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Now takes into account the last (and last!) modification of the operator interace:

Browse source 
no more invalidate, but a bool returned for simple operators, and a better description
of the eoPopulator/eoOpContainer links.
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evomarc 2001-02-17 08:22:53 +00:00
commit e0ace0794f
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eo/tutorial/html/eoOperators.html
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@ -2,7 +2,7 @@
<html> <html>
<head> <head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<meta name="GENERATOR" content="Mozilla/4.75 [en] (X11; U; Linux 2.2.17-21mdksmp i686) [Netscape]"> <meta name="GENERATOR" content="Mozilla/4.75 [en] (X11; U; Linux 2.2.17-21mdk i686) [Netscape]">
<title>Variation Operators</title> <title>Variation Operators</title>
</head> </head>
<body text="#000000" link="#0000EF" vlink="#51188E" alink="#FF0000" background="beige009.jpg"> <body text="#000000" link="#0000EF" vlink="#51188E" alink="#FF0000" background="beige009.jpg">
@ -24,10 +24,10 @@ combinations</a>- <a href="#advanced_general">Advanced operators</a>
<b><font color="#CC0000">Variation Operators</font></b></h1></center> <b><font color="#CC0000">Variation Operators</font></b></h1></center>
<a NAME="introduction"></a><b><font color="#000099"><font size=+2>Variation <a NAME="introduction"></a><b><font color="#000099"><font size=+2>Variation
Operators</font></font></b> Operators</font></font></b>
<br>Variation operators modify individuals, or, equivalently, move them <br>Variation operators modify the gnotype of individuals, or, equivalently,
in the search space. In Evolutionary Algorithms, varitaion operators are move them in the search space. In Evolutionary Algorithms, varitaion operators
almost always <b><font color="#FF6600">stochastic</font></b>, i.e. they are almost always <b><font color="#FF6600">stochastic</font></b>, i.e.
are based on random numbers, or equivalently, perform random modifications they are based on random numbers, or equivalently, perform random modifications
of their arguments. Variation operators are classified depending on the of their arguments. Variation operators are classified depending on the
number of arguments they use and/or modify. number of arguments they use and/or modify.
<ul> <ul>
@ -75,7 +75,15 @@ operators</a>, such as crossover operators where the mate is chosen according
to <b><font color="#FF6600">sexual preference</font></b> rather than fitness-based to <b><font color="#FF6600">sexual preference</font></b> rather than fitness-based
preferences.</li> preferences.</li>
</ul> </ul>
<b><font color="#FF0000">EO classes for variation operators</font></b>: <b><font color="#FF0000">Implementation</font></b>
<p>The basic idea of EO variation operators is that they operate on genotypes
only. Hence there should be generally no reference to anything related
to the fitness within a variation operator. However, whenever the genotype
of an individual has been modified, it will be necessary to recompute its
fitness before any selection process. This is why <b><font color="#FF6600">all
variation operator return</font></b> a bool that indicates whether or not
the genotype argument has been modified or not.
<p><b><font color="#FF0000">EO classes for variation operators</font></b>:
<ul> <ul>
<li> <li>
<b><font color="#FF0000">Base classes</font></b>: all variation operators <b><font color="#FF0000">Base classes</font></b>: all variation operators
@ -127,9 +135,9 @@ way to generate two new parents from that!).
modifications</font></b>, i.e. modifying the arguments rather than generating modifications</font></b>, i.e. modifying the arguments rather than generating
new (modified) individuals. This results in the following interfaces for new (modified) individuals. This results in the following interfaces for
the functor objects eoBinOp and eoQuadOp: the functor objects eoBinOp and eoQuadOp:
<p><b><tt><font color="#993300">void operator()(EOT &amp; , const EOT &amp;)&nbsp;</font></tt></b>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <p><b><tt><font color="#993300">bool operator()(EOT &amp; , const EOT &amp;)&nbsp;</font></tt></b>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
for eoBinOp (note the const) for eoBinOp (note the const)
<br><b><tt><font color="#993300">void operator()(EOT &amp; , EOT &amp; <br><b><tt><font color="#993300">bool operator()(EOT &amp; , EOT &amp;
)&nbsp;</font></tt></b>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; )&nbsp;</font></tt></b>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
for eoQuadOp for eoQuadOp
<p>which you could have guessed from the inheritance diagrams up to the <p>which you could have guessed from the inheritance diagrams up to the
@ -139,28 +147,42 @@ an eoQuad object.
