone;
return $self->slurp( $clone );
}
#=======================================================================
# CHARTS ###############################################################
#=======================================================================
sub chart {
GD->require or croak(q/You need "/.GD.q/" module to draw chart of evolution!/);
my ($self, %params) = (shift, @_);
my $graph = GD()->new(($params{-width} || 640), ($params{-height} || 480));
lib/AI/Genetic/Pro.pm view on Meta::CPAN
return @array if wantarray;
return \@array;
}else{
my $cnt = 0;
my @array = map { $self->_translations->[$cnt++]->[$_] } @$chromosome;
return @array if wantarray;
return \@array;
}
}
#=======================================================================
sub as_string_def_only {
my ($self, $chromosome) = @_;
return $self->as_string($chromosome)
if not $self->variable_length or $self->variable_length < 2;
my $array = $self->as_array_def_only($chromosome);
return join(q//, @$array) if $self->type eq q/bitvector/;
return join(q/___/, @$array);
}
#=======================================================================
sub as_string {
return join(q//, @{$_[1]}) if $_[0]->type eq q/bitvector/;
return join(q/___/, map { defined $_ ? $_ : q/ / } $_[0]->as_array($_[1]));
}
#=======================================================================
sub as_value {
my ($self, $chromosome) = @_;
croak(q/You MUST call 'as_value' as method of 'AI::Genetic::Pro' object./)
unless defined $_[0] and ref $_[0] and ( ref $_[0] eq 'AI::Genetic::Pro' or ref $_[0] eq 'AI::Genetic::Pro::MCE');
croak(q/You MUST pass 'AI::Genetic::Pro::Chromosome' object to 'as_value' method./)
unless defined $_[1] and ref $_[1] and ref $_[1] eq 'AI::Genetic::Pro::Chromosome';
return $self->fitness->($self, $chromosome);
}
#=======================================================================
# ALGORITHM ############################################################
#=======================================================================
sub _calculate_fitness_all {
my ($self) = @_;
$self->_fitness( { } );
$self->_fitness->{$_} = $self->fitness()->($self, $self->chromosomes->[$_])
for 0..$#{$self->chromosomes};
# sorting the population is not necessary
# my (@chromosomes, %fitness);
# for my $idx (sort { $self->_fitness->{$a} <=> $self->_fitness->{$b} } keys %{$self->_fitness}){
# push @chromosomes, $self->chromosomes->[$idx];
# $fitness{$#chromosomes} = $self->_fitness->{$idx};
# delete $self->_fitness->{$idx};
# delete $self->chromosomes->[$idx];
# }
#
# $self->_fitness(\%fitness);
# $self->chromosomes(\@chromosomes);
return;
}
#=======================================================================
sub _select_parents {
my ($self) = @_;
unless($self->_selector){
croak "You must specify a selection strategy!"
