415b419671
I also changed
- the eoQuadratic into eoQuad (as dicussed with Maarten)
- the eoBin into eoBit, with more appropriate names for the "binary"
operators (that can be unary!) as no one protested when I posted on
eodev list
676 lines
37 KiB
HTML
676 lines
37 KiB
HTML
<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
|
|
<html>
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
|
<meta name="GENERATOR" content="Mozilla/4.75 [en] (X11; U; Linux 2.2.17-21mdk i686) [Netscape]">
|
|
<title>Genetic Engine</title>
|
|
</head>
|
|
<body text="#000000" link="#0000EF" vlink="#51188E" alink="#FF0000" background="beige009.jpg">
|
|
<b><font color="#CC0000">General: </font></b><a href="eoTopDown.html">Algorithm-Based</a>
|
|
- <a href="eoBottomUp.html">Component-Based</a> - <a href="eoProgramming.html">Programming
|
|
hints</a> - <b><font face="Arial,Helvetica"><font size=+1><a href="../../doc/html/index.html">EO
|
|
documentation
|
|
<hr WIDTH="100%"></a></font></font><font color="#CC0000">Local: </font></b><a href="#introduction">Introduction</a>
|
|
- <a href="#selection">Selection</a> - <a href="#replacement">Replacement</a>
|
|
- <a href="#popular">Popular evolution engines</a> - <a href="#tournament">Tournaments</a>
|
|
- <a href="#merge">Merge</a> - <a href="#reduce">Reduce</a> - <a href="#howmany">HowMany</a>
|
|
- <a href="#SAD">SurviveAndDie</a>
|
|
<hr WIDTH="100%">
|
|
<center>
|
|
<h1>
|
|
<b><font color="#CC0000">Evolution Engine</font></b></h1></center>
|
|
|
|
<hr WIDTH="100%">
|
|
<br><a NAME="introduction"></a><b><font color="#000099"><font size=+2>Evolution
|
|
Engines</font></font></b>
|
|
<p>The term <b><font color="#FF6600">evolution engine</font></b> denotes
|
|
the different parts of an Evolutionary Algorithm that simulate the Darwinism:
|
|
<center>
|
|
<p><i><font color="#009900">The fittest individuals are more likely to
|
|
reproduce and survive.</font></i></center>
|
|
|
|
<p>Darwinism takes place in two different phases of an EA, though in many
|
|
<a href="#popular">popular
|
|
variants</a>, only one phase is activated.
|
|
<p><a href="#selection">Selection</a> is the Darwinistic choice of parents
|
|
that will be allowed to <b><font color="#009900">reproduce</font></b><font color="#CC33CC">.</font>
|
|
<br><a href="#replacement">Replacement</a> takes place after reproduction,
|
|
and is the Darwinistic choice of those individuals that will <b><font color="#009900">survive</font></b>,
|
|
i.e. become the parents of the next generation.
|
|
<p>Both selection and replacement will be discussed in turn, before some
|
|
helper classes that are used within selection and replacement procedures
|
|
are presented.
|
|
<p>
|
|
<hr WIDTH="100%"><a NAME="selection"></a><b><font color="#000099"><font size=+2>Selection</font></font></b>
|
|
<p>The very beginning of the generation loop is the selection phase, where
|
|
some individuals from the population are chosen to become the parents,
|
|
to be later modified by the variation operators and become the offspring.
|
|
This is the first step of the <font color="#009900">artificial Darwinism</font>,
|
|
where the <i><font color="#FF6600">fittest individuals are allowed to reproduce</font></i>.
|
|
<br>Conceptually, there are two distinct ways to choose the lucky ones:
|
|
one by one from the very same population (i.e. with replacement), which
|
|
means that at the extreme the same individual can be chosen every time;
|
|
or as a whole, in some sort of batch procedure. Of course, repeated selection
|
|
of one individual results in a batch selection!
|
|
<p>There are hence two basic EO classes for selection: <font color="#009900">eoSelectOne</font>
|
|
and <font color="#009900">eoSelect</font>, with different interfaces.
|
|
<br>
|
|
<hr WIDTH="50%">
|
|
<br><b><font color="#000099">eoSelectOne: </font><font color="#FF0000">The
|
|
interface</font></b>
|
|
<p>The abstract class for selection of a single individual from a population
|
|
is <font color="#009900">eoSelectOne</font>, and the interface for its
|
|
<tt><font color="#993300">operator()</font></tt>
|
|
is
|
|
<center>
|
|
<p><b><tt><font color="#993300">const EOT & operator()(const eoPop<EOT>&
|
|
_parents)</font></tt></b></center>
|
|
|
|
<p>which you could have guessed from the inheritance tree for class <b><font face="Arial,Helvetica"><font size=+1><a href="../../doc/html/class_eoselectone.html">eoSelectOne</a></font></font></b>.,
|
|
as you see there that <font color="#009900">eoSelectOne</font> derives
|
|
from <tt><font color="#993300">class eoUF<const eoPop<EOT>&,
|
|
const EOT&></font></tt>.
|
|
<br>This means that it takes <font color="#FF6600">1 population</font>
|
|
(without the right to modify it - see the <b><tt><font color="#993300">const</font></tt></b>
|
|
keyword in argument) and returns a const reference to an individual (again,
|
|
the <b><tt><font color="#993300">const</font></tt></b> keyword ensures
|
|
that nothing will happen to the individual in the population - remember
|
|
it returns a reference).
