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<br><font color="#000000">This argument is mandatory, and
</font><font color="#FF0000">default
is [-inf,+inf]</font><font color="#000000">, i.e. unbounded variables.</font>
<p><b><font color="#FF0000">Examples</font></b><font color="#000000">:
</font><b><tt><font color="#CC33CC"><font size=+1>10[-1,1]</font></font></tt></b><font color="#000000">is
equivalent to simply </font><b><tt><font color="#CC33CC"><font size=+1>[-1,1]</font></font></tt></b><font color="#000000">
or to the extended&nbsp; </font><b><tt><font color="#CC33CC"><font size=+1>[-1,1][-1,1][-1,1][-1,1][-1,1][-1,1][-1,1][-1,1][-1,1][-1,1]</font></font></tt></b><font color="#000000">.</font>
<br><font color="#000000">And </font><b><tt><font color="#CC33CC"><font size=+1>[-1,1];2[0,1];[-inf,10]</font></font></tt></b>results
in the first variable staying in [-1,1], the second and the third in [0,1]
and all remaining variables below 10.
<p><b><tt><font color="#CC33CC"><font size=+1># --operator=SGA # -o : Description
of the operator (SGA only now)</font></font></tt></b>
<br><font color="#FF0000">String parameter:</font><font color="#000000">
Describes the way the operators are applied. At the moment, </font><b><font color="#FF6600">only
SGA</font></b><font color="#000000"> is available. SGA </font><b><font color="#FF6600">sequentially</font></b><font color="#000000">
applies a (quadratic) crossover operator with probability </font><b><tt><font color="#CC33CC"><font size=+1>pCross</font></font></tt></b><font color="#000000">
and a mutation operator with probability&nbsp; </font><b><tt><font color="#CC33CC"><font size=+1>pMut</font></font></tt></b><font color="#000000">.
Both these operators can in turn be </font><b><font color="#FF6600">proportional
combinations</font></b><font color="#000000"> of simple operators of the
same arity.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --pCross=0.6 # -C : Probability
of Crossover</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
The probability that a given couple of selected genitors is applied the
crossover operator. In SGA operator model, each couple of selected genitors
is applied the crossover operator with that probability (and remains unchanged
with probability </font><b><tt><font color="#CC33CC"><font size=+1>1-pCross</font></font></tt></b><font color="#000000">.
Whenever a couple undergoes crossover, a choice is made upon available
crossover operators </font><b><font color="#FF6600">proportionaly to their
relative rates</font></b><font color="#000000"> (see below). </font><font color="#FF0000">Default
is 0.6</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --pMut=0.1 # -M : Probability
of Mutation</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
The probability that a given individual (resulting from a crossover or
a non-crossover operation, see above) is applied the mutation operator.
Whenever an individual undergoes mutation, a choice is made upon available
mutation operators </font><b><font color="#FF6600">proportionaly to their
relative rates</font></b><font color="#000000"> (see below). </font><font color="#FF0000">Default
is 0.1</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --alpha=0 # -a : bound
for combination factor in real crossover</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
Bound for the choices of linear combination factors in both crossover belows
(similar to BLX-alpha notation). </font><font color="#FF0000">Default is
0</font><font color="#000000"> (i.e. combination factor are chosen in [0,1]).</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --segmentRate=1 # -s :
Relative rate for segment crossover</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
Rate of application of the segment crossover </font><b><font color="#FF6600">relatively</font></b><font color="#000000">
to hypercube and uniform crossovers (see </font><b><tt><font color="#CC33CC"><font size=+1>pCross</font></font></tt></b><font color="#000000">
parameter). Segment crossover generates offspring uniformly on the segment
joining both parents, i.e. constructs two linear combinations of the parents
with a random number uniformly drawn in [</font><b><tt><font color="#CC33CC"><font size=+1>alpha</font></font></tt></b><font color="#000000">,1+</font><b><tt><font color="#CC33CC"><font size=+1>alpha</font></font></tt></b><font color="#000000">].