unless defined $self->selection;
my @tmp = @{$self->selection};
my $selector = q/AI::Genetic::Pro::Selection::/ . shift @tmp;
$selector->require or die $!;
$self->_selector($selector->new(@tmp));
}
$self->_parents($self->_selector->run($self));
return;
}
#=======================================================================
sub _crossover {
my ($self) = @_;
unless($self->_strategist){
my @tmp = @{$self->strategy};
my $strategist = q/AI::Genetic::Pro::Crossover::/ . shift @tmp;
$strategist->require or die $!;
$self->_strategist($strategist->new(@tmp));
}
my $a = $self->_strategist->run($self);
$self->chromosomes( $a );
return;
}
#=======================================================================
sub _mutation {
my ($self) = @_;
unless($self->_mutator){
my $mutator = q/AI::Genetic::Pro::Mutation::/ . ucfirst(lc($self->type));
unless($mutator->require){
$mutator = q/AI::Genetic::Pro::Mutation::Listvector/;
$mutator->require;
}
$self->_mutator($mutator->new);
}
return $self->_mutator->run($self);
}
#=======================================================================
sub _save_history {
my @tmp;
if($_[0]->history){ @tmp = $_[0]->getAvgFitness; }
else { @tmp = (undef, undef, undef); }
push @{$_[0]->_history->[0]}, $tmp[0];
push @{$_[0]->_history->[1]}, $tmp[1];
push @{$_[0]->_history->[2]}, $tmp[2];
return 1;
}
#=======================================================================
sub inject {
my ($self, $candidates) = @_;
for(@$candidates){
push @{$self->chromosomes},
AI::Genetic::Pro::Chromosome->new_from_data($self->_translations, $self->type, $self->_package, $_, $self->_fix_range);
$self->_fitness->{$#{$self->chromosomes}} = $self->fitness()->($self, $self->chromosomes->[-1]);
}
$self->_strict( [ ] );
$self->population( $self->population + scalar( @$candidates ) );
return 1;
}
#=======================================================================
sub _state {
my ( $self ) = @_;
my @res;
if( $self->_package ){
@res = map {
[
${ tied( @{ $self->chromosomes->[ $_ ] } ) },
$self->_fitness->{ $_ },
]
} 0 .. $self->population - 1
}else{
@res = map {
[
$self->chromosomes->[ $_ ],
$self->_fitness->{ $_ },
]
} 0 .. $self->population - 1
}
return \@res;
}
#=======================================================================
sub evolve {
my ($self, $generations) = @_;
# generations must be defined
$generations ||= -1;
if($self->strict and $self->_strict){
for my $idx (0..$#{$self->chromosomes}){
croak(q/Chromosomes was modified outside the 'evolve' function!/) unless $self->chromosomes->[$idx] and $self->_strict->[$idx];
my @tmp0 = @{$self->chromosomes->[$idx]};
my @tmp1 = @{$self->_strict->[$idx]};
croak(qq/Chromosome was modified outside the 'evolve' function from "@tmp0" to "@tmp1"!/) unless compare(\@tmp0, \@tmp1);
}
}
# split into two loops just for speed
unless($self->preserve){
for(my $i = 0; $i != $generations; $i++){
# terminate ----------------------------------------------------
last if $self->terminate and $self->terminate->($self);
# update generation --------------------------------------------
$self->generation($self->generation + 1);
# update history -----------------------------------------------
$self->_save_history;
# selection ----------------------------------------------------
$self->_select_parents();
# crossover ----------------------------------------------------
$self->_crossover();
# mutation -----------------------------------------------------
$self->_mutation();
}
}else{
croak('You cannot preserve more chromosomes than is in population!') if $self->preserve > $self->population;
my @preserved;
for(my $i = 0; $i != $generations; $i++){
# terminate ----------------------------------------------------
last if $self->terminate and $self->terminate->($self);
# update generation --------------------------------------------
$self->generation($self->generation + 1);
# update history -----------------------------------------------
$self->_save_history;
#---------------------------------------------------------------
# preservation of N unique chromosomes
@preserved = map { clone($_) } @{ $self->getFittest_as_arrayref($self->preserve - 1, 1) };
# selection ----------------------------------------------------
$self->_select_parents();
# crossover ----------------------------------------------------
$self->_crossover();
# mutation -----------------------------------------------------
$self->_mutation();
#---------------------------------------------------------------
for(@preserved){
my $idx = int rand @{$self->chromosomes};
$self->chromosomes->[$idx] = $_;
$self->_fitness->{$idx} = $self->fitness()->($self, $_);
}
}
}
if($self->strict){
$self->_strict( [ ] );
push @{$self->_strict}, $_->clone for @{$self->chromosomes};
}
}
#=======================================================================
# ALIASES ##############################################################
#=======================================================================
sub people { $_[0]->chromosomes() }
#=======================================================================
sub getHistory { $_[0]->_history() }
#=======================================================================
sub mutProb { shift->mutation(@_) }
#=======================================================================
sub crossProb { shift->crossover(@_) }
#=======================================================================
sub intType { shift->type() }
#=======================================================================
# STATS ################################################################
#=======================================================================
sub getFittest_as_arrayref {
my ($self, $n, $uniq) = @_;
$n ||= 1;
$self->_calculate_fitness_all() unless scalar %{ $self->_fitness };
my @keys = sort { $self->_fitness->{$a} <=> $self->_fitness->{$b} } 0..$#{$self->chromosomes};
if($uniq){
my %grep;
my $chromosomes = $self->chromosomes;
if( my $pkg = $self->_package ){
my %tmp;
@keys = grep {
my $key = ${ tied( @{ $chromosomes->[ $_ ] } ) };
#my $key = md5_hex( ${ tied( @{ $chromosomes->[ $_ ] } ) } ); # ?