|
|
<br>
|
|
<hr WIDTH="50%">
|
|
<br><b><font color="#000099">eoSelectOne: </font><font color="#FF0000">Instances</font></b>
|
|
<ul>
|
|
<li>
|
|
<b><tt><font color="#009900">eoDetTournamentSelect</font></tt></b> uses
|
|
the <a href="#detTournament">(deterministic) tournament</a> to choose one
|
|
individual. Its constructor has one parameter, the tournament size (integer
|
|
>= 2).</li>
|
|
|
|
<li>
|
|
<b><tt><font color="#009900">eoStochTournamentSelect</font></tt></b> uses
|
|
the <a href="#stochTournament">binary stochastic tournament</a> to choose
|
|
one individual. Its constructor has one parameter, the tournament rate
|
|
(real in [0.5,1]).</li>
|
|
|
|
<li>
|
|
<b><tt><font color="#009900">eoProportionalSelect</font></tt></b>
|
|
is the original <font color="#FF6600">roulette wheel</font> selection:
|
|
each parent is selected with a probability proportional to its fitness.</li>
|
|
|
|
<li>
|
|
<b><tt><font color="#009900">eoRandomSelect</font></tt></b> is the <font color="#FF6600">random</font>
|
|
selection and should give bad results! At the moment, it selects one individual
|
|
uniformly, but it would be easy to use any probability distribution.</li>
|
|
</ul>
|
|
|
|
<hr WIDTH="50%">
|
|
<br><b><font color="#000099">eoSelect: </font><font color="#FF0000">The
|
|
interface</font></b>
|
|
<p>The abstract class for batch selection of a whole set of individuals
|
|
from a population is <font color="#009900">eoSelect</font>, and the interface
|
|
for its
|
|
<tt><font color="#993300">operator()</font></tt> is
|
|
<center>
|
|
<p><b><tt><font color="#993300">void operator()(const eoPop<EOT>&
|
|
_source, eoPop<EOT>& _dest)</font></tt></b></center>
|
|
|
|
<p>which you could have guessed from the inheritance tree for class <b><font face="Arial,Helvetica"><font size=+1><a href="../../doc/html/class_eoselect.html">eoSelect</a></font></font></b>.,
|
|
as you see there that <font color="#009900">eoSelect</font> derives from
|
|
<tt><font color="#993300">class
|
|
eoBF<const eoPop<EOT>&, eoPop<EOT>&, void></font></tt>.
|
|
<br>This means that it takes <font color="#FF6600">2 populations</font>,
|
|
and fills the second one with individuals from the first one without modifying
|
|
it (see the <b><tt><font color="#993300">const</font></tt></b> keyword).
|
|
This raises two questions:
|
|
<ul>
|
|
<li>
|
|
How does it know how many individuals to select?</li>
|
|
|
|
<li>
|
|
How to use repeated selection of one individual (see above the <font color="#009900">eoSelectOne</font>
|
|
class)?</li>
|
|
</ul>
|
|
|
|
<hr WIDTH="50%">
|
|
<br><b><font color="#000099">eoSelect: </font><font color="#FF0000">HowMany</font></b>
|
|
<p>There are two ways an can derive the number of individuals it
|
|
has to select: either it is a fixed number, or it is some percentage of
|
|
the source population size (any positive real number). In both case, this
|
|
must be passed to the constructor. In most instances, however, the constructor
|
|
will accept a real number (double) and a boolean indicating whether this
|
|
real number should be used as an absolute integer or as a rate, thanks
|
|
to the <a href="#howmany">eoHowMany</a> class.
|
|
<p><b><font color="#FF0000">Note</font></b>: an <font color="#009900">eoSelect</font>
|
|
can select more individuals than there are in the original population.
|
|
It is the job of the <font color="#009900">replacement</font> to ensure
|
|
that the population size does not grow along the generations.
|
|
<p>
|
|
<hr WIDTH="50%"><b><font color="#000099">eoSelectMany: </font><font color="#FF0000">Encapsulating
|
|
eoSelectOne</font></b>
|
|
<p>It is clear that repeated selection of a single individual is a way
|
|
to do batch selection. This is why it is possible to encapsulate an object
|
|
of class <font color="#009900">eoSelectOne</font> into an object of class
|
|
<font color="#009900">eoSelect</font>
|
|
using the class <font color="#009900">eoSelectMany</font>. Class <font color="#009900">eoSelectMany</font>
|
|
is derived from class <font color="#009900">eoSelect</font> and takes in
|
|
its constructor an <font color="#009900">eoSelectOne</font> (plus the number
|
|
of individuals it should select, according to the <a href="#howmany">eoHowMany</a>
|
|
paradigm).
|
|
<p><b><font color="#FF0000">Note</font></b>: some procedures for selecting
|
|
a single individual require some pre-processing of the whole population
|
|
that takes place before any selection, and will be repeated identically
|
|
for every individual. The encapsulation of an into an allows
|
|
to call such technical processing only once through the use of method setup
|
|
of class . This method does nothing by default, but is mandatory
|
|
<br>
|
|
<hr WIDTH="50%">
|
|
<br><b><font color="#000099">eoSelect: </font><font color="#FF0000">Other
|
|
instances</font></b>
|
|
<ul>
|
|
<li>
|
|
<b><tt><font color="#009900">eoDetSelect</font></tt></b> selects individuals
|
|
<b><font color="#FF6600">deterministically</font></b>,
|
|
i.e. starting from the best ones down to the worse ones. If the total number
|
|
to select is less than the size of the source populations, the best individuals
|
|
are selected once. If more individuals are needed after reaching the bottom
|
|
of the population, then the selection starts again at top. It the total
|
|
number required is N times that of the source size, all individuals are
|
|
selected exactly N times.</li>
|
|
</ul>
|
|
No other instances of <font color="#009900">eoSelect</font> that are not
|
|
encapsualtions of <font color="#009900">eoSelectOne</font> procedures are
|
|
avaiable as of today (Jan. 4 2001).
