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eodev/eo/tutorial/html/eoLesson4.html
evomarc 5508869d00 A full working version of ES is now available in tutorial/Lesson4, 
that makes full use of libes.a.
The user guide is in Lesson4 of the tutorial - programmer's guide
will come later.
Plus many small changes here and there
2001-05-04 16:51:29 +00:00

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<title>Tutorial: Lesson 3</title>
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<body text="#000000" link="#0000EE" vlink="#551A8B" alink="#FF0000" background="beige009.jpg">
<a href="eoLesson2.html">Lesson 3</a> -
<a href="eoLesson4.html">Lesson
5</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 WIDTH="100%"><!-- -------------- End of header ------------------ --><!-- ----------------------------------------------- -->
<center>
<h1>
<font color="#FF0000">Tutorial Lesson 4: fully operational EA</font></h1></center>
In this lesson, you will still use the same Evolutionary Algorithm. But
this time you will have <b><font color="#FF6600">full control of all components</font></b>
from the c<b><font color="#FF6600">ommand-line or a parameter file</font></b>.
You can even use the algorithm decribed here without any other knowledge
of EO, just by writing your fitness function as a plain C++ function. This
is why this lesson starts with a <a href="#userguide">user's guide</a>,
most of it being representation-independent, with some parts that are specific
of respectively the <a href="#binary">binary</a> and the <a href="#real">real</a>
algorithms.
<br>However, the ultimate purpose of this tutorial is to be able to do
your own experiments - and these these will likely fall outside the scope
of these two programs. This is why you should also read the <a href="#programmerguide">programmer's
guides</a>, as the structure and memory managements are here radically
different that in the 3 previous lessons - though relying of course on
the same objects.
<br>&nbsp;
<p>
<hr WIDTH="100%">
<br><a NAME="userguide"></a><b><font color="#000099"><font size=+2>User's
guide</font></font></b>
<p><font color="#000000">As already said, the behavior of the algorithms
will be exactly the same as the previous one as far as optimization is
concerned. Only now you will be able to tune every component of the algorithms
(except the type of genotype) using run-time parameters.</font>
<br><font color="#000000">Also, as in previous lessons, most of the code
is representation-independent, i.e. is the same for both the binary genotypes
and the real-valued genotypes. This small user's guide reflects that, but
you can go directly to the <a href="#binary">binary</a> or the <a href="#real">real</a>
parts if you wish.</font>
<p><b><font color="#FF0000">Warning</font></b><font color="#000000">: this
is a user guide, not a programming guide. In particular, the </font><font color="#FF6600">keywords</font><font color="#000000">
of the parameters are </font><b><font color="#FF6600">not</font></b><font color="#000000">
the </font><font color="#FF6600">names</font><font color="#000000"> of
the underlying classes (though they should be similar in most cases).</font>
<p><b><font color="#000099"><font size=+1>User's guide:</font></font><font color="#FF0000">
Parameter input</font></b><font color="#000000"> The way to input parameters
has already be described in <a href="eoLesson3.html#paraminput">Lesson
3</a>. To get a list of parameters, type the command with option --help
(or -h): with both testBit and testReal this will result in</font>
<ul>
<li>
<font color="#000000">Printing the list of keywords on the standard output</font></li>
<li>
<font color="#000000">Creating (or overwriting) a file name testBit.status
or testReal.status that contains the list of all recognized parameters
and has the format of an input parameter file.</font></li>
</ul>
<b><font color="#000099"><font size=+1>User's guide:</font></font><font color="#FF0000">The
status file</font></b>
<br><font color="#000000">This file will always contain the list of the
parameters that have been actually used by the last run of the program,
however thay have been entered (try </font><b><tt><font color="#FF6666"><font size=+1>testBit
-G1</font></font></tt></b><font color="#000000"> and take a look a the
status file). The parameters that are commented out (a # character comments
out the rest of the line) in the file are those that were not specified
by the user.</font>
<br><font color="#000000">On the status file, the parameters are organized
in sections. Note, however, that this format is not mandatory in the param
file, as </font><font color="#FF6600">only the keywords</font><font color="#000000">
are processed.</font>
<p><b><font color="#000099"><font size=+1>User's guide:</font></font><font color="#FF0000">Representation-independent
parameters</font></b>
<br><font color="#000000">In what follows, the fixed font colored text
is directly taken from the status file and is commented between the lines.