$tmp{ $key } && 0 or $tmp{ $key } = 1;
} @keys;
#@keys = grep {
# my $add_to_list = 0;
# my $key = md5_hex(${tied(@{$chromosomes->[$_]})});
# unless($grep{$key}) {
# $grep{$key} = 1;
# $add_to_list = 1;
# }
# $add_to_list;
# } @keys;
}else{
my %tmp;
@keys = grep {
my $key = md5_hex( join( q[:], @{ $chromosomes->[ $_ ] } ) );
$tmp{ $key } && 0 or $tmp{ $key } = 1;
} @keys;
}
}
$n = scalar @keys if $n > scalar @keys;
return [ reverse @{$self->chromosomes}[ splice @keys, $#keys - $n + 1, $n ] ];
}
#=======================================================================
sub getFittest { return wantarray ? @{ shift->getFittest_as_arrayref(@_) } : shift @{ shift->getFittest_as_arrayref(@_) }; }
#=======================================================================
sub getAvgFitness {
my ($self) = @_;
my @minmax = minmax values %{$self->_fitness};
my $mean = sum(values %{$self->_fitness}) / scalar values %{$self->_fitness};
return $minmax[1], int($mean), $minmax[0];
}
#=======================================================================
1;
__END__
=head1 NAME
AI::Genetic::Pro - Efficient genetic algorithms for professional purpose with support for multiprocessing.
=head1 SYNOPSIS
use AI::Genetic::Pro;
sub fitness {
my ($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
-mce => 1, # optional MCE support
-workers => 3, # number of workers (MCE)
);
# 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
$ga->load('genetic.sga');
=head1 DESCRIPTION
This module provides efficient implementation of a genetic algorithm for
professional purpose with support for multiprocessing. It was designed to operate as fast as possible
even on very large populations and big individuals/chromosomes. C<AI::Genetic::Pro>
was inspired by C<AI::Genetic>, so it is in most cases compatible
(there are some changes). Additionally C<AI::Genetic::Pro> isn't a pure Perl solution, so it
doesn't have limitations of its ancestor (such as slow-down in the
case of big populations ( >10000 ) or vectors with more than 33 fields).
If You are looking for a pure Perl solution, consider L<AI::Genetic>.
=over 4
=item Speed
To increase speed XS code is used, however with portability in
mind. This distribution was tested on Windows and Linux platforms
(and should work on any other).
Multicore support is available through Many-Core Engine (C<MCE>).
You can gain the most speed up for big populations or time/CPU consuming
fitness functions, however for small populations and/or simple fitness
function better choice will be single-process version.
You can get even more speed up if you turn on use of native arrays
(parameter: C<native>) instead of packing chromosomes into single scalar.
However you have to remember about expensive memory use in that case.
=item Memory
This module was designed to use as little memory as possible. A population
of size 10000 consisting of 92-bit vectors uses only ~24MB (C<AI::Genetic>
would use about 78MB). However - if you use MCE - there will be bigger
memory consumption. This is consequence of necessity of synchronization
between many processes.