|
|
<br>
|
|
<hr WIDTH="100%">
|
|
<br><a NAME="replacement"></a><b><font color="#000099"><font size=+2>Replacement</font></font></b>
|
|
<p>The replacement phase takes plac<font color="#000000">e after the birth
|
|
of all offspring through </font>variation operators. This is the second
|
|
step of the <font color="#009900">artificial Darwinism</font>, where the
|
|
<i><font color="#FF6600">fittest
|
|
individuals are allowed to survive</font></i>.
|
|
<br>It can also be viewed on the algorithmic side as closing the generation
|
|
loop, i.e. building the population that will be the initial population
|
|
of next generation. That population will be <font color="#FF6600">built
|
|
upon the old parents and the new-born offspring</font>. In all algorithms
|
|
that come up with EO, the <font color="#FF6600">population size</font>
|
|
is supposed to be <font color="#FF6600">constant</font> from one generation
|
|
to the next one - though nothing stops you from writing an algorithm with
|
|
varying population size.
|
|
<br>
|
|
<hr WIDTH="50%">
|
|
<br><b><font color="#000099">Replacement: </font><font color="#FF0000">The
|
|
interface</font></b>
|
|
<p>The abstract class for replacement procedures is the functor class
|
|
<font color="#009900">eoReplacement</font>,
|
|
and the interface for its <tt><font color="#993300">operator()</font></tt>
|
|
is
|
|
<center>
|
|
<p><b><tt><font color="#993300">void operator()(eoPop<EOT>& _parents,
|
|
eoPop<EOT>& _offspring)</font></tt></b></center>
|
|
|
|
<p>which you could have guessed from the inheritance tree for class <b><font face="Arial,Helvetica"><font size=+1><a href="../../doc/html/class_eoreplacement.html">eoReplacement</a></font></font></b>.,
|
|
as you see there that <font color="#009900">eoReplacement</font> derives
|
|
from <tt><font color="#993300">class eoBF<eoPop<EOT>&, eoPop<EOT>&,
|
|
void></font></tt>.
|
|
<br>This means that it takes <font color="#FF6600">2 populations</font>
|
|
(called, for obvious anthropomorphic reasons, _parents and _offspring :-)
|
|
and is free to modify both, but the resulting population should be placed
|
|
in the first argument (usually called_parents) to close the loop and go
|
|
to next generation.
|
|
<br>
|
|
<hr WIDTH="50%">
|
|
<br><b><font color="#000099">Replacement: </font><font color="#FF0000">Instances</font></b>
|
|
<ul>
|
|
<li>
|
|
<b><tt><font color="#009900">eoGenerationalReplacement </font></tt></b>This
|
|
is the most straightforward replacement, called <font color="#FF6600">generational
|
|
replacement</font>: all offspring replace all parents (used in Holland's
|
|
and Goldberg's traditional GAs). It takes no argument, and supposes
|
|
that offspring and parents are of the same size (but does not check!).</li>
|
|
|
|
<br>
|
|
<li>
|
|
<a NAME="SSGA"></a><b><tt><font color="#009900">eoMergeReduce</font></tt></b>
|
|
This is one the basic types of replacement in EO. It has two major steps,
|
|
<font color="#FF6600">merging</font>
|
|
both populations of parents and offspring, and <font color="#FF6600">reducing</font>
|
|
this big population to the right size. It <font face="Arial,Helvetica"><font size=+1><a href="../../doc/html/class_eomegereduce.html">contains
|
|
two objects</a></font></font> of respective types <b><font color="#009900"><a href="#merge">eoMerge</a></font></b>
|
|
and <b><font color="#009900"><a href="#reduce">eoReduce</a></font></b>
|
|
and you can probably guess what each of them actually does :-)</li>
|
|
|
|
<br>
|
|
<p>
|
|
<p>Available <font color="#FF6600">instances of eoMergeReduce</font> replacement
|
|
include
|
|
<ul>
|
|
<li>
|
|
<b><tt><font color="#009900">eoCommaReplacement</font></tt></b>, one of
|
|
the two standard strategies in <font color="#000000">Evolution Strategies</font>,
|
|
<b><font color="#FF6600">selects
|
|
the best offspring</font></b>. It is an
|
|
<b><tt><font color="#993300">eoMergeReduce(eoNoElitism,
|
|
eoTruncate)</font></tt></b>.</li>
|
|
|
|
<li>
|
|
<b><tt><font color="#009900">eoPlusReplacement</font></tt></b>, the other
|
|
standar<font color="#000000">d Evolution Startegies repla</font>cement,
|
|
where <b><font color="#FF6600">the best from offspring+parents</font></b>
|
|
become the next generation. It is an <b><tt><font color="#993300">eoMergeReduce(eoPlus,
|
|
eoTruncate)</font></tt></b>.</li>
|
|
|
|
<li>
|
|
<b><tt><font color="#009900">eoEPReplacement</font></tt></b>, used in th<font color="#000000">e
|
|
Evolutionary Programming historical </font>algorithm, does an EP stochastic
|
|
tournament among parents + offspring. It is an <b><tt><font color="#993300">eoMergeReduce(eoPlus,
|
|
eoEPReduce)</font></tt></b> and its constructor requires as argument T,
|
|
the size of the tournament (unsigned int).</li>
|
|
</ul>
|
|
|
|
<li>
|
|
<b><tt><font color="#009900">eoReduceMerge</font></tt></b> is another important
|
|
type of eoReplacement: the parents are first reduced, and then merged with
|
|
the offspring. Note that the parent population is reduced of the exact
|
|
number of offspring.</li>
|
|
|
|
<br>Though not mandatory, it is implicitely assumed that few offspring
|
|
have been generated. Hence, all derived replacement procedures of class
|
|
<b><tt><font color="#009900">eoReduceMerge</font></tt></b>
|
|
are termed <b><tt><font color="#009900">eoSSGAxxx</font></tt></b>, as they
|
|
are the ones to use in SteadyState Genetic Algorithm engine. This gives
|
|
the following <font color="#FF6600">instances of eoReduceMerge</font>:
|
|
<ul>
|
|
<li>
|
|
<b><tt><font color="#009900">eoSSGAWorseReplacement</font></tt></b>
|
|
in which the worse parents are killed and replaced by all offsprings (no
|
|
additional argument needed);</li>
|
|
|
|
<li>
|
|
<b><tt><font color="#009900">eoSSGADetTournamentReplacement</font></tt></b>
|
|
in which parents to be killed are chosen by a (reverse) determinitic tournament.
