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with a Gaussian noise, with standard deviation passed in the constructor.</font></ul>
<b><font color="#FF0000">Note:</font></b> A third optional argument in
method <b><tt><font color="#660000">add</font></tt></b> is a boolean (defaulted
to false). When true, the actual rates for all operators are displayed
on the screen as percentages: you don't have to input rates that sum up
to 1, all rates are scaled anyway.
<p><a NAME="transform"></a><b><font color="#FF0000">Note:</font></b> The
operators have to be encapsulated into an <b><tt><font color="#CC33CC">eoTransform</font></tt></b>
object (<a href="FirstBitEA.html#transform">Bit</a> - <a href="FirstRealEA.html#transform">Real</a>)
to be passed to the <b><tt><font color="#FF6666">eoEasyEA </font></tt></b>algorithm.
The <b><tt><font color="#CC33CC">eoSGATransform</font></tt></b> is a simple
<b><tt><font color="#CC33CC">eoTransform</font></tt></b>
that does exactly the same thing than <b><tt><font color="#FF6666">eoSGA</font></tt></b>:
each pair from the selected parents undergoes the <font color="#CC33CC">crossover
operator with given probability</font>, and all individuals (after crossover
eventually) undergo <font color="#CC33CC">mutation with given probability</font>.
The arguments to the <b><tt><font color="#CC33CC">eoSGATransform</font></tt></b>
are an <b><tt><font color="#CC33CC">eoQuadOp</font></tt></b> with its probability
and an <b><tt><font color="#CC33CC">eoMonOp</font></tt></b> with the associated
probability.
<br>&nbsp;
<li>
<a NAME="combinedContinue"></a><font color="#000000">You can use </font><b><font color="#3366FF">combinations
</font></b><font color="#000000">of
several stopping criteria by using an object of the class </font><b><tt><font color="#3366FF">eoCombinedContinue
</font></tt></b><font color="#000000">(<a href="FirstBitEA.html#stop">Bit</a>
- <a href="FirstRealEA.html#stop">Real</a>). Initialize it with an object
of class </font><font color="#3366FF"><b><tt>eoContinue</tt></b>, </font><font color="#000000">and
</font><b><tt><font color="#3366FF">add</font></tt></b><font color="#000000">
as many of other such objects as you wish. And as an </font><b><tt><font color="#3366FF">eoCombinedContinue
</font></tt><font color="#FF6600">is
an</font><tt><font color="#3366FF"> eoContinue</font></tt></b><font color="#000000">,
simply pass it to the algorithm (<a href="FirstBitEA.html#generation">Bit</a>
- <a href="FirstRealEA.html#generation">Real</a>). To find out more, and
to get the list and syntax of existing eoContinue subclasses, check out
the corresponding <a href="eoCheckPoint.html#existingContinue">component-based
page</a>.</font></li>

<br>&nbsp;
<li>
<a NAME="evolution"></a><font color="#000000">The</font><b><font color="#009900">
full selection/replacement mechanism </font></b><font color="#000000">is
now in place through the </font><font color="#FF6666"><b><tt>eoEasyEA</tt></b>
algorithm.</font></li>

<br>This means that you can use different <font color="#009900">selectors</font>.
which was already true in Lesson 1, but also different <font color="#009900">replacement
strategies</font> (see <a href="#Exercise3">Exercise 3</a>) whereas <font color="#009900">generational
replacement</font> was hard-coded in the algorithm <b><tt><font color="#FF6666">eoSGA</font></tt></b>
used in Lesson1.
<p>Beware that we have to encapsulate&nbsp; <font color="#000000">(<a href="FirstBitEA.html#select_encapsulate">Bit</a>
- <a href="FirstRealEA.html#select_encapsulate">Real</a>) </font>the <font color="#FF6600">eoDetTournament</font>,
which is of class <font color="#FF6600">eoSelectOne</font> (i.e. allows
to select one individual from a population, its <b><tt><font color="#660000">operator()</font></tt></b>
returning a single individual) into an object of the <font color="#FF6600">eoSelectPerc</font>
(perc stands for percentage) which allows to select a ... percentage of
a population (his <b><tt><font color="#660000">operator()</font></tt></b>&nbsp;
returns a population). This was done internally in the&nbsp; <a href="../../doc/html/classeo_s_g_a.html#a0">constructor
of eoSGA</a>&nbsp; - see lesson1.</ul>

<hr WIDTH="100%"><a NAME="Exercise1"></a><b><font size=+2><font color="#000099">Exercise
1: </font><font color="#FF0000">minimizing</font></font></b>
<br><font color="#000000">Modify the algorithm so that it minimizes the
fitness.</font>
<ul>
<li>
<font color="#000000">For the bitstring case, you only have to modify the
<a href="FirstBitEA.html#representation">declaration
of the representation</a>, using </font><b><tt><font color="#999900">eoMinimizingFitness</font></tt></b><font color="#000000">
instead of </font><b><tt><font color="#999900">double</font></tt></b><font color="#000000">.
But is that really all? Give it a try, look at the output, and do it right
the second time!!!</font></li>