=item Advanced options
To provide more flexibility C<AI::Genetic::Pro> supports many
statistical distributions, such as C<uniform>, C<natural>, C<chi_square>
and others. This feature can be used in selection and/or crossover. See
the documentation below.
=back
=head1 METHODS
=over 4
=item I<$ga>-E<gt>B<new>( %options )
Constructor. It accepts options in hash-value style. See options and
an example below.
=over 8
=item -fitness
This defines a I<fitness> function. It expects a reference to a subroutine.
=item -terminate
This defines a I<terminate> function. It expects a reference to a subroutine.
=item -type
This defines the type of chromosomes. Currently, C<AI::Genetic::Pro> supports four types:
=over 12
=item bitvector
Individuals/chromosomes of this type have genes that are bits. Each gene can be in one of two possible states, on or off.
=item listvector
Each gene of a "listvector" individual/chromosome can assume one string value from a specified list of possible string values.
=item 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.
=item combination
Each gene of a "combination" individual/chromosome can assume one string value from a specified list of possible string values. B<All genes are unique.>
=back
=item -population
This defines the size of the population, i.e. how many chromosomes
simultaneously exist at each generation.
=item -crossover
This defines the crossover rate. The fairest results are achieved with
crossover rate ~0.95.
lib/AI/Genetic/Pro.pm view on Meta::CPAN
=item -variable_length
This defines whether variable-length chromosomes are turned on (default off)
and a which types of mutation are allowed. See below.
=over 8
=item 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
=item level 1
Feature is active, but chromosomes can varies B<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
=item level 2
Feature is active and chromosomes can varies B<on the left side and on
the right side>; unwanted values/genes on the left side are replaced with C<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 ($ga-E<gt>as_array($chromosome))
can have B<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 C<undef> or space, just use C<as_array_def_only> and C<as_string_def_only>
instead of C<as_array> and C<as_string>.
=back
=item -parents
This defines how many parents should be used in a crossover.
=item -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:
=over 8
=item B<RouletteBasic>
Each individual/chromosome can be selected with probability proportional to its fitness.
=item B<Roulette>
First the best individuals/chromosomes are selected. From this collection
parents are selected with probability poportional to their fitness.
=item B<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.
=over 12
=item C<-selection =E<gt> [ 'RouletteDistribution', 'uniform' ]>
Standard uniform distribution. No additional parameters are needed.
=item C<-selection =E<gt> [ 'RouletteDistribution', 'normal', $av, $sd ]>
Normal distribution, where C<$av> is average (default: size of population /2) and $C<$sd> is standard deviation (default: size of population).
=item C<-selection =E<gt> [ 'RouletteDistribution', 'beta', $aa, $bb ]>
I<Beta> distribution. The density of the beta is:
X^($aa - 1) * (1 - X)^($bb - 1) / B($aa , $bb) for 0 < X < 1.
C<$aa> and C<$bb> are set by default to number of parents.
B<Argument restrictions:> Both $aa and $bb must not be less than 1.0E-37.
=item C<-selection =E<gt> [ 'RouletteDistribution', 'binomial' ]>
Binomial distribution. No additional parameters are needed.
=item C<-selection =E<gt> [ 'RouletteDistribution', 'chi_square', $df ]>
Chi-square distribution with C<$df> degrees of freedom. C<$df> by default is set to size of population.
=item C<-selection =E<gt> [ 'RouletteDistribution', 'exponential', $av ]>
Exponential distribution, where C<$av> is average . C<$av> by default is set to size of population.
=item C<-selection =E<gt> [ 'RouletteDistribution', 'poisson', $mu ]>
Poisson distribution, where C<$mu> is mean. C<$mu> by default is set to size of population.
=back
=item B<Distribution>
Chromosomes/individuals are selected with specified distribution. See below.
=over 12
=item C<-selection =E<gt> [ 'Distribution', 'uniform' ]>
Standard uniform distribution. No additional parameters are needed.