<p><b><font color="#FF0000">Using crossover operators</font></b>: <p><b><font color="#FF0000">Using crossover operators</font></b>:
<br>Directly applying crossover operators is straightforward from the interface <br>Directly applying crossover operators is straightforward from the interface
above: above:
<br><b><tt><font color="#993300">eoBinOpDerivedClass&lt;Indi> myBinOp(parameters);&nbsp;&nbsp;&nbsp;&nbsp; <br><tt><font color="#993300"><b>eoBinOpDerivedClass&lt;Indi> myBinOp(parameters);&nbsp;&nbsp;
//&nbsp; use constructor to pass</font></tt></b>
<br><b><tt><font color="#993300">eoQuadOpDerivedClass&lt;Indi> myQuadOp(parameters);&nbsp;&nbsp; </b>//&nbsp; use constructor to pass</font></tt>
//&nbsp; any useful argument</font></tt></b> <br><tt><font color="#993300"><b>eoQuadOpDerivedClass&lt;Indi> myQuadOp(parameters);
<br><b><tt><font color="#993300">Indi eo1= ..., eo2= ...;&nbsp;&nbsp; //
the candidates to crossover</font></tt></b> </b>//&nbsp; any useful argument</font></tt>
<br><b><tt><font color="#993300">myBinOp(eo1, eo2);&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br><tt><font color="#993300"><b>Indi eo1= ..., eo2= ...;&nbsp;&nbsp;&nbsp;
// will modify eo1 only</font></tt></b>
<br><b><tt><font color="#993300">myQuadOp(eo1, eo2);&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </b>// the candidates to crossover</font></tt>
// will modify eo1 and eo2</font></tt></b> <br><b><tt><font color="#993300">if (myBinOp(eo1, eo2))</font></tt></b>
<p>However, you will hardly have to do so, as operators are used within <br><tt><font color="#993300"><b>&nbsp;&nbsp; { ...&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
other classes, and are applied systematically to whole sets of individuals
(e.g. that have already been selected, in standard generational evolutionary </b>// eo1 has been modified, <b>not</b> eo2</font></tt>
algorithms). <br><b><tt><font color="#993300">&nbsp;&nbsp; }</font></tt></b>
<br>Hence the way to use such operators will more likely ressemble, if <br><tt><font color="#993300"><b>else ...&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
you are using for instance an SGA, this (<a href="FirstRealGA.html#operators">definition</a>,
<a href="FirstRealGA.html#generation">usage</a>). </b>// none has been modified</font></tt>
See also the different ways that are described below, encapsulating the <br><b><tt><font color="#993300">if (myQuadOp(eo1, eo2))</font></tt></b>
operators into combined operators objects. <br><tt><font color="#993300"><b>&nbsp;&nbsp; { ...&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</b>// both eo1 and eo2 have been modified</font></tt>
<br><b><tt><font color="#993300">&nbsp;&nbsp; }</font></tt></b>
<br><tt><font color="#993300"><b>else ...&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</b>// none has been modified</font></tt>
<p>However, you will hardly have to actually apply operators to individuals,
as operators are used within other classes, and are applied systematically
to whole sets of individuals (e.g. that have already been selected, in
standard generation-based evolutionary algorithms).
<br>Hence the way to use such operators will more likely ressemble <a href="FirstRealGA.html#operators">this</a>
if you are using for instance an SGA. See also the different ways that
are described below, encapsulating the operators into combined operators
objects.
<p><a NAME="writing_crossover"></a><b><font color="#FF0000">Writing a crossover <p><a NAME="writing_crossover"></a><b><font color="#FF0000">Writing a crossover
operator:</font></b> operator:</font></b>
<br>There are only two things to modify in the <a href="../Templates/crossover.tmpl">template <br>There are three things to modify in the <a href="../Templates/crossover.tmpl">template
class definitions</a> provided (apart from the name of the class you are class definitions</a> provided (apart from the name of the class you are
creating!) creating!)
<ul> <ul>
@ -173,8 +195,8 @@ The <font color="#FF6600">operator()</font> method, which performs the
actual crossover.</li> actual crossover.</li>
<li> <li>
<b><font color="#FF6600">Warning</font></b>: don't forget to <b><font color="#FF6600">invalidate</font></b> The <font color="#FF6600">return value</font>, that should be <b><tt><font color="#993300">true</font></tt></b>
the fitness of any individual that has actually been modified. Otherwise, as soon as at least one genotype has actually been modified. Otherwise,
the <a href="eoEval.html#lazy">lazy fitness evaluation procedure</a> in the <a href="eoEval.html#lazy">lazy fitness evaluation procedure</a> in
EO might not know it should compute the fitness again and will keep the EO might not know it should compute the fitness again and will keep the
old value.</li> old value.</li>
@ -192,27 +214,32 @@ for <b><font face="Arial,Helvetica"><font size=+1><a href="doc/html/class_eomono
modifications</font></b>, i.e. modifying the arguments rather than generating modifications</font></b>, i.e. modifying the arguments rather than generating
new (modified) individuals. This results in the following interface for new (modified) individuals. This results in the following interface for
the functor objects eoMonOp: the functor objects eoMonOp:
<p><b><tt><font color="#993300">void operator()(EOT &amp; )</font></tt></b> <p><b><tt><font color="#993300">bool operator()(EOT &amp; )</font></tt></b>
<p>which you could have guessed from the inheritance diagrams up to the <p>which you could have guessed from the inheritance diagrams up to the
eoUF abstract class. eoUF abstract class.
<p><b><font color="#FF0000">Using mutation operators</font></b>: <p><b><font color="#FF0000">Using mutation operators</font></b>:
<br>Directly applying mutation operators is straightforward from the interface <br>Directly applying mutation operators is straightforward from the interface
above: above:
<br><b><tt><font color="#993300">eoMonOpDerivedClass&lt;Indi> myMutation(parameters); <br><tt><font color="#993300"><b>eoMonOpDerivedClass&lt;Indi> myMutation(parameters);</b>
//pass parameters in constructor</font></tt></b> //pass parameters in constructor</font></tt>
<br><b><tt><font color="#993300">Indi eo1 = ...;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br><tt><font color="#993300"><b>Indi eo = ...;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
// eo1 is candidate to mutation</font></tt></b> /</b>/ eo is candidate to mutation</font></tt>
<br><b><tt><font color="#993300">myMutation(eo1);&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br><b><tt><font color="#993300">if (myMutation(eo))</font></tt></b>
// will modify eo1</font></tt></b> <br><tt><font color="#993300"><b>&nbsp;&nbsp; { ...&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<p>However, you will hardly have to do so, as operators are used within
other classes, and are applied systematically to whole sets of individuals </b>// eo has been modified</font></tt>
(e.g. that have already been selected, in standard generational evolutionary <br><b><tt><font color="#993300">&nbsp;&nbsp; }</font></tt></b>
algorithms). <br><tt><font color="#993300"><b>else&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<br>Hence the way to use such operators will more likely ressemble, if
you are using for instance an SGA, this (<a href="FirstRealGA.html#operators">definition</a>, </b>// eo has not been modified</font></tt>
<a href="FirstRealGA.html#generation">usage</a>). <p>However, you will hardly have to actually apply operators to individuals,
See also the different ways that are described below, encapsulating the as operators are used within other classes, and are applied systematically
operators into combined operators objects. to whole sets of individuals (e.g. that have already been selected, in
standard generational evolutionary algorithms).