</font><font color="#FF0000">Default
is 1</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --hypercubeRate=1 # -A
: Relative rate for hypercube crossover</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
Rate of application of the hypercube crossover </font><b><font color="#FF6600">relatively</font></b><font color="#000000">
to segment and uniform crossovers (see </font><b><tt><font color="#CC33CC"><font size=+1>pCross</font></font></tt></b><font color="#000000">
parameter). Hypercube crossover generates offspring uniformly on the hypercube
whose diagonal is the segment joining both parents, i.e. by doing linear
combinations of each variable independently (a random number in [</font><b><tt><font color="#CC33CC"><font size=+1>alpha</font></font></tt></b><font color="#000000">,1+</font><b><tt><font color="#CC33CC"><font size=+1>alpha</font></font></tt></b><font color="#000000">]
is drawn anew for each variable). </font><font color="#FF0000">Default
is 1</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --uxoverRate=1 # -A : Relative
rate for uniform crossover</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
Rate of application of the segment crossover </font><b><font color="#FF6600">relatively</font></b><font color="#000000">
to hypercube and segment crossovers (see </font><b><tt><font color="#CC33CC"><font size=+1>pCross</font></font></tt></b><font color="#000000">
parameter). Uniform crossover simply exchanges values of variables, i.e.
uniformly picks up two other summits of the hypercube defined by the parents.
</font><font color="#FF0000">Default
is 1</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --epsilon=0.01 # -e : Half-size
of interval for Uniform Mutation</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
The uniform and deterministic-uniform mutations will choose values of variable
X uniformly in </font><b><tt><font size=+1><font color="#993300">[X-</font><font color="#CC33CC">epsilon</font><font color="#993300">,
X+</font><font color="#CC33CC">epsilon</font><font color="#993300">]</font></font></tt></b><font color="#000000">.
</font><font color="#FF0000">Default
is 0.01</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --uniformMutRate=1 # -u
: Relative rate for uniform mutation</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
Rate of aplication of the uniform mutation </font><b><font color="#FF6600">relatively</font></b><font color="#000000">
to determinitic uniform and the normal mutations (see </font><b><tt><font color="#CC33CC"><font size=+1>pMut</font></font></tt></b><font color="#000000">
above). Uniform mutation modifies all variables by choosing new values
uniformly on an interval centered on the old value of width </font><b><tt><font size=+1><font color="#993300">2*</font><font color="#CC33CC">epsilon</font></font></tt></b><font color="#000000">
(see above). </font><font color="#FF0000">Default is1</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --detMutRate=1 # -d : Relative
rate for deterministic uniform mutation</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
Rate of aplication of the determinisitc-uniform mutation </font><b><font color="#FF6600">relatively</font></b><font color="#000000">
to uniform and normal mutations (see </font><b><tt><font color="#CC33CC"><font size=+1>pMut</font></font></tt></b><font color="#000000">
above). Deterministic-uniform mutation modifies one single variable uniformly
based on epsilon </font><b><tt><font color="#CC33CC"><font size=+1>epsilon</font></font></tt></b><font color="#000000">.
</font><font color="#FF0000">Default
is1</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --normalMutRate=1 # -d
: Relative rate for Gaussian mutation</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
Rate of aplication of the normal mutation </font><b><font color="#FF6600">relatively</font></b><font color="#000000">
to two uniform mutations above (see </font><b><tt><font color="#CC33CC"><font size=+1>pMut</font></font></tt></b><font color="#000000">
above). </font><font color="#FF0000">Default is1</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --sigma=0.3 # -s : Sigma
(fixed) for Gaussian mutation</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
The value of standard deviation for Gaussian mutation - fixed along evolution
(see the Evolution Strategy program below for self-adaptive mutations).</font>
<p>
<hr ALIGN=LEFT SIZE=5 WIDTH="100%">
<p><a NAME="ES"></a><b><font size=+1><font color="#000099">User's guide:</font><font color="#FF0000">ES
with self-adative mutation parameters</font></font></b>
<br>
To run your own SA-ES application, write your fitness function
(see <b><tt><font color="#993300" size=+1>real_value.h</font></font></tt></b>), 
recompile, and run from the command line <br>
<center><b><tt><font color="#993300" size=+1>ESEA @ESEA.param</font></tt></b></center><br>
in order to use sensible parameters! (see <a href="eoLesson3.html#paraminput">Lesson 3</a> 
for details on the parameter file). 
