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355 lines
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<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
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<meta name="GENERATOR" content="Mozilla/4.75 [en] (X11; U; Linux 2.2.17-21mdksmp i686) [Netscape]">
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<title>Tutorial: Lesson 2</title>
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<!-- Changed by: Marc Schoenauer, 29-Nov-2000 -->
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</head>
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<body text="#000000" link="#0000EE" vlink="#551A8B" alink="#FF0000" background="beige009.jpg">
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<a href="eoLesson1.html">Lesson 1</a> -
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<a href="eoLesson3.html">Lesson
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3</a> -
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<a href="eoTutorial.html">Main page</a> -
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<a href="eoTopDown.html">Top-Down</a>
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- <a href="eoBottomUp.html">Bottom-up</a> - <a href="eoProgramming.html">Hints</a>
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-<font size=+1> <b><font face="Arial,Helvetica"><a href="../../doc/html/index.html">EO
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documentation</a></font></b></font>
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<br>
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<hr WIDTH="100%"><!-- -------------- End of header ------------------ --><!-- ----------------------------------------------- -->
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<center>
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<h1>
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<font color="#FF0000">Tutorial Lesson 2: more encapsulations</font></h1></center>
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In this lesson, the same Evolutionary Algorithm will be rewritten in a
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much more general context.
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<br>First, look at the <a href="#changes">changes</a> that have been done
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to the algorithms. Then benefit from the new features by
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<ul>
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<li>
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<a href="#minimize">minimizing</a> (and not only maximize) the fitness</li>
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<li>
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<a href="#combined_operators">combining</a> <font color="#CC33CC">several
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operators</font> of the same type</li>
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<li>
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<a href="#combinedContinue">combining</a> <font color="#3366FF">several
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stopping criteria</font></li>
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<li>
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use <font color="#009900"><a href="#evolution">alternate</a> selection/replacement</font>
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engines, deviating from the pure generational GA</li>
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</ul>
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<p><br>Again, two basic algorithms are provided, namely <a href="FirstBitEA.html">FirstBitEA</a>
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and <a href="FirstRealEA.html">FirstRealEA</a>.
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<br><font color="#FF6600">To compile and run</font> them, go to the <font color="#FF6600">Lesson2
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sub-directory</font> of the tutorial dir and simply type <b><tt><font color="#990000"><font size=+1>make</font></font></tt></b>.
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Both examples should get compiled, and you can then run them by calling
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their name from the system prompt.
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<p>Note the slim difference in names, from <font color="#FF6600">GA</font>
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to <font color="#FF6600">EA</font>: the behavior of these EAs is
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almost identical to that of their GA counterpart, at least with the default
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settings that are provided. But their potentialities for easy modifications
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are much larger, both in terms of <b><font color="#CC33CC">variation operators</font></b>
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and of <b><font color="#009900">evolution engine</font></b> (i.e. <font color="#009900">selection/replacement</font>
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mechanism).
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<hr WIDTH="100%"><a NAME="changes"></a><b><font color="#000099"><font size=+2>Changes</font></font></b>
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<p>Browse through the code, and discover them one after the other:
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<ul>
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<li>
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<font color="#000000">The</font><font color="#CC0000"> fitness function
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</font><font color="#000000">now
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lies in a </font><b><font color="#CC0000">separate file
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</font></b><font color="#000000">(<a href="FirstBitEA.html#evalfunc">Bit</a>
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- <a href="FirstRealEA.html#evalfunc">Real</a>). But, more important, its
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argument is a <a href="binary_value.html">vector<bool></a> or a <a href="real_value.html">vector<double></a>,
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and not an unknown type. This will allow to use the same file for any EO
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object that is a sub-class of the corresponding STL vector class.</font></li>
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<br>
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<p>