<br>Hence the way to use such operators will more likely ressemble <a href="FirstRealGA.html#operators">this</a>
if you are using for instance an SGA. See also the different ways that
are described below, encapsulating the operators into combined operators
objects.
<p><a NAME="writing_mutation"></a><b><font color="#FF0000">Writing a mutation <p><a NAME="writing_mutation"></a><b><font color="#FF0000">Writing a mutation
operator:</font></b> operator:</font></b>
<br>There are only two things to modify in the <a href="../Templates/mutation.tmpl">template <br>There are only two things to modify in the <a href="../Templates/mutation.tmpl">template
@ -228,11 +255,11 @@ The <font color="#FF6600">operator()</font> method, which performs the
actual crossover.</li> actual crossover.</li>
<li> <li>
<b><font color="#FF6600">Warning</font></b>: don't forget to <b><font color="#FF6600">invalidate</font></b> The <font color="#FF6600">return value</font>, that should be <b><tt><font color="#993300">true</font></tt></b>
the fitness of the individual - if it has actually been modified. Otherwise, as soon as the genotype has actually been modified.&nbsp; Otherwise, the
the <a href="eoEval.html#lazy">lazy fitness evaluation procedure</a> in <a href="eoEval.html#lazy">lazy
EO might not know it should compute the fitness again and will keep the fitness evaluation procedure</a> in EO might not know it should compute
old value.</li> the fitness again and will keep the old value.</li>
</ul> </ul>
<hr WIDTH="100%"><a NAME="proportional_simple"></a><b><font size=+1><font color="#000099">Combining <hr WIDTH="100%"><a NAME="proportional_simple"></a><b><font size=+1><font color="#000099">Combining
@ -240,9 +267,9 @@ simple operators: </font><font color="#FF0000">proportional combinations</font><
<p>The best thing to do is to go to the <a href="eoLesson2.html#combined_operators">Lesson2</a> <p>The best thing to do is to go to the <a href="eoLesson2.html#combined_operators">Lesson2</a>
of the tutorial, where everything is explained. You will find out how you of the tutorial, where everything is explained. You will find out how you
can use can use
<br>several mutations (respectiveley crossovers) as a single operator: <br>several mutations (respectiveley quadratic crossovers) as a single
every time the operator is called, one of the available operators is chosen operator: every time the operator is called, one of the available operators
by some roulette wheel selection using realtive weights. is chosen by some roulette wheel selection using realtive weights.
<p> <p>
<hr WIDTH="100%"><a NAME="general"></a><b><font color="#000099"><font size=+2>General <hr WIDTH="100%"><a NAME="general"></a><b><font color="#000099"><font size=+2>General
Operators</font></font></b> Operators</font></font></b>
@ -256,51 +283,46 @@ and it is as usual templatized by the type of individual it can handle
(see documentation for <b><font face="Arial,Helvetica"><font size=+1><a href="doc/html/class_eomonop.html">eoGenOp</a></font></font></b> (see documentation for <b><font face="Arial,Helvetica"><font size=+1><a href="doc/html/class_eomonop.html">eoGenOp</a></font></font></b>
:-) :-)
<p><a NAME="interface"></a><b><font color="#FF0000">Interface</font></b>: <p><a NAME="interface"></a><b><font color="#FF0000">Interface</font></b>:
<br><font color="#000000">The interface for </font><b><font color="#CC33CC">eoGenOp</font></b><font color="#000000"> <br>All the work a general operator is done within the <b><tt><font color="#993300">apply()</font></tt></b>
method. WHy not in the usual operator() method? Because some memory management
are needed, that are performed in the base class itself - which then calls
the virtual <b><tt><font color="#993300">apply()</font></tt></b> method.
The interface for a <b><font color="#CC33CC">eoGenOp</font></b> thus is
not deducible from its inheritance diagram, and actually is
<p><b><tt><font color="#993300">&nbsp;&nbsp;&nbsp; void apply(eoPopulator&lt;EOT>&amp;
_plop)</font></tt></b>
<p><font color="#000000">As you can see,the interface for </font><b><font color="#CC33CC">eoGenOp</font></b><font color="#000000">
is based on that of another class, called </font><b><font color="#999900">eoPopulator</font><font color="#CC33CC">. is based on that of another class, called </font><b><font color="#999900">eoPopulator</font><font color="#CC33CC">.
</font></b>An </font></b>An
<b><font color="#999900">eoPopulator</font></b> <b><font color="#999900">eoPopulator</font></b>
is a <b><font color="#FF6600">population</font></b>, but also behaves like is a <b><font color="#FF6600">population</font></b>, but also behaves like
an <b><font color="#FF6600">iterator</font></b> over a population (hence an <b><font color="#FF6600">iterator</font></b> over a population (hence
the name, <b><font color="#FF6600">Popul</font></b>ation-Iter<b><font color="#FF6600">ator</font></b>). the name, <b><font color="#FF6600">Popul</font></b>ation-Iter<b><font color="#FF6600">ator</font></b>).&nbsp;
<p><a NAME="populator_interface"></a>The <b><font color="#FF6600">basic However, please note that you should probably never use an eoGenOp alone,
interface</font></b> of an <b><font color="#999900">eoPopulator</font></b> but rather through objects of type <a href="#general_combination">eoOpContainer</a>.
(see also <a href="../../doc/html/class_eogenop.html">the documentation</a>,
of course) is the following: Individuals are accessed through the <b><tt><font color="#993300">operator*</font></tt></b>;
Basic iterator operations are available, like (pre)incrementation through
<b><tt><font color="#993300">operator++</font></tt></b>,
position management through <b><tt><font color="#993300">seekp</font></tt></b>
(returns the current position) and <b><tt><font color="#993300">tellp</font></tt></b>
(go to a given position); Individuals can also be <b><font color="#993300">insert</font></b>ed
and <b><font color="#993300">erase</font></b>d at current position using
the corresponding methods; last but not least, as the individuals are returned
by reference, it is mandatory to ensure that they will not be moved around
later: the memory management&nbsp; routine reserve is called whenever there
is a chance to add some individuals in the population.