|
|
Additional parameter (in the constructor) is the tournament size, an <b><tt><font color="#993300">unsigned
|
|
int</font></tt></b>.</li>
|
|
|
|
<li>
|
|
<b><tt><font color="#009900">eoSSGAStochTournamentReplacement</font></tt></b>
|
|
in which parents to be killed are chosen by a (reverse) stochastic tournament.
|
|
Additional parameter (in the constructor) is the tournament rate, a <b><tt><font color="#993300">double</font></tt></b>.</li>
|
|
</ul>
|
|
|
|
<li>
|
|
<a NAME="SADreplacement"></a><b><tt><font color="#009900">eoSurviveAndDie</font></tt></b>
|
|
replacement strategies are a generalization of both the above that allows
|
|
strong elitist and eugenism in both the parent population and the offspring
|
|
population. The <b><tt><font color="#009900"><a href="#SAD">eoSurviveAndDie</a></font></tt></b>
|
|
building block takes one population, kills the worse and moves the best
|
|
to some safe place. The corresponding replacements apply an <b><tt><font color="#009900">eoSurviveAndDie</font></tt></b>
|
|
to the parents, another one to the offspring, and finally merges the remaining
|
|
parents and offspring before reducing the resulting population to the right
|
|
size. Available instances of <b><tt><font color="#009900">eoSurviveAndDieReplacement</font></tt></b>
|
|
are limited todayto the <b><tt><font color="#009900">eoDeterministicSaDReplacement</font></tt></b>,
|
|
the that uses a deterministic MergeReduce.</li>
|
|
|
|
<p><br><b><font color="#FF0000">Note</font></b>: The basic use (and initial
|
|
motivation) for <b><tt><font color="#009900">eoSurviveAndDie</font></tt></b>
|
|
takes 2 arguments, an eoMergeReduce and a number of surviving parents.
|
|
It starts by copying the best parents to the new populations, then merges
|
|
the remaining parents with the offspring before reducing to the number
|
|
of remaining seats in the new population.</ul>
|
|
|
|
<hr WIDTH="50%">
|
|
<br><a NAME="weakelitism"></a><b><font color="#000099">Replacement: </font><font color="#FF0000">Adding
|
|
(weak) elitism</font></b>
|
|
<p>You can add what is called <font color="#FF6600">weak elitism</font>
|
|
to any replacement by encapsulating it into an <b><tt><font color="#009900">eoWeakElitismReplacement</font></tt></b>
|
|
object. Weak elitism ensures that the overall <font color="#FF6600">best
|
|
fitness</font> in the population <font color="#FF6600">will never decrease</font>:
|
|
if the best fitness in the new population is less than the best fitness
|
|
of the parent population, then the best parent is added back to the new
|
|
population, replacing the worse.
|
|
<p>Within EO, this is very easy to add:
|
|
<p>First, declare your replacement functor (here, generational, but it
|
|
can be any replacement object):
|
|
<br><b><tt><font color="#009900">eoGenerationalReplacement<Indi> genReplace;</font></tt></b>
|
|
<br>Then wrap the weak elitism around it:
|
|
<br><b><tt><font color="#009900">eoWeakElitismReplacement<Indi> replace(genReplace);</font></tt></b>
|
|
<br>and use now replace as your replacement procedure within your algorithm.
|
|
<p><font color="#FF0000">Note</font>: of course, adding weak elitism to
|
|
an elitist replacement makes no sense - but will not harm either :-)
|
|
<br>
|
|
<hr WIDTH="50%">
|
|
<br><b><font color="#000099">Replacement: </font><font color="#FF0000">Test
|
|
file</font></b>
|
|
<p>The file <b><tt><font color="#993300">t-eoReplacement</font></tt></b>
|
|
in the <b><font color="#FF6600">test directory</font></b> implements all
|
|
above replacement procedures within a very simple and easy-to-monitor Dummy
|
|
EO class.