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<p><b><font color="#FF0000">Note:</font></b> <font color="#000000">Also,
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a non-templatized fitness can be </font><b><font color="#FF6600">compiled
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separately</font></b><font color="#000000"> (not done here) into an object
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file once and for all (<a href="eoProgramming.html#templates">remember</a>
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that templates forbid that).</font>
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<br>
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<li>
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<a NAME="minimize"></a><font color="#000000">The </font><font color="#CC0000"><b>encapsulation
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</b>of
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the fitness </font><font color="#000000">(<a href="FirstBitEA.html#eval">Bit</a>
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- <a href="FirstRealEA.html#eval">Real</a>) looks more complicated: you
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have to declare 3 template arguments: the type of EO object it will be
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applied to, the return type and the type of argument the function actually
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requires.</font></li>
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<br>
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<p>
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<br>
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<br>
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<p><b><font color="#FF0000">Note:</font></b> <font color="#000000">In the
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previous files (<a href="FirstBitGA.html#eval">Bit</a> - <a href="FirstRealGA.html#eval">Real</a>)
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, the last 2 types were deduced from the first (2nd argument = fitness
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type of EO object, third = first).</font>
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<br>
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<li>
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<font color="#000000">Both the above modifications makes it very easy to
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</font><b><font color="#CC0000">minimize</font></b><font color="#000000">
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rather than maximize a fitness function (see <a href="#Execrise1">Exercise
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1)</a>.</font></li>
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<br>
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<li>
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<font color="#000000">The</font><font color="#CC33CC"> initialization</font><font color="#000000">
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of the population is now </font><b><font color="#CC33CC">encapsulated</font></b><font color="#000000">into
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a </font><font color="#CC33CC"><b>separate initializer</b> </font><font color="#000000">(based
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on a <a href="FirstBitEA.html#init">boolean generator</a> or a <a href="FirstRealEA.html#init">double-number
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generator</a> -see <a href="../../doc/html/class_random_generator.html">random_generators.h</a>)
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that is then used in the constructor of the population to build the individuals.
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You can also use different initializers and call them in turn through the
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call to <a href="../../doc/html/class_eopop.html#a2">pop.append()</a> function
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(see <a href="#exercise2">Exercise 2</a>).</font></li>
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<br>
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<p>
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<p><b><font color="#FF0000">Note</font><font color="#CC33CC">: </font></b><font color="#000000">Don't
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forget to </font><b><font color="#CC0000">evaluate the population</font></b><font color="#000000">:
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the eoPop has no idea of the eval function, so it has to be done from outside!!!</font>
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<br>
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<li>
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<a NAME="combined_operators"></a><font color="#000000">You can now use
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</font><font color="#CC33CC"><b>different
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</b>crossover
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</font><font color="#000000">and</font><font color="#CC33CC">
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mutation
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<b>operators</b></font><font color="#000000">in the same algorithm,
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choosing among them according to
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</font><b><font color="#FF6600">relative
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rates.</font></b><font color="#CC33CC"> </font><font color="#000000">The
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class </font><font color="#CC33CC"><b>eoPropCombinedxxxOp</b>,
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</font><font color="#000000">where
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xxx is either Mon (for mutations, of class <b><font face="Arial,Helvetica"><font size=+1><a href="../../doc/html/class_eomonop.html">eoMonOp</a></font></font></b></font><font color="#CC33CC">)</font><font color="#000000">
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or Quad (for crossovers, of class <b><font face="Arial,Helvetica"><font size=+1><a href="../../doc/html/class_eoquadraticop.html">eoQuadOp</a></font></font></b>),
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is derived from the corresponding eoxxxOp class. When applying the eoPropCombinedxxxOp,
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one of the eoxxxOp it contains is chosen by a <a href="../../doc/html/class_eorng.html#a12">roulette
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wheel,</a> according to their respective rates, and is applied to the arguments.