<p>This results in the following general interface for an <b><font color="#CC33CC">eoGenOp</font></b>: <p>This results in the following general interface for an <b><font color="#CC33CC">eoGenOp</font></b>:
It receives as argument an <b><font color="#999900">eoPopulator</font></b>, It receives as argument an <b><font color="#999900">eoPopulator</font></b>,
gets the individuals it needs using the <b><tt><font color="#993300">operator*</font></tt></b>, gets the individuals it needs using the <b><tt><font color="#993300">operator*</font></tt></b>,
and must handle the positinning of the&nbsp; using the <b><tt><font color="#993300">operator++</font></tt></b> and must handle the positinning of the&nbsp; using the <b><tt><font color="#993300">operator++</font></tt></b>
method. method.
<p><b><tt><font color="#993300">void operator()(</font><font color="#999900">eoPopulator</font><font color="#993300">&amp; <p><a NAME="apply"></a><b><tt><font color="#993300">bool apply()(</font><font color="#999900">eoPopulator</font><font color="#993300">&amp;
_pop)</font></tt></b> _pop)</font></tt></b>
<br><b><tt><font color="#993300">{</font></tt></b> <br><b><tt><font color="#993300">{</font></tt></b>
<br><tt><font color="#993300"><b>&nbsp; EOT &amp; eo1 = *_pop; </b>// get <br><tt><font color="#993300"><b>&nbsp;&nbsp; EOT&amp; parent1 = *_pop;
(select if necessary) the guy</font></tt> </b>//
<br><tt><font color="#993300"><b>&nbsp; ++_pop;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; select the first parent</font></tt>
<br><tt><font color="#993300"><b>&nbsp;&nbsp; ++_plop;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</b>// advance</font></tt> </b>// advance once for each selected parents</font></tt>
<br><tt><font color="#993300"><b>&nbsp; EOT &amp; eo2 = *_pop; </b>// get <br><b><tt><font color="#993300">&nbsp;&nbsp; ...</font></tt></b>
(select if necessary) the guy</font></tt> <br><tt><font color="#993300"><b>&nbsp;&nbsp; EOT&amp; parentN = *_pop;
<br><tt><font color="#993300"><b>&nbsp; ++_pop;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </b>//
select the last parent</font></tt>
<br><tt><font color="#993300"><b>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</b>// advance</font></tt> </b>// don't advance after the last one: _plop always</font></tt>
<br><b><tt><font color="#993300">...</font></tt></b> <br><tt><font color="#993300">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<br><tt><font color="#993300"><b>&nbsp; EOT &amp; eoN = *_pop; </b>// get // points to the last that has already been treated</font></tt>
(select if necessary) the guy</font></tt>
<br><tt><font color="#993300"><b>&nbsp; ++_pop;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</b>// advance</font></tt>
<p><tt><font color="#993300">// do whatever the operator is supposed to <p><tt><font color="#993300">// do whatever the operator is supposed to
do</font></tt> do</font></tt>
<br><b><tt><font color="#993300">}</font></tt></b> <br><b><tt><font color="#993300">}</font></tt></b>
@ -318,29 +340,40 @@ were parents</font>, it needs to insert them into the list using the <b><tt><fon
method of the class <b><font color="#999900">eoPopulator</font></b> as method of the class <b><font color="#999900">eoPopulator</font></b> as
in the following:</li> in the following:</li>
<p><br><b><tt><font color="#993300">void operator()(</font><font color="#999900">eoPopulator</font><font color="#993300">&amp; <br>&nbsp;
<p>&nbsp;
<br>&nbsp;
<br>&nbsp;
<p><b><tt><font color="#993300">void apply()(</font><font color="#999900">eoPopulator</font><font color="#993300">&amp;
_pop)</font></tt></b> _pop)</font></tt></b>
<br><b><tt><font color="#993300">{</font></tt></b> <br><b><tt><font color="#993300">{</font></tt></b>
<br><tt><font color="#993300"><b>&nbsp; EOT &amp; eo1 = *_pop; </b>// get <br><tt><font color="#993300"><b>&nbsp; </b>// get the necessary number
(select if necessary) the guy</font></tt> of parents (see <a href="#apply">above</a>)</font></tt>
<br><tt><font color="#993300"><b>&nbsp; ++_pop;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br><tt><font color="#993300">&nbsp; ...</font></tt>
<br><tt><font color="#993300">&nbsp; // Now create any supplementary offspring</font></tt>
</b>// advance</font></tt> <br><b><tt><font color="#993300">&nbsp; EOT ofs1 = create_individual(...);</font></tt></b>
<br><tt><font color="#993300">&nbsp; // Now create second offspring - eo1 <br><b><tt><font color="#993300">&nbsp; ...</font></tt></b>
is modified too!</font></tt> <br><b><tt><font color="#993300">&nbsp; EOT ofsK = create_individual(...);</font></tt></b>
<br><b><tt><font color="#993300">&nbsp; EOT eo2 = create_individual(eo1);</font></tt></b> <br><tt><font color="#993300">&nbsp; // inserts offspring in _pop after
<br><tt><font color="#993300">&nbsp; // inserts eo2 in _pop after eo1</font></tt> parentN</font></tt>
<br><b><tt><font color="#993300">&nbsp; _pop.insert(eo2);</font></tt></b> <br><b><tt><font color="#993300">&nbsp; _pop.insert(ofs1);</font></tt></b>
<br><b><tt><font color="#993300">...</font></tt></b> <br><b><tt><font color="#993300">&nbsp; ...</font></tt></b>
<br>Of course the size of the resulting population will grow - and you <p><tt><font color="#993300"><b>&nbsp; </b>// invalidate the parents that
should have a replacement procedure that takes care of that. have been modified</font></tt>
<br><b><tt><font color="#993300">&nbsp; parent1.invalidate();</font></tt></b>
<br><b><tt><font color="#993300">&nbsp; ...</font></tt></b>
<br><b><tt><font color="#993300">&nbsp; parentN.invalidate();</font></tt></b>
<br><tt><font color="#993300"><b>}</b>&nbsp;&nbsp; // over</font></tt>
<p>Of course the size of the resulting population will grow - and you should
have a replacement procedure that takes care of that.