|
|
<p>
|
|
<hr WIDTH="100%">
|
|
<br><a NAME="popular"></a><b><font color="#000099"><font size=+2>Popular
|
|
evolution engines</font></font></b>
|
|
<p>This section will be completed soon - in the meantime just trust us
|
|
that all of these are already implemented in EO (except maybe some of the
|
|
last category :-) !!!!!!
|
|
<p>The most popular evolution engines are listed below, together with the
|
|
way to use them in EO. If you don't find your particuler algorithm, please
|
|
send it to us, and we might include it here! In the following, P will denote
|
|
the number of individuals in the initial population.
|
|
<ul>
|
|
<li>
|
|
<a NAME="GGA"></a><b><font color="#000099">Generational Genetic Algorihtm</font></b><font color="#000000">:
|
|
popularized by Holland (75) and Goldberg (89), it uses</font></li>
|
|
|
|
<br><font color="#FF0000">Number of offspring: </font><font color="#000000">
|
|
P</font>
|
|
<br><font color="#FF0000">Selection:</font><font color="#000000"> Proportional
|
|
(the historical roulette wheel) </font><b><font color="#FF6600">when maximizing
|
|
a positive scalar fitness</font></b><font color="#000000">, ranking or
|
|
tournament (stochatic or deterministic) in all cases.</font>
|
|
<br><font color="#FF0000">Replacement:</font><font color="#000000"> Generational.</font>
|
|
<br><font color="#FF0000">Remark:</font><font color="#000000"> You could
|
|
use also the Comma replacement, with exactly the same result as there are
|
|
as many offspring as we need indiviudals in the next population. And using
|
|
the eoSSGAWorseReplacement would also give the same result, but would be
|
|
very inefficient!</font>
|
|
<br><font color="#000000">You can also add <a href="#weakelitism">weak
|
|
elitism</a> to preserve the best individual.</font>
|
|
<li>
|
|
<a NAME="SSGA"></a><b><font color="#000099">Steady-State Genetic Algorithm</font></b><font color="#000000">:
|
|
widely used in GA/GP community</font></li>
|
|
|
|
<br><font color="#FF0000">Number of offspring: </font><font color="#000000">
|
|
small (historically, 1)</font>
|
|
<br><font color="#FF0000">Selection:</font><font color="#000000"> tournament
|
|
(you can use ranking or proportional, but it will be rather inefficient).</font>
|
|
<br><font color="#FF0000">Replacement:</font><font color="#000000"> An
|
|
eoSSGAxxxReplacement.</font>
|
|
<br><font color="#FF0000">Remark:</font><font color="#000000"> You can
|
|
also use the eoPlusReplacement, but you divert from the original SSGA</font>
|
|
<li>
|
|
<a NAME="ESPlus"></a><b><font color="#000099">(MU+Lambda)-Evolution Strategy</font></b><font color="#000000">:
|
|
The elitist ES strategy (Rechenberg 71 and Schwefel 81)</font></li>
|
|
|
|
<br><font color="#FF0000">Number of offspring: </font><font color="#000000">
|
|
Any</font>
|
|
<br><font color="#FF0000">Selection:</font><font color="#000000"> eoDetSelect
|
|
(batch deterministic).</font>
|
|
<br><font color="#FF0000">Replacement:</font><font color="#000000"> eoPlusReplacement</font>
|
|
<br><font color="#FF0000">Remark:</font><font color="#000000"> You could
|
|
also use eoEPReplacement, to smoothen the selective pressure during replacement,
|
|
thus getting close to EP evolution engine</font>
|
|
<li>
|
|
<a NAME="ESComma"></a><b><font color="#000099">(MU,Lambda)-Evolution Strategy</font></b><font color="#000000">:
|
|
The non-elitist ES strategy</font></li>
|
|
|
|
<br><font color="#FF0000">Number of offspring: </font><font color="#000000">
|
|
> P</font>
|
|
<br><font color="#FF0000">Selection:</font><font color="#000000"> eoDetSelect
|
|
(batch deterministic).</font>
|
|
<br><font color="#FF0000">Replacement:</font><font color="#000000"> eoCommaReplacement</font>
|
|
<br><font color="#FF0000">Remark:</font><font color="#000000"> You can
|
|
also add <a href="#weakelitism">weak elitism</a> to preserve the best individual
|
|
- though you'd probably use the plus strategy if you want (strong) elitism.</font>
|
|
<li>
|
|
<a NAME="EP"></a><b><font color="#000099">Evolutionary Programming</font></b><font color="#000000">:
|
|
The historical method of L. Fogel (65)</font></li>
|
|
|
|
<br><font color="#FF0000">Number of offspring: </font><font color="#000000">
|
|
P</font>
|
|
<br><font color="#FF0000">Selection:</font><font color="#000000"> eoDetSelect
|
|
(batch deterministic). Every individual reproduces exactly once.</font>
|
|
<br><font color="#FF0000">Replacement:</font><font color="#000000"> eoEPReplacement,
|
|
though one historical replacement was the determnistic replacement - i.e.
|
|
in EO the eoPlusReplacement).</font>
|
|
<br><font color="#FF0000">Remark:</font><font color="#000000"> Close to
|
|
an (P+P)-ES</font>
|
|
<li>
|
|
<a NAME="General"></a><font color="#FF0000">You name it :-)</font><font color="#000000">:
|
|
you can of course choose whatever combination you like - respecting a few
|
|
constraints and common-sense remarks. For instance, eoProportionalSelect
|
|
should be used only when maximizing a positive fitness, eoCommaReplacement
|
|
requires more offspring than parents, and, over all, existing EO algorithms
|
|
wirk with fixed size population - and it is your responsability to use
|
|
a cmbinatino of selection/replacement that fulfills this requirement (or
|
|
to create your own eoAlgo that handles varying size populations).</font></li>
|
|
</ul>
|
|
|
|
<hr WIDTH="100%">
|
|
<br><a NAME="tournament"></a><b><font color="#000099"><font size=+2>Tournaments</font></font></b>
|
|
<p>Tournaments are an easy and quick way to <b><font color="#FF6600">select</font></b>
|
|
individuals within a population based on simple comparisons. Though usually
|
|
based on fitness comparisons, they can use any comparison operator.