<li>
<font color="#000000">For the real-valued problem, you also need to modify
the file <b><tt><a href="real_value.html">real_value.h</a></tt></b> so
that it returns the sum of squares instead of its inverse. And again there
is something else to modify...</font></li>
</ul>
<a NAME="exercise2"></a><b><font size=+2><font color="#000099">Exercise
2: </font><font color="#FF0000">initialization</font></font></b>
<br><font color="#000000">Use different initializers: for instance, on
the real-valued sphere function minimization, try to initialize half of
the population in [-2,-1] and the other half in [1,2], with and without
the segment and hypercube crossovers (and for large values of VEC_SIZE,
the size of the vectors). Amazing, isn't it! Explain that result.</font>
<p><a NAME="Exercise3"></a><b><font size=+2><font color="#000099">Exercise
3:&nbsp; </font><font color="#FF0000">full selection/replacement</font></font></b>
<br><font color="#000000">You can now twiddle the number of offspring that
will be generated from the parents. But of course you need to adjust the
replacement to keep a constant population size.</font>
<ul>
<li>
<font color="#000000">To </font><font color="#FF6600">modify the number
of offspring</font><font color="#000000">, use the second argument of the
</font>encapsulator<font color="#000000">
(<a href="FirstBitEA.html#select_encapsulate">Bit</a> - <a href="FirstRealEA.html#select_encapsulate">Real</a>)
of the </font><font color="#009900">selector</font><font color="#000000">
of class </font><b><tt><font color="#009900">eoSelectOne</font></tt></b><font color="#000000">
into an eoSelectPerc object. For instance, try</font></li>

<br><b><tt><font color="#009900">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
eoSelectPerc&lt;Indi> select(selectOne,2.0)</font></tt></b>
<br><font color="#000000">to generate twice as many offspring as there
are parents.</font>
<br><font color="#000000">You can also use the other encapsulator that
takes as second argument an absolute number (e.g. if you want to generate
2 offspring whatever the population size):</font>
<br><b><tt><font color="#009900">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
eoSelectNumber&lt;Indi> select(selectOne,2)</font></tt></b>
<br><font color="#000000">Or you can use the <a href="eoEngine.html#howmany">HowMany</a>
paradigm and the </font><b><tt><font color="#009900">eoSelectMany </font></tt></b><font color="#000000">to
do either one depending on some command-line input (advanced).</font>
<li>
<font color="#000000">To </font><font color="#FF6600">keep a constant population
size</font><font color="#000000">, you can use either the </font><b><tt><font color="#009900">eoCommaReplacement</font></tt></b><font color="#000000">
class, or the </font><b><tt><font color="#009900">eoPlusReplacement</font></tt></b><font color="#000000">.
The former selects the best offspring to replace the parents, the latter
selects the best among parents+offspring. Of course you cannot use </font><b><tt><font color="#009900">eoCommaReplacement</font></tt></b><font color="#000000">
if you have less offspring than parents!</font></li>

<br>Now if you use <b><tt><font color="#009900">eoSelectRandom</font></tt></b>
as selector with a rate of
<i>lambda</i>, you end up with exactly the <i>(mu+lambda)</i>
or
<i>(mu,lambda)</i> strategies from <a href="intro.html#ES">Evolution
Strategies</a>.
<li>
<font color="#FF0000">Question</font><font color="#000000">: what do you
get if you select 1 offspring only, and an </font><b><tt><font color="#009900">eoPlusReplacement</font></tt></b><font color="#000000">
strategy? Yes, you get almost the replace_worst Steady-State GA, though
rather inefficient, as you sort the population at every generation.</font></li>

<li>
<font color="#FF0000">Hint</font><font color="#000000">: there are a few
Steady-State replacement strategies already there in EO. See the <a href="eoEngine.html#SSGA">Replacement
page</a>.</font></li>
</ul>
<font color="#FF0000">Remember</font><font color="#000000">: all solutions
are in the same sub-directory of the Tutorial dir than the examples (i.e.
here Lesson2), and are described <a href="NoWay.html">here</a>.</font>
<p>
<hr WIDTH="100%">
<br><b><font color="#000099"><font size=+2>Lessons learned:</font></font></b>
<ul>
<li>
How to write a <font color="#CC0000">fitness function</font> that only
needs a genotype, not a full individual. Moreover you can compile it separately.</li>

<br>How to <font color="#CC33CC">initialize</font> the population using
random generators
<li>
How to use other <font color="#009900">evolution engine</font> than the
simple generational GA.</li>

<li>
How to combine different objects of the same kind into a single object
that you can use like a simple basic object (<font color="#CC33CC">operators</font>
and <font color="#3366FF">stopping criteria</font> here).</li>
</ul>

<hr WIDTH="100%"><a href="eoLesson1.html">Lesson 1</a> -
<a href="eoLesson3.html">Lesson
3</a> -
<a href="eoTutorial.html">Main page</a> -
<a href="eoTopDown.html">Algorithm-Based</a>
- <a href="eoBottomUp.html">Component-Based</a> - <a href="eoProgramming.html">Hints</a>
- <b><font face="Arial,Helvetica"><font size=+1><a href="../../doc/html/index.html">EO
documentation</a></font></font></b>
<br>
<hr>
<address>
<a href="mailto:[e-mail]">Marc Schoenauer</a></address>

<br><!-- Created: Fri Nov  3 18:49:12 CET 2000 --><!-- hhmts start -->Last
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