<br>&nbsp;
<li> <li>
The case where <font color="#FF6600">more parents are needed than offspring The case where <font color="#FF6600">more parents are needed than offspring
will be created</font> is a little more delicate: think about <b><font color="#CC33CC">eoBinOp</font></b>, will be created</font> is a little more delicate: think about <b><font color="#CC33CC">eoBinOp</font></b>,
and try to imagine the reasons why no crossover of that class asre used and try to imagine the reasons why no crossover of that class are used
in the first lessons of the tutorial, within the SGA framework. There are in the first lessons of the tutorial, within the SGA framework.</li>
two possibilities:</li>
<br>There are two possibilities:
<ul> <ul>
<li> <li>
If you think "generational", the first idea is to get the parents from If you think "generational", the first idea is to get the parents from
@ -351,41 +384,47 @@ and you can access it from inside the GenOp method. For instance</li>
<br>&nbsp; <br>&nbsp;
<p>&nbsp; <p>&nbsp;
<p><b><tt><font color="#993300">void operator()(</font><font color="#999900">eoPopulator</font><font color="#993300">&amp; <br>&nbsp;
<br>&nbsp;
<p><b><tt><font color="#993300">void apply()(</font><font color="#999900">eoPopulator</font><font color="#993300">&amp;
_pop)</font></tt></b> _pop)</font></tt></b>
<br><b><tt><font color="#993300">{</font></tt></b> <br><b><tt><font color="#993300">{</font></tt></b>
<br><tt><font color="#993300"><b>&nbsp; EOT &amp; eo1 = *_pop; </b>// get <br><tt><font color="#993300"><b>&nbsp; </b>// get the necessary number
(select if necessary) the guy</font></tt> of parents (see <a href="#apply">above</a>)</font></tt>
<br><tt><font color="#993300"><b>&nbsp; ++_pop;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br><tt><font color="#993300">&nbsp; ...</font></tt>
<br><tt><font color="#993300"><b>&nbsp; // </b>get extra parents - use
</b>// advance</font></tt> private selector</font></tt>
<br><b><tt><font color="#993300">&nbsp; const EOT &amp; eo2 = </font><font color="#009900">select</font><font color="#993300">(_pop.source());</font></tt></b> <br><b><tt><font color="#993300">&nbsp; const EOT&amp; parentN+1 = </font><font color="#009900">select</font><font color="#993300">(_pop.source());</font></tt></b>
<p>where select is any selector you like. Note the const: you are not allowed <br><b><tt><font color="#993300">&nbsp; ...</font></tt></b>
to modify an element of the original population (but you could of course <br><b><tt><font color="#993300">&nbsp; const EOT&amp; parentM = </font><font color="#009900">select</font><font color="#993300">(_pop.source());</font></tt></b>
have copied it!). Now to find out where that selector comes from, you'll <p>where select is any selector you like. <font color="#FF6600">Note the
have to wait until next section. If you can't wait, go directly there. const:</font> you are not allowed to modify an element of the original
population (but you could of course have copied it!). As usual, the <b><tt><font color="#009900">select</font></tt></b>
selector was pased to the operator at construct time.
<li> <li>
If you don't care about the size of the offspring population, you can use If you don't care about the size of the offspring population, you can use
the delete method of the class <b><font color="#999900">eoPopulator</font></b>. the delete method of the class <b><font color="#999900">eoPopulator</font></b>.
For instance</li> For instance</li>
<br><b><tt><font color="#993300">void operator()(</font><font color="#999900">eoPopulator</font><font color="#993300">&amp; <br><b><tt><font color="#993300">void apply()(</font><font color="#999900">eoPopulator</font><font color="#993300">&amp;
_pop)</font></tt></b> _pop)</font></tt></b>
<br><b><tt><font color="#993300">{</font></tt></b> <br><b><tt><font color="#993300">{</font></tt></b>
<br><tt><font color="#993300"><b>&nbsp; EOT &amp; eo1 = *_pop; </b>// get <br><tt><font color="#993300"><b>&nbsp; </b>// get the necessary number
(select if necessary) the guy</font></tt> of parents (see <a href="#apply">above</a>)</font></tt>
<br><tt><font color="#993300"><b>&nbsp; ++_pop;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br><tt><font color="#993300">&nbsp; ...</font></tt>
<br><tt><font color="#993300">&nbsp; // do whatever needs to be done to
</b>// advance</font></tt> any parent</font></tt>
<br><tt><font color="#993300"><b>&nbsp; EOT &amp; eo2 = *_pop; </b>// get <p><tt><font color="#993300">&nbsp; // then kill the ones that are now
(select if necessary) the guy</font></tt> useless</font></tt>
<br><tt><font color="#993300"><b>&nbsp; ++_pop;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br><tt><font color="#993300">&nbsp; <b>_plop.erase();</b>&nbsp;&nbsp;
// as many times as necessary</font></tt>
</b>// advance</font></tt> <br><tt><font color="#993300">&nbsp; <b>...</b></font></tt>
<br><tt><font color="#993300">&nbsp; // do whatever needs to be done, modifying <br><tt><font color="#993300">&nbsp; // invalidate fitnesses of remaining
eo1 but not eo2</font></tt> modified parents</font></tt>
<br><tt><font color="#993300"><b>&nbsp; _pop.delete();&nbsp;&nbsp; </b>// <br><tt><font color="#993300">&nbsp; <b>parent1.invalidate();</b></font></tt>
removes (untouched) eo2 from the list</font></tt></ul> <br><b><tt><font color="#993300">&nbsp; ...</font></tt></b>
<br><b><tt><font color="#993300">&nbsp; parentK.invalidate();</font></tt></b>
<br><tt><font color="#993300">}</font></tt></ul>
</ul> </ul>
<b><font color="#FF6600">Warning</font></b>: if you use operators that <b><font color="#FF6600">Warning</font></b>: if you use operators that
have different number of parents than offspring, you are deviating from have different number of parents than offspring, you are deviating from
@ -398,36 +437,84 @@ for all forthcoming EO algorithms.