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For more details on these classes, go to the <a href="eoOperators.html#crossover">top-down
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corresponding pages</a>, or to their respective documentation pages.</font></li>
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<ul>
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<li>
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<font color="#000000"><a href="FirstBitEA.html#operators">Bit</a></font></li>
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<br><font color="#000000">Three </font><b><font color="#FF6600">crossover
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operators</font></b><font color="#000000"> are available: the </font><font color="#FF6600">one-point</font><font color="#000000">
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crossover is still there (class ), but now you also have the </font><font color="#FF6600">N-point</font><font color="#000000">
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crossover </font><font color="#CC33CC">eoBinNxOver</font><font color="#000000">
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(the number of points is 2 by default, but as always you can change
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that in the constructor), and the </font><font color="#FF6600">Uniform</font><font color="#000000">
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crossover </font><font color="#CC33CC">eoBinUxOver</font><font color="#000000">
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(where you can eventually twidle the choice from one parent to the other
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by providing a probability in the constructore - defaulted to 0.5, which
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amounts to symmetrical choice).</font>
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<br><font color="#000000">As for </font><b><font color="#FF6600">mutation
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operators</font></b><font color="#000000">, apart from the </font><font color="#CC33CC">eoBinMutation</font><font color="#000000">
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(standard bitstring mutation flipping one bit with a given probability)
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you can also use the </font><font color="#CC33CC">eoDetBitFlip</font><font color="#000000">
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that always filps the same number of bits (1 by default, but you can change
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that in the constructor), randomly chosen in the bitstring. Even though
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the average number of bits flipped is the same if the </font><font color="#CC33CC">eoBinMutation
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</font><font color="#000000">is
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used with a rate of 1/N (N is the bitstring length) </font><font color="#FF6600">the
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behavior of these mutation can be very different</font><font color="#000000">
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on many problems.</font>
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<li>
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<font color="#000000"><a href="FirstRealEA.html#operators">Real</a></font></li>
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<br><font color="#000000">Two </font><b><font color="#FF6600">crossover
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operators</font></b><font color="#000000"> are available: the </font><font color="#CC33CC">eoSegmentCrossover</font><font color="#000000">
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chooses one point uniformly on the segment joining the parents, while the
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</font><font color="#CC33CC">eoArithmeticCrossover</font><font color="#000000">
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performs a segment crossover on each coordinate independently, which amount
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to choosing the offspring uniformly in the hypercube whose diagonal is
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the segment joining the parents.</font>
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<br><font color="#000000">As for </font><b><font color="#FF6600">mutation
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operators</font></b><font color="#000000">, apart from the </font><font color="#CC33CC">eoBinMutation</font><font color="#000000">
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(standard bitstring mutation flipping one bit with a given probability)
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you can also use the </font><font color="#CC33CC">eoDetBitFlip</font><font color="#000000">
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that always filps the same number of bits (1 by default, but you can change
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that in the constructor), randomly chosen in the bitstring. And last but
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not least, the normal mutation eoNormMutation modifies all coordinates
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with a Gaussian noise, with standard deviation passed in the constructor.</font></ul>
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<b><font color="#FF0000">Note:</font></b> A third optional argument in
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method <b><tt><font color="#660000">add</font></tt></b> is a boolean (defaulted
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to false). When true, the actual rates for all operators are displayed
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on the screen as percentages: you don't have to input rates that sum up
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to 1, all rates are scaled anyway.
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<p><a NAME="transform"></a><b><font color="#FF0000">Note:</font></b> The
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operators have to be encapsulated into an <b><tt><font color="#CC33CC">eoTransform</font></tt></b>
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object (<a href="FirstBitEA.html#transform">Bit</a> - <a href="FirstRealEA.html#transform">Real</a>)
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to be passed to the <b><tt><font color="#FF6666">eoEasyEA </font></tt></b>algorithm.
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The <b><tt><font color="#CC33CC">eoSGATransform</font></tt></b> is a simple
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<b><tt><font color="#CC33CC">eoTransform</font></tt></b>
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that does exactly the same thing than <b><tt><font color="#FF6666">eoSGA</font></tt></b>:
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each pair from the selected parents undergoes the <font color="#CC33CC">crossover
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operator with given probability</font>, and all individuals (after crossover
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eventually) undergo <font color="#CC33CC">mutation with given probability</font>.
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The arguments to the <b><tt><font color="#CC33CC">eoSGATransform</font></tt></b>
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are an <b><tt><font color="#CC33CC">eoQuadOp</font></tt></b> with its probability
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and an <b><tt><font color="#CC33CC">eoMonOp</font></tt></b> with the associated
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probability.