|
|
<br>In EO, there are two variants of tournaments used to select one single
|
|
individual, namely <b><tt><font color="#009900">Deterministic Tournament</font></tt></b>
|
|
and <b><tt><font color="#009900">Stochastic Tournament</font></tt></b>,
|
|
that are used in selection and in replacement procedures, and a global
|
|
tournament-based selection of a whole bunch of individuals, the <b><tt><font color="#009900">EP
|
|
Tournament</font></tt></b>. Though the single-selection tournaments can
|
|
be repeated to select more than one individual, and the batch tournament
|
|
selection can be used to select a single individual, both uses are probably
|
|
a waste of CPU time.
|
|
<ul>
|
|
<li>
|
|
<a NAME="detTournament"></a><b><tt><font color="#009900">Deterministic
|
|
Tournament</font></tt></b> of size T returns the best of T uniformly chosen
|
|
individuals in the population. Its size T should be an integer >= 2. It
|
|
is implemented in the <b><tt><font color="#009900">eoDetTournamentSelect</font></tt></b>
|
|
class, a sub-class of eoSelectOne, as well as in the <b><tt><font color="#009900">eoDetTournamentTruncate</font></tt></b>
|
|
class that repeatidly removes from the population the "winner" of the inverse
|
|
tournament. These objects use the C++ function determinitic_tournament
|
|
in <a href="../../doc/html/selectors_h-source.html">selectors.h</a>.</li>
|
|
|
|
<li>
|
|
<a NAME="stochTournament"></a><b><tt><font color="#009900">Stochastic Tournament</font></tt></b>
|
|
of rate R first choses two individuals from the population, and selects
|
|
the best one with probability R (the worse one with probability 1-R). Real
|
|
parameter R should be in [0.5,1]. It is implemented in the <b><tt><font color="#009900">eoStochTournamentSelect</font></tt></b>
|
|
class, a sub-class of eoSelectOne, as well as in the <b><tt><font color="#009900">eoStochTournamentTruncate</font></tt></b>
|
|
class that repeatidly removes from the population the "winner" of the inverse
|
|
tournament. These objects use the C++ function determinitic_tournament
|
|
in <a href="../../doc/html/selectors_h-source.html">selectors.h</a>.</li>
|
|
|
|
<br><b><font color="#FF0000">Note</font></b>: A stochastic tournament with
|
|
rate 1.0 is strictly identical to a deterministic tournament of size 2.
|
|
<li>
|
|
<a NAME="EPTournament"></a><b><tt><font color="#009900">EP Tournament</font></tt></b>
|
|
of size T is a global tournament: it works by assigning a score to all
|
|
individuals in the population the following way: starting with a score
|
|
of 0, each individual I is "opposed" T times to a uniformly chosen individual.
|
|
Everytime I wins, its score in incremented by 1 (and by 0.5 for every draw).
|
|
The individuals are then selected deterministically based on their scores
|
|
from that procedure. The <b><tt><font color="#009900">EP Tournament</font></tt></b>
|
|
is implemented in the <b><tt><font color="#009900">eoEPReduce</font></tt></b>
|
|
truncation method used in the <b><tt><font color="#009900">eoEPReplacement</font></tt></b>
|
|
procedure.</li>
|
|
|
|
<br><b><font color="#FF0000">Note</font></b>: whereas both the determinitic
|
|
and the stochastic tournament select one individual, the EP tournament
|
|
is designed for batch selection. Of course it could be used to select a
|
|
single individual, but at a rather high computational cost.</ul>
|
|
|
|
<p><br>
|
|
<hr WIDTH="100%">
|
|
<br><a NAME="merge"></a><b><font color="#000099"><font size=+2>Merging
|
|
populations</font></font></b>
|
|
<p>In replacement procedures, one frequently needs to merge two populations
|
|
(computed form old parents and new-born offspring). Classes derived from
|
|
the abstract class eoMerge are written for that purpose.
|
|
<br>
|
|
<hr WIDTH="50%">
|
|
<br><b><font color="#000099">eoMerge</font></b>: <b><font color="#FF0000">interface</font></b>
|
|
<br>The abstract class for merging procedures is the functor class
|
|
<font color="#009900">eoMerge</font>,
|
|
and the interface for its <tt><font color="#993300">operator()</font></tt>
|
|
is
|
|
<center>
|
|
<p><b><tt><font color="#993300">void operator()(const eoPop<EOT>&
|
|
_parents, eoPop<EOT>& _offspring)</font></tt></b></center>
|
|
|
|
<p>which you could have guessed from the inheritance tree for class <b><font face="Arial,Helvetica"><font size=+1><a href="../../doc/html/class_eomerge.html">eoMerge</a></font></font></b>,
|
|
as you see there that <font color="#009900">eoMerge</font> derives from
|
|
<br><tt><font color="#993300">class eoBF<const eoPop<EOT>&, eoPop<EOT>&,
|
|
void></font></tt>.