<br>Directly applying general operators to given individuals is impossible <br>Directly applying general operators to given individuals is impossible
in EO, due to its <a href="#interface">interface</a>. You need the help in EO, due to its <a href="#interface">interface</a>. You need the help
of an individual dispenser of class <b><font color="#999900">eoPopulator</font></b>. of an individual dispenser of class <b><font color="#999900">eoPopulator</font></b>.
But anyway general operators were thought to be used mainly in combination But anyway general operators were thought to be used putely in <b><tt><font color="#CC33CC">eoOpContainer</font></tt></b>,
of one another, as described <a href="#general_combination">below</a>. as described <a href="#general_combination">below</a>.
<p><a NAME="writing_mutation"></a><b><font color="#FF0000">Writing a general <p><a NAME="writing_mutation"></a><b><font color="#FF0000">Writing a general
operator:</font></b> operator:</font></b>
<br>There are many things to modify in the <a href="../Templates/mutation.tmpl">template <br>There are many things to modify in the <a href="../Templates/genop.tmpl">template
class definitions</a> provided. class definitions</a> provided.
<ul> <ul>
<li> <li>
The <font color="#FF6600">constructor</font>, where you pass to the object First you have to choose <font color="#FF6600">which kind</font> of general
any useful parameter (see private data at end of class definition).</li> operator you want, i.e. with more (or as many) offspring than parents,
or less offspring than parents.</li>
<li> <li>
The <font color="#FF6600">operator()</font> method, which performs the In the latter case (more parents than offspring), you can decide either
actual crossover. Remember you must use the argument <b><font color="#999900">eoPopulator</font></b>to to get the extra parents from the populator (to delete them later), or
access the members of the [p[ulation in turn (method to select extra parents using a private selector.</li>
<li>
Now you can modify the <font color="#FF6600">constructor</font>, where
you pass to the object any useful parameter (see private data at end of
class definition). In case you need an external selector, you have to choose
it (or write it!) - it should be an <a href="eoEngine.html#selection">eoSelectOne</a>
object.</li>
<li>
Finally, write the core of the operator in method <font color="#FF6600">apply()</font>.
Remember you must use the argument <b><font color="#999900">eoPopulator</font></b>to
access the members of the population in turn (method
<b><tt><font color="#993300">operator*</font></tt></b>), <b><tt><font color="#993300">operator*</font></tt></b>),
you may use the initial population (method <b><tt><font color="#993300">source()</font></tt></b>), you may use the initial population (method <b><tt><font color="#993300">source()</font></tt></b>),
as well as the <b><tt><font color="#993300">insert</font></tt></b> or <b><tt><font color="#993300">delete</font></tt></b> as well as the <b><tt><font color="#993300">insert</font></tt></b> or <b><tt><font color="#993300">delete</font></tt></b>
methods.</li> methods.</li>
</ul>
<br><b><font color="#FF6600">Warning</font></b>: as usual, don't forget <ul><b><font color="#FF6600">Warning</font></b>: in general operators,
to <b><font color="#FF6600">invalidate</font></b> the fitness of the individual you must not forget to <b><font color="#FF6600">invalidate</font></b> the
- if it has actually been modified. Otherwise, the <a href="eoEval.html#lazy">lazy fitness of any individual that has actually been modified. this implicitely
implies that general operators can only be applied to EO object (i.e. objects
with a fitness), and not to any type of structure.
<br>It you don't invalidate the individual, the <a href="eoEval.html#lazy">lazy
fitness evaluation procedure</a> in EO will not know it should compute fitness evaluation procedure</a> in EO will not know it should compute
the fitness again and will keep the old value.</ul> the fitness again and will keep the old obsolete value.</ul>
<hr WIDTH="100%"><a NAME="populators"></a><b><font color="#000099"><font size=+2>The <hr WIDTH="100%"><a NAME="populators"></a><b><font color="#000099"><font size=+2>The
populators:</font></font></b> populators:</font></font></b>
<br>The public interface class <b><font color="#999900">eoPopulator</font></b> <br>As has been said above, an
has been described above. However, a protected method, termed <b><tt><font color="#993300">select</font></tt></b>,&nbsp; <b><font color="#999900">eoPopulator</font></b>
is a <b><font color="#FF6600">population</font></b>, but also behaves like
an <b><font color="#FF6600">iterator</font></b> over a population (hence
the name, <b><font color="#FF6600">Popul</font></b>ation-Iter<b><font color="#FF6600">ator</font></b>).