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<br>
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<li>
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<a NAME="combinedContinue"></a><font color="#000000">You can use </font><b><font color="#3366FF">combinations
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</font></b><font color="#000000">of
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several stopping criteria by using an object of the class </font><b><tt><font color="#3366FF">eoCombinedContinue
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</font></tt></b><font color="#000000">(<a href="FirstBitEA.html#stop">Bit</a>
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- <a href="FirstRealEA.html#stop">Real</a>). Initialize it with an object
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of class </font><font color="#3366FF"><b><tt>eoContinue</tt></b>, </font><font color="#000000">and
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</font><b><tt><font color="#3366FF">add</font></tt></b><font color="#000000">as
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many of other such objects as you wish. And as an </font><b><tt><font color="#3366FF">eoCombinedContinue
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</font></tt><font color="#FF6600">is
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an</font><tt><font color="#3366FF">eoContinue</font></tt></b><font color="#000000">,
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simply pass it to the algorithm (<a href="FirstBitEA.html#generation">Bit</a>
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- <a href="FirstRealEA.html#generation">Real</a>).</font></li>
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<br>
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<li>
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<a NAME="evolution"></a><font color="#000000">The</font><b><font color="#009900">
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full selection/replacement mechanism </font></b><font color="#000000">is
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now in place through the </font><font color="#FF6666"><b><tt>eoEasyEA</tt></b>
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algorithm.</font></li>
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<br>This means that you can use different <font color="#009900">selectors</font>.
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which was already true in Lesson 1, but also different <font color="#009900">replacement
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strategies</font> (see <a href="#Exercise3">Exercise 3</a>) whereas <font color="#009900">generational
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replacement</font> was hard-coded in the algorithm <b><tt><font color="#FF6666">eoSGA</font></tt></b>
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used in Lesson1.
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<p>Beware that we have to encapsulate <font color="#000000">(<a href="FirstBitEA.html#select_encapsulate">Bit</a>
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- <a href="FirstRealEA.html#select_encapsulate">Real</a>) </font>the <font color="#FF6600">eoDetTournament</font>,
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which is of class <font color="#FF6600">eoSelectOne</font> (i.e. allows
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to select one individual from a population, its <b><tt><font color="#660000">operator()</font></tt></b>
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returning a single individual) into an object of the <font color="#FF6600">eoSelectPerc</font>
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(perc stands for percentage) which allows to select a ... percentage of
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a population (his <b><tt><font color="#660000">operator()</font></tt></b>
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returns a population). This was done internally in the <a href="../../doc/html/class_eosga.html#a0">constructor
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of eoSGA</a> - see lesson1.</ul>
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<hr WIDTH="100%"><a NAME="Exercise1"></a><b><font size=+2><font color="#000099">Exercise
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1: </font><font color="#FF0000">minimizing</font></font></b>
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<br><font color="#000000">Modify the algorithm so that it minimizes the
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fitness.</font>
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<ul>
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<li>
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<font color="#000000">For the bitstring case, you only have to modify the
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<a href="FirstBitEA.html#representation">declaration
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of the representation</a>, using </font><b><tt><font color="#999900">eoMinimizingFitness</font></tt></b><font color="#000000">
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instead of </font><b><tt><font color="#999900">double</font></tt></b><font color="#000000">.
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But is that really all? Give it a try, look at the output, and do it right
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the second time!!!</font></li>
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<li>
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<font color="#000000">For the real-valued problem, you also need to modify
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the file <b><tt><a href="real_value.html">real_value.h</a></tt></b> so
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that it returns the sum of squares instead of its inverse. And again there
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is something else to modify...</font></li>
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</ul>
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<a NAME="exercise2"></a><b><font size=+2><font color="#000099">Exercise
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2: </font><font color="#FF0000">initialization</font></font></b>
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<br><font color="#000000">Use different initializers: for instance, on
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the real-valued sphere function minimization, try to initialize half of
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the population in [-2,-1] and the other half in [1,2], with and without
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the segment and arithmetic crossovers (and for large values of VEC_SIZE,
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the size of the vectors). Amazing, isn't it! Explain that result.</font>
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<p><a NAME="Exercise3"></a><b><font size=+2><font color="#000099">Exercise
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3: </font><font color="#FF0000">replacement</font></font></b>
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<br><font color="#000000">You can now twiddle the number of offspring that
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will be generated from the parents. But of course you need to adjust the
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replacement to keep a constant population size.</font>
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<ul>
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<li>
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<font color="#000000">To </font><font color="#FF6600">modify the number
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of offspring</font><font color="#000000">, use the second argument of the
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</font>encapsulator<font color="#000000">
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(<a href="FirstBitEA.html#select_encapsulate">Bit</a> - <a href="FirstRealEA.html#select_encapsulate">Real</a>)
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of the </font><font color="#009900">selector</font><font color="#000000">
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of class </font><b><tt><font color="#009900">eoSelectOne</font></tt></b><font color="#000000">
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into an eoSelectPerc object. For instance, try</font></li>
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<br><b><tt><font color="#009900">
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eoSelectPerc<Indi> select(selectOne,2.0)</font></tt></b>
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<br><font color="#000000">to generate twice as many offspring as there
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are parents.</font>
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<li>
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<font color="#000000">To </font><font color="#FF6600">keep a constant population
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size</font><font color="#000000">, you can use either the </font><b><tt><font color="#009900">eoCommaReplacement</font></tt></b><font color="#000000">
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class, or the </font><b><tt><font color="#009900">eoPlusReplacement</font></tt></b><font color="#000000">.