=item C<-selection =E<gt> [ 'Distribution', 'normal', $av, $sd ]>
Normal distribution, where C<$av> is average (default: size of population /2) and $C<$sd> is standard deviation (default: size of population).
=item C<-selection =E<gt> [ 'Distribution', 'beta', $aa, $bb ]>
I<Beta> distribution. The density of the beta is:
X^($aa - 1) * (1 - X)^($bb - 1) / B($aa , $bb) for 0 < X < 1.
C<$aa> and C<$bb> are set by default to number of parents.
B<Argument restrictions:> Both $aa and $bb must not be less than 1.0E-37.
=item C<-selection =E<gt> [ 'Distribution', 'binomial' ]>
Binomial distribution. No additional parameters are needed.
=item C<-selection =E<gt> [ 'Distribution', 'chi_square', $df ]>
Chi-square distribution with C<$df> degrees of freedom. C<$df> by default is set to size of population.
=item C<-selection =E<gt> [ 'Distribution', 'exponential', $av ]>
Exponential distribution, where C<$av> is average . C<$av> by default is set to size of population.
=item C<-selection =E<gt> [ 'Distribution', 'poisson', $mu ]>
Poisson distribution, where C<$mu> is mean. C<$mu> by default is set to size of population.
=back
=back
=item -strategy
This defines the astrategy of crossover operation. It expects an array
reference listed below:
-strategy => [ $type, @params ]
where type is one of:
=over 4
=item PointsSimple
Simple crossover in one or many points. The best chromosomes/individuals are
selected for the new generation. For example:
-strategy => [ 'PointsSimple', $n ]
where C<$n> is the number of points for crossing.
=item 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', $n ]
where C<$n> is the number of points for crossing.
=item 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', $n ]
where C<$n> is number of points for crossing.
=item 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', $n ]
where C<$n> is the number of points for crossing.
=item Distribution
In I<distribution> crossover parents are crossed in points selected with the
specified distribution. See below.
=over 8
=item C<-strategy =E<gt> [ 'Distribution', 'uniform' ]>
Standard uniform distribution. No additional parameters are needed.
=item C<-strategy =E<gt> [ 'Distribution', 'normal', $av, $sd ]>
Normal distribution, where C<$av> is average (default: number of parents/2) and C<$sd> is standard deviation (default: number of parents).
=item C<-strategy =E<gt> [ 'Distribution', 'beta', $aa, $bb ]>
I<Beta> distribution. The density of the beta is:
X^($aa - 1) * (1 - X)^($bb - 1) / B($aa , $bb) for 0 < X < 1.
C<$aa> and C<$bb> are set by default to the number of parents.
B<Argument restrictions:> Both $aa and $bb must not be less than 1.0E-37.
=item C<-strategy =E<gt> [ 'Distribution', 'binomial' ]>
Binomial distribution. No additional parameters are needed.
=item C<-strategy =E<gt> [ 'Distribution', 'chi_square', $df ]>
Chi-squared distribution with C<$df> degrees of freedom. C<$df> by default is set to the number of parents.
=item C<-strategy =E<gt> [ 'Distribution', 'exponential', $av ]>
Exponential distribution, where C<$av> is average . C<$av> by default is set to the number of parents.
=item C<-strategy =E<gt> [ 'Distribution', 'poisson', $mu ]>
Poisson distribution, where C<$mu> is mean. C<$mu> by default is set to the number of parents.
=back
=item PMX
PMX method defined by Goldberg and Lingle in 1985. Parameters: I<none>.
=item OX
OX method defined by Davis (?) in 1985. Parameters: I<none>.
=back
=item -cache
This defines whether a cache should be used. Allowed values are 1 or 0
(default: I<0>).
=item -history
This defines whether history should be collected. Allowed values are 1 or 0 (default: I<0>).
=item -native
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