<p><a NAME="populator_interface"></a>The <b><font color="#FF6600">basic
interface</font></b> of an <b><font color="#999900">eoPopulator</font></b>
(see also <a href="../../doc/html/class_eogenop.html">the documentation</a>,
of course) is the following:
<ul>
<li>
Individuals are accessed through the <b><tt><font color="#993300">operator*</font></tt></b>;</li>
<li>
Basic iterator operations are available, like (pre)incrementation through
<b><tt><font color="#993300">operator++</font></tt></b>,
position management through <b><tt><font color="#993300">seekp</font></tt></b>
(returns the current position) and <b><tt><font color="#993300">tellp</font></tt></b>
(go to a given position);</li>
<li>
Individuals can also be <b><font color="#993300">insert</font></b>ed and
<b><font color="#993300">erase</font></b>d
at current position using the corresponding methods;</li>
<li>
last but not least, as the individuals are returned by reference, it is
mandatory to ensure that they will not be moved around later: the memory
management&nbsp; routine <b><tt><font color="#993300">reserve</font></tt></b>
is called whenever there is a chance to add some individuals in the population
- i.e. in the eoGenOp base class operator() method.</li>
</ul>
Moreover, a protected method, termed <b><tt><font color="#993300">select</font></tt></b>,&nbsp;
is used inside the object to get new parents for the following operator, is used inside the object to get new parents for the following operator,
and its implementation distinguishes two types of <b><font color="#999900">eoPopulator</font></b>: and its implementation distinguishes two types of <b><font color="#999900">eoPopulator</font></b>:
<ul> <ul>
@ -447,19 +534,29 @@ object (passed at construct time). Hence it can handle any number of parents
at will. The idea of such populator is to handle the whole <b><font color="#FF6600">breeding</font></b> at will. The idea of such populator is to handle the whole <b><font color="#FF6600">breeding</font></b>
process, i.e. selection and variation operators.</li> process, i.e. selection and variation operators.</li>
</ul> </ul>
An immediate consequence is that if you are not sure of the numebr of&nbsp; An immediate consequence is that if you are not sure of the number of&nbsp;
parents you will need in some operators (e.g. because of some stochastic parents you will need in some operators (e.g. because of some stochastic
proportional selection ebtween operators that don't need the same number proportional selection ebtween operators that don't need the same number
of parents, then you <b><font color="#FF6600">must</font></b> use an <b><font color="#CC33CC">eoSelectivePopulator</font></b> of parents, then you <b><font color="#FF6600">must</font></b> use an <b><font color="#CC33CC">eoSelectivePopulator</font></b>
to apply the variation operators to the population. to apply the variation operators to the population, and thus get exactly
the number of offspring you want.
<p><b><font color="#FF0000">Example</font></b>: An <b><font color="#CC33CC">eoSelectivePopulator</font></b>
is the main ingredient of the <b><tt><font color="#FF6666">eoGeneralBreeder</font></tt></b>
<a href="../../doc/html/eogeneralbreeder_h-source.html#l00061">operator()
method</a> - a class that creates a population of offspring from the parents
applying an eoGenOp (usually an eoOpContainer) to all selected parents
in turn.
<br> <br>
<hr WIDTH="100%"><a NAME="general_combination"></a><b><font color="#000099"><font size=+2>General <hr WIDTH="100%"><a NAME="general_combination"></a><b><font color="#000099"><font size=+2>General
Combinations:</font></font></b> Operator Containers:</font></font></b>
<br>There are two main ways to use and combine general operators in EO: <br>General operators in EO are meant to be used withing eoOpContainer
the proportional combination, similar to what has been described for simple objects, that allow to combine them in a hierarchical and flexible way.
operators <a href="#proportional_simple">above</a>, and the sequential There are two ways to do that: the <b><font color="#FF6600">proportional
combination, which amounts to apply all operators in turn to a bunch of combination</font></b>, similar to what has been described for simple operators
individuals, each operator being applied with a specific probability. <a href="#proportional_simple">above</a>,
and the <b><font color="#FF6600">sequential combination</font></b>, which
amounts to apply all operators in turn to a bunch of individuals, each
operator being applied with a specific probability.
<p><a NAME="prop_container"></a><b><font color="#FF0000">Proportional combinations</font></b> <p><a NAME="prop_container"></a><b><font color="#FF0000">Proportional combinations</font></b>
<br>When called upon a population (through an <b><font color="#999900">eoPopulator</font></b> <br>When called upon a population (through an <b><font color="#999900">eoPopulator</font></b>
object), an <b><font color="#CC33CC">eoProportionalOpContainer</font></b> object), an <b><font color="#CC33CC">eoProportionalOpContainer</font></b>
@ -519,6 +616,25 @@ Next pending parent</li>
<li> <li>
Next operator</li> Next operator</li>
</ul> </ul>
<b><font color="#FF6600">Warning</font></b>: the way <b><tt><font color="#993300">rate</font></tt></b>
will be used is highly dependent on the type of <b><font color="#CC33CC">eoOpContainer</font></b>
your are creating there:
<ul>
<li>
The rates for <b><font color="#CC33CC">eoProportionalOpContainer</font></b>
will be used in a roulette wheel choice among all operators. They can take
any value, the only important thing is their <b><font color="#FF6600">relative
values</font></b>.</li>
<li>
The "rates" for <b><font color="#CC33CC">eoSequentialOpContainer </font></b>actually
are <b><font color="#FF6600">probabilities</font></b>, i.e. they will be
used in a coin-flipping to determine whether that particuler operator will
be applied to the next candidates at hand. They should be <b><font color="#FF6600">in
[0,1]</font></b> (no error will happen if they are not, but the operator
will be applied systematically - this is equivalent of a rate equal to
1).</li>
</ul>
<font color="#FF6600">Remark:</font>The eoSGATransform presented in <a href="eoLesson2.html#transform">Lesson2</a> <font color="#FF6600">Remark:</font>The eoSGATransform presented in <a href="eoLesson2.html#transform">Lesson2</a>
can be viewed as a particular type of <b><font color="#CC33CC">eoSequentialOpContainer</font></b>. can be viewed as a particular type of <b><font color="#CC33CC">eoSequentialOpContainer</font></b>.