<br><br>
The following describes the specific parameters for program <b><tt><font color="#993300"><font size=+1>ESEA</font></font></tt></b>,
that implements the full Evolution-Strategy self-adaptive mutation mechanism
- together with specific ES crossover operators. The initialization section
is the same as the one for plain vector&lt;double> above, so only the opeartor
sections will be described here. A new section is now concerned with deciding
what kind of self-adaptive mutation strategy will be applied - it has been
separated from the other variation operators because it has consequences
on the choice of the genotype.
<br><b><font color="#FF6600">Warning</font></b>: if you choose not to use
any self-adaptive mechanism (i.e. setting all parameters of this section
to false) you end up with ... an algorithm that is identical to <b><tt><font color="#993300"><font size=+1>RealEA</font></font></tt></b>
above (try it and take alook at the status file).
<p>
<hr SIZE=5 WIDTH="30%">
<p><b><font size=+1><font color="#FF0000">Section </font><tt><font color="#CC33CC">######&nbsp;&nbsp;&nbsp;&nbsp;
ES mutation&nbsp;&nbsp;&nbsp; ######</font></tt></font></b>
<br><font color="#000000">This section allows to decide which type of self-adaptive
mutation will be used. There are three available types: isotropic mutation,
using one standard deviation for each individual, that will be applied
to all variables; anisotropic mutation, where each individual carries as
many standard deviations as it has variables; and correlated mutation where
each individuals has its own full correlation matrix.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --Isotropic=1 # -i : Isotropic
self-adaptive mutation</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
If true, at least one self-adaptive parameter will be used for each individual.
</font><font color="#FF0000">Default
is true</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --Stdev=0 # -s : One self-adaptive
stDev per variable</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
If true, at least one self-adaptive parameter per variable will be used
for each individual. </font><font color="#FF0000">Default is false</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --Correl=0 # -c : Use correlated
mutations</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
If true, full correalted self-adaptive mutation will be used for each individual.
</font><font color="#FF0000">Default
is false</font><font color="#000000">.</font>
<p><b><font color="#FF6600">Note</font></b><font color="#000000">: The
default values result in an isotropic self-adaptive mutation to be chosen.</font>
<p>
<hr SIZE=5 WIDTH="30%">
<p><b><font size=+1><font color="#FF0000">Section </font><tt><font color="#CC33CC">######&nbsp;&nbsp;&nbsp;
Variation Operators&nbsp;&nbsp;&nbsp; ######</font></tt></font></b>
<br><font color="#000000">Only the parameters that are specific to ESEA
are presented here - the </font><b><tt><font color="#CC33CC"><font size=+1>objectBounds,operator,pCross</font></font></tt></b><font color="#000000">
and </font><b><tt><font color="#CC33CC"><font size=+1>pMut</font></font></tt></b><font color="#000000">
are exactly the same as for </font><b><tt><font color="#993300"><font size=+1>RealEA</font></font></tt></b><font color="#000000">
above.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --crossType=global # -C
: Type of ES recombination (global or standard)</font></font></tt></b>
<br><font color="#FF0000">String parameter:</font><font color="#000000">&nbsp;
Es crossover can involve only two parents - and it is then identical to
the </font><b><tt><font color="#CC33CC"><font size=+1>standard</font></font></tt></b><font color="#000000">
hypercube crossover describe for the </font><b><tt><font color="#993300"><font size=+1>RealEA</font></font></tt></b><font color="#000000">
parameters above. But new parents can also be chosen anew for each variable
before doing the crossover for that variable - and this is called </font><b><tt><font color="#CC33CC"><font size=+1>global</font></font></tt></b><font color="#000000">
recombination.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --crossObj=discrete # -O