|
|
<br>This means that it takes <font color="#FF6600">2 populations</font>
|
|
and modifies the seond one by adding some individuals from the first one
|
|
(which is supposed to remain <b><tt><font color="#993300">const</font></tt></b>ant).
|
|
<br>
|
|
<hr WIDTH="50%">
|
|
<br><b><font color="#000099">eoMerge</font></b>: <b><font color="#FF0000">instances</font></b>
|
|
<br>Available <font color="#FF6600">instances of eoMerge</font> objects
|
|
are <b><tt><font color="#009900">eoPlus</font></tt></b>, that simply adds
|
|
the parents to the offspring, or <b><tt><font color="#009900">eoElitism</font></tt></b>,
|
|
that adds only some of the (best) parents to the offspring. A special case
|
|
of eoElistism is <b><tt><font color="#009900">eoNoElitism</font></tt></b>,
|
|
an eoMerge that does nothing.
|
|
<p>
|
|
<hr WIDTH="100%">
|
|
<br><a NAME="reduce"></a><b><font color="#000099"><font size=+2>Reducing
|
|
populations</font></font></b>
|
|
<p>The other useful component of replacement procedures, <font color="#009900">eoReduce</font>,
|
|
<font color="#FF6600">kills
|
|
some individuals</font> from a given population.
|
|
<br>
|
|
<hr WIDTH="50%">
|
|
<br><b><font color="#000099">eoReduce</font></b>: <b><font color="#FF0000">interface</font></b>
|
|
<br>The abstract class for reducing procedures is the functor class
|
|
<font color="#009900">eoReduce</font>,
|
|
and the interface for its <tt><font color="#993300">operator()</font></tt>
|
|
is
|
|
<center>
|
|
<p><b><tt><font color="#993300">void operator()(eoPop<EOT>& _parents,
|
|
unsigned int new_size)</font></tt></b></center>
|
|
|
|
<p>which you could have guessed from the inheritance tree for class <b><font face="Arial,Helvetica"><font size=+1><a href="../../doc/html/class_eoreduce.html">eoReduce</a></font></font></b>,
|
|
as you see there that <font color="#009900">eoReduce</font> derives from
|
|
<br><tt><font color="#993300">class eoBF<eoPop<EOT>&, unsigned
|
|
int, void></font></tt>.
|
|
<br>An <font color="#009900">eoReduce</font> shoud take a<font color="#FF6600">
|
|
population</font> and shrink it to the required size.
|
|
<br>
|
|
<hr WIDTH="50%">
|
|
<br><b><font color="#000099">eoReduce</font></b>: <b><font color="#FF0000">instances</font></b>
|
|
<br>Available <font color="#FF6600">instances of eoReduce</font> are
|
|
<ul>
|
|
<li>
|
|
<b><tt><font color="#009900">eoTruncate</font></tt></b>, deterministically
|
|
kills the worse individuals, keeping only the required number. It starts
|
|
by sorting teh populations, and hence does <font color="#FF6600">modify
|
|
its order</font>.</li>
|
|
|
|
<li>
|
|
<b><tt><font color="#009900">eoLinearTruncate</font></tt></b>, deterministically
|
|
kills the worse individuals, keeping only the required number. It does
|
|
so by repeatedly removing the worsr individual. Hence does <font color="#FF6600">not
|
|
modify its order</font>, but takes longer time than <b><tt><font color="#009900">eoTruncate</font></tt></b>
|
|
in case of many offspring.</li>
|
|
|
|
<li>
|
|
<b><tt><font color="#009900">eoEPReduce</font></tt></b>, uses the <a href="#EPtournament">EP
|
|
stochastic tournament</a> to reduce the population. It requires an additinal
|
|
argument, the tournament size.</li>
|
|
|
|
<li>
|
|
<b><tt><font color="#009900">eoDetTournamentTruncate</font></tt></b> uses
|
|
inverse deterministic tournament to repeatidly kill one individual until
|
|
the propoer size is reached. As <b><tt><font color="#009900">eoLinearTruncate</font></tt></b>,
|
|
it might take some time in the case of many offspring. It requires the
|
|
size of the tournament (<b><tt><font color="#993300">unsigned int</font></tt></b>)
|
|
as parameter in the constructor (default is 2).</li>
|
|
|
|
<li>
|
|
<b><tt><font color="#009900">eoStochTournamentruncate</font></tt></b>
|
|
uses inverse stochastic tournament to repeatidly kill individuals from
|
|
the population. It requires the rate of the tournament (<b><tt><font color="#993300">double</font></tt></b>)
|
|
as parameter in the constructor (default is 0.75).</li>
|
|
</ul>
|
|
|
|
<hr WIDTH="100%">
|
|
<br><a NAME="howmany"></a><b><font color="#000099"><font size=+2>eoHowMany:
|
|
Choosing a number of individuals</font></font></b>
|
|
<p>Many classes in selection/replacement procedures will handle a number
|
|
of individuals that may either be fixed or be a fraction of some argument-population
|
|
size.
|
|
<br>Of course, it is possible to write two different classes that will
|
|
only differ by the way they compute the number of individuals they have
|
|
to treat, as it is done for selectors with the two classes <font color="#009900">eoSelectPerc</font>
|
|
and <font color="#009900">eoSelectNumber</font> (it could also have been
|
|
possible to have some pure abstrat class and implement the computation
|
|
of the number of individuals to treat in some derived classes).
|
|
<br>However, rather than multiply the number of class, EO has defined a
|
|
class that will handle the problem once and for all, the class <b><tt><font color="#993300">eoHowMany</font></tt></b>.