It was not coded that way in order to provide a gradual introduction to It was not coded that way in order to provide a gradual introduction to
@ -541,28 +657,16 @@ Gen</font></b>:
<p><b><tt><font color="#993300">someOperatorType&lt;Indi> myOperator;</font></tt></b> <p><b><tt><font color="#993300">someOperatorType&lt;Indi> myOperator;</font></tt></b>
<br><b><tt><font color="#993300">eoYYYOpContainer&lt;Indi> myOpContainer;</font></tt></b> <br><b><tt><font color="#993300">eoYYYOpContainer&lt;Indi> myOpContainer;</font></tt></b>
<br><tt><font color="#993300"><b>myOpContainer.add(myOperator, rate); </b>// <br><tt><font color="#993300"><b>myOpContainer.add(myOperator, rate); </b>//
rate: double whose <b>meaning depends on XXX</b></font></tt> rate: double whose <b>meaning depends on YYY</b></font></tt>
<p>where YYY can be one of Proportional and Sequential. <p>where YYY can be one of Proportional and Sequential. Note that before
<br><b><font color="#FF6600">Warning</font></b>: the way <b><tt><font color="#993300">rate</font></tt></b> being added to the container, all simple operators are wrapped into the
will be used is highly dependent on the type of <b><font color="#CC33CC">eoOpContainer</font></b> corresponding eoGenOp (see e.g. how an <b><font color="#CC33CC">eoMonOp</font></b>
your are creating there: <a href="../../doc/html/eogenop_h-source.html#l00079">is wrapped</a> into
<ul> an <b><font color="#CC33CC">eoMonGenOp</font></b>- or how <a href="../../doc/html/eogenop_h-source.html#l00169">any
<li> operator is handled</a> by calling the appropriate wrapper). In particular,
The rates for <b><font color="#CC33CC">eoProportionalOpContainer</font></b> the wrapper ensures that <b><font color="#FF6600">individuals who have
will be used in a roulette wheel choice among all operators. They can take been modified are invalidated</font></b>.
any value, the only important thing is their <b><font color="#FF6600">relative <p><a NAME="container_and_populator"></a><b><font color="#FF0000">Containers,
values</font></b>.</li>
<li>
The "rates" for <b><font color="#CC33CC">eoSequentialOpContainer </font></b>actually
are <b><font color="#FF6600">probabilities</font></b>, i.e. they will be
used in a coin-flipping to determine whether that particuler operator will
be applied to the next candidates at hand. They should be <b><font color="#FF6600">in
[0,1]</font></b> (no error will happen if they are not, but the operator
will be applied systematically - this is equivalent of a rate equal to
1).</li>
</ul>
<a NAME="container_and_populator"></a><b><font color="#FF0000">Containers,
Selectors and Populators</font></b> Selectors and Populators</font></b>
<br>The way the <b><font color="#CC33CC">eoOpContainer</font></b> are applied <br>The way the <b><font color="#CC33CC">eoOpContainer</font></b> are applied
on a population using an <b><font color="#999900">eoPopulator</font></b> on a population using an <b><font color="#999900">eoPopulator</font></b>
@ -633,20 +737,20 @@ general operators:</font></font></b>
preferences</font></b>, i.e. choose a mate for a first parent according preferences</font></b>, i.e. choose a mate for a first parent according
to some characteritics of that first parent). to some characteritics of that first parent).
<br>This is made possible in EO because the general operators have a handle <br>This is made possible in EO because the general operators have a handle
on the initial population through the method source() of the argument eoPopulator on the initial population through the method <b><tt><font color="#993300">source()</font></tt></b>
they work on. Their <b><tt><font color="#993300">operator()</font></tt></b> of the argument eoPopulator they work on. Their <b><tt><font color="#993300">apply()</font></tt></b>
method shoudl look like method shoudl look like
<p><b><tt><font color="#993300">void operator()(</font><font color="#999900">eoPopulator</font><font color="#993300">&amp; <p><b><tt><font color="#993300">void apply()(</font><font color="#999900">eoPopulator</font><font color="#993300">&amp;
_pop)</font></tt></b> _pop)</font></tt></b>
<br><b><tt><font color="#993300">{</font></tt></b> <br><b><tt><font color="#993300">{</font></tt></b>
<br><tt><font color="#993300"><b>&nbsp; EOT &amp; eo1 = *_pop; </b>// get <br><tt><font color="#993300"><b>&nbsp; EOT &amp; eo1 = *_pop; </b>// get
(select if necessary) the first guy</font></tt> (select if necessary) the first guy</font></tt>
<br><b><tt><font color="#993300">&nbsp; ++_pop;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br><tt><font color="#993300"><b>&nbsp; ++_pop;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</font></tt></b><tt><font color="#993300">// advance</font></tt> </b>// advance</font></tt>
<br><b><tt><font color="#993300">&nbsp; EOT &amp; eo2 = </font><font color="#009900">findBlonde</font><font color="#993300">(_pop.source()); <br><b><tt><font color="#993300">&nbsp; EOT &amp; eo2 = </font><font color="#009900">findBlonde</font><font color="#993300">(_pop.source());
</font></tt></b><tt><font color="#993300">//
</font></tt></b><tt><font color="#993300">// select mate</font></tt> select mate</font></tt>
<br><tt><font color="#993300">// do whatever the operator is supposed to <br><tt><font color="#993300">// do whatever the operator is supposed to
do</font></tt> do</font></tt>
<br><b><tt><font color="#993300">}</font></tt></b> <br><b><tt><font color="#993300">}</font></tt></b>
@ -671,7 +775,7 @@ documentation</a></font></font></b>
<a href="mailto:Marc.Schoenauer@polytechnique.fr">Marc Schoenauer</a></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 <br><!-- Created: Mon Oct 30 07:27:13 CET 2000 --><!-- hhmts start -->Last
modified: Fri Dec. 8 2000&nbsp;<!-- hhmts end --> modified: Sat. Feb. 17 2001&nbsp;<!-- hhmts end -->
<br>&nbsp; <br>&nbsp;
</body> </body>
</html> </html>