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The former selects the best offspring to replace the parents, the latter
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selects the best among parents+offspring. Of course you cannot use </font><b><tt><font color="#009900">eoCommaReplacement</font></tt></b><font color="#000000">
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if you have less offspring than parents!</font></li>
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<br>Now if you use <b><tt><font color="#009900">eoSelectRandom</font></tt></b>
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as selector with a rate of
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<i>lambda</i>, you end up with exactly the <i>(mu+lambda)</i>
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or
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<i>(mu,lambda)</i> strategies from <a href="intro.html#ES">Evolution
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Strategies</a>.
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<li>
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<font color="#FF0000">Question</font><font color="#000000">: what do you
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get if you have use a rate of 1/POP_SIZE for the selection, and an </font><b><tt><font color="#009900">eoPlusReplacement</font></tt></b><font color="#000000">
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strategy? Yes, you get almost the replace_worst Steady-State GA, though
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rather inefficient, as you sort the population at every generation, which
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could be avoided - and will be in a later lesson).</font></li>
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<li>
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<font color="#FF0000">Homework</font><font color="#000000">: Write the
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</font><b><tt><font color="#009900">eoCommaPlusReplacement</font></tt></b><font color="#000000">
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that would start by taking the best of the offspring, and if some are still
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missing to keep the population size constant, take the best of the parents.
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Write the </font><b><tt><font color="#009900">eoConservativeReplacement</font></tt></b><font color="#000000">
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that starts by taking a percentage of the parents (the best ones) and then
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adds the best from the offspring. In both cases, </font><font color="#FF6600">send
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use the code </font><font color="#000000">as we haven't done that yet (and
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hence there is no solution available at the moment - Nov. 29 :-)</font></li>
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</ul>
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<font color="#FF0000">Remember</font><font color="#000000">: all solutions
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are in the same sub-directory of the Tutorial dir than the examples (i.e.
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here Lesson2), and are described <a href="NoWay.html">here</a>.</font>
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<p>
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<hr WIDTH="100%">
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<br><b><font color="#000099"><font size=+2>Lessons learned:</font></font></b>
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<ul>
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<li>
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How to write a <font color="#CC0000">fitness function</font> that only
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needs a genotype, not a full individual. Moreover you can compile it separately.</li>
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<br>How to <font color="#CC33CC">initialize</font> the population using
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random generators
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<li>
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How to use other <font color="#009900">evolution engine</font> than the
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simple generational GA.</li>
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<li>
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How to combine different objects of the same kind into a single object
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that you can use like a simple basic object (<font color="#CC33CC">operators</font>
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and <font color="#3366FF">stopping criteria</font> here).</li>
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</ul>
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<hr WIDTH="100%"><a href="eoLesson1.html">Lesson 1</a> -
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<a href="eoLesson3.html">Lesson
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3</a> -
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<a href="eoTutorial.html">Main page</a> -
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<a href="eoTopDown.html">Top-Down</a>
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- <a href="eoBottomUp.html">Bottom-up</a> - <a href="eoProgramming.html">Hints</a>
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- <b><font face="Arial,Helvetica"><font size=+1><a href="../../doc/html/index.html">EO
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documentation</a></font></font></b>
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<br>
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<hr>
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<address>
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<a href="mailto:Marc.Schoenauer@polytechnique.fr">Marc Schoenauer</a></address>
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<br><!-- Created: Fri Nov 3 18:49:12 CET 2000 --><!-- hhmts start -->Last
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modified: Fri Nov 3 18:49:12 CET 2000<!-- hhmts end -->
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</body>
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</html>
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