|
|
It receives a <b><tt><font color="#993300">double</font></tt></b>, and
|
|
a <b><tt><font color="#993300">boolean</font></tt></b> indicating whether
|
|
that double is to be treated <b><font color="#FF6600">as a rate</font></b>
|
|
or as <b><font color="#FF6600">an absolute (unisgned) interger.</font></b>
|
|
<br>
|
|
<hr WIDTH="50%">
|
|
<br><b><font color="#000099">eoHowMany</font></b>: <b><font color="#FF0000">interface</font></b>
|
|
<br>The class interface for its <tt><font color="#993300">operator()</font></tt>
|
|
is
|
|
<center>
|
|
<p><b><tt><font color="#993300">unsigned int operator()(unsigned int _pop_size)</font></tt></b></center>
|
|
|
|
<p>which you could have guessed from the inheritance tree for class <b><font face="Arial,Helvetica"><font size=+1><a href="../../doc/html/class_eohowmany.html">eoHowMany</a></font></font></b>,
|
|
as you see there that <b><tt><font color="#993300">eoHowMany</font></tt></b>
|
|
derives from
|
|
<br><tt><font color="#993300">class eoUF<unsigned int, unsigned int></font></tt>.
|
|
<p>Its constructor takes 2 argumenrts:
|
|
<center>
|
|
<p><b><tt><font color="#993300">eoHowMany(double _rate, bool _interpret_as_rate
|
|
= true)</font></tt></b></center>
|
|
so by default the double is indeed interpreted as a rate.
|
|
<p>It is used in <font color="#009900">eoSelectMany</font> (which supersedes
|
|
<font color="#009900">eoSelectPerc</font>
|
|
and <font color="#009900">eoSelectNumber</font>, but they are left there
|
|
for tutorial reasons!) as well as in many <a href="#reduce">truncation</a>
|
|
methods.
|
|
<p>
|
|
<hr WIDTH="100%">
|
|
<br><a NAME="SAD"></a><b><font color="#000099"><font size=+2>Survive and
|
|
Die</font></font></b>
|
|
<br>This class is highly politically incorrect: it implements strong elitism
|
|
and eugenism :-)
|
|
<br>It starts by killing the worse individuals from the source argument,
|
|
then appends the best ones to the destination argument and removes them
|
|
from the source argument. It is used in <b><tt><a href="#SADreplacement">eoSurviveAndDieReplacement</a></tt></b>,
|
|
where the same dest is used successively for the parents and the offspring.
|
|
<p><b><font color="#000099">eoSurviveAndDie</font></b>: <b><font color="#FF0000">interface</font></b>
|
|
<br>The class interface for its <tt><font color="#993300">operator()</font></tt>
|
|
is
|
|
<center>
|
|
<p><b><tt><font color="#993300">void operator()(eoPop<EOT>& _source,
|
|
eoPop<EOT>& _dest)</font></tt></b></center>
|
|
|
|
<p>which you could have guessed from the inheritance tree for class <b><font face="Arial,Helvetica"><font size=+1><a href="../../doc/html/class_eosurviveanddie.html">eoSurviveAndDie</a></font></font></b>,
|
|
as you see there that <b><tt><font color="#993300">eoSurviveAndDie</font></tt></b>
|
|
derives from <tt><font color="#993300">class eoBF<eoPop<EOT>&,
|
|
eoPop<EOT>&, void></font></tt>.
|
|
<p>Its constructor takes 3 argumenrts:
|
|
<center>
|
|
<p><b><tt><font color="#993300">eoHowMany(double _survive, double _die,
|
|
bool _interpret_as_rate = true)</font></tt></b></center>
|
|
|
|
<p>to indicate how many (or what proportion, according to <b><tt><font color="#993300">_interpret_as_rate</font></tt></b>)
|
|
of the source should be copied to the dest population, and how many (or
|
|
what proportion, according to <b><tt><font color="#993300">_interpret_as_rate</font></tt></b>)
|
|
should be erased from the source.
|
|
<p>
|
|
<hr WIDTH="100%"><b><font color="#CC0000">Local: </font></b><a href="#introduction">Introduction</a>
|
|
- <a href="#selection">Selection</a> - <a href="#replacement">Replacement</a>
|
|
- <a href="#popular">Popular evolution engines</a> - <a href="#tournament">Tournaments</a>
|
|
- <a href="#merge">Merge</a> - <a href="#reduce">Reduce</a> - <a href="#howmany">HowMany</a>
|
|
- <a href="#SAD">SurviveAndDie</a>
|
|
<br>
|
|
<hr WIDTH="100%">
|
|
<br><b><font color="#CC0000">General: </font></b><a href="eoTopDown.html">Algorithm-Based</a>
|
|
- <a href="eoBottomUp.html">Component-Based</a> - <a href="eoProgramming.html">Programming
|
|
hints</a> - <b><font face="Arial,Helvetica"><font size=+1><a href="../../doc/html/index.html">EO
|
|
documentation</a></font></font></b>
|
|
<hr WIDTH="100%">
|
|
<address>
|
|
<a href="mailto:Marc.Schoenauer@polytechnique.fr">Marc Schoenauer</a></address>
|
|
|
|
<br><!-- Created: Mon Oct 30 07:27:13 CET 2000 --><!-- hhmts start -->Last
|
|
modified: Tue. Jan. 9 2001 <!-- hhmts end -->
|
|
</body>
|
|
</html>
|