The presentation follows the status file format - only two sections are
representation-dependent (see the corresponding <a href="#binary">binary</a>
or <a href="#real">real</a> sections). All other sections are presented
now:</font>
<p>
<hr SIZE=5 WIDTH="30%">
<br><b><font size=+1><font color="#FF0000">Section </font><tt><font color="#993300">######
General ######</font></tt></font></b>
<br><b><tt><font color="#993300"><font size=+1># --help=0 # -h : Prints
this message</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter </font><font color="#000000">of
absolutely no interest: tells whether or not help was requested.</font>
<p><b><tt><font color="#993300"><font size=+1># --seed=988700289 # -S :
Random number seed</font></font></tt></b>
<br><font color="#FF0000">Unsigned long parameter:</font><font color="#000000">
the seed for the <a href="eoProgramming.html#random">Random Number Generator</a>
If the parameter is absent, then time(0) is used, which indicates the number
of seconds since Jan. 1 1980, is used ... and stored in the status file,
of course, so you can repeat the same run by simply assigning that value
again. There is </font><font color="#FF0000">no default value ("true" random
seed)</font><font color="#000000">.</font>
<p>
<hr SIZE=5 WIDTH="30%">
<p><b><font size=+1><font color="#FF0000">Section </font><tt><font color="#009900">######
engine ######</font></tt></font></b>
<br><font color="#000000">In this section, one chooses all components of
the <a href="eoEngine.html">Evolution Engine</a> (selection, replacemenet
and the like).</font>
<p><b><tt><font color="#009900"><font size=+1># --popSize=20 # -P : Population
Size</font></font></tt></b>
<br><font color="#FF0000">Integer parameter:</font><font color="#000000">
the size of the population (constant along evolution). And yes, this is
a representation independent parameter, as the population is created either
from a file or using an eoInit object - and only that object is representation-dependent.</font>
<br><b><tt><font color="#009900"><font size=+1># --selection=DetTour(2)
# -S : Selection: Roulette, DetTour(T), StochTour(t) or Sequential(ordered/unordered)</font></font></tt></b>
<br><font color="#FF0000">String parameter:</font><font color="#000000">
Name of <a href="eoEngine.html#selection">selection procedure.</a> Availabable
are the </font><b><font color="#FF6600">roulette wheel</font></b><font color="#000000">
(name </font><b><tt><font color="#009900"><font size=+1>Roulette</font></font></tt></b><font color="#000000">,
fitness scaling coming soon); </font><b><font color="#FF6600">deterministic
tournament</font></b><font color="#000000"> (name </font><b><tt><font color="#009900"><font size=+1>DetTour</font></font></tt></b><font color="#000000">
with size - integer > 2 - in parentheses right after the name, use double
quotes on the command line);&nbsp; </font><b><font color="#FF6600">stochastic
tournament</font></b><font color="#000000"> (name </font><b><tt><font color="#009900"><font size=+1>StochTour</font></font></tt></b><font color="#000000">
with probability - float in [0.5, 1] - in parentheses); </font><b><font color="#FF6600">sequential</font></b><font color="#000000">
(name
</font><b><tt><font color="#009900"><font size=+1>Sequential</font></font></tt></b><font color="#000000">,
all individuals in turn), either from best to worst (option </font><b><tt><font color="#009900"><font size=+1>ordered</font></font></tt></b><font color="#000000">
in parentheses), or in random ordered (option </font><b><tt><font color="#009900"><font size=+1>unordered</font></font></tt></b><font color="#000000">);
and finally repeated </font><b><font color="#FF6600">independent uniform
choices</font></b><font color="#000000">&nbsp; (name </font><b><tt><font color="#009900"><font size=+1>Random</font></font></tt></b><font color="#000000">).
Default is </font><font color="#FF0000">DetTour(2)</font><font color="#000000">.</font>
<p><b><tt><font color="#009900"><font size=+1># --nbOffspring=100% # -O
: Nb of offspring (percentage or absolute)</font></font></tt></b>
<br><font color="#FF0000">Integer or real-valued parameter:</font><font color="#000000">
this parameter indicates the </font><b><font color="#FF6600">amount of
offspring</font></b><font color="#000000"> that will be generated from
the genitors every generation. However, this amount can be specified either
</font><font color="#FF6600">relative</font><font color="#000000">
to the population size, and it should then end with percent character (%),
or as an </font><font color="#FF6600">absolute</font><font color="#000000">
integer number (without the percent char).</font>
<br><font color="#000000">Indeed, you can either want, say 7 times more
offspring than parents (a rather common situation in Evolution Strategies),
in which case you give value 700% to </font><b><tt><font color="#009900"><font size=+1>nbOffspring</font></font></tt></b><font color="#000000">
parameter; or you might want a single offspring whatever the population
size, like in Steady-State evolution engines, in which case you simply
enter value 1. </font><font color="#FF0000">Default is 100%</font><font color="#000000">.</font>
<p><b><tt><font color="#009900"><font size=+1># --replacement=Comma # -R
: Replacement: Comma, Plus, EPTour(T), SSGAWorst, SSGADet(T), SSGAStoch(t)</font></font></tt></b>
<br><font color="#FF0000">String parameter:</font><font color="#000000">
Name of replacement procedure. Availabable are the </font><b><font color="#FF6600">ES
plus and comma</font></b><font color="#000000"> deterministic replacement
strategies (named respectively </font><b><tt><font color="#009900"><font size=+1>Plus</font></font></tt></b><font color="#000000">
and&nbsp; </font><b><tt><font color="#009900"><font size=+1>Comma</font></font></tt></b><font color="#000000">);
</font><b><font color="#FF6600">EP
stochastic tournament</font></b><font color="#000000"> (name </font><b><tt><font color="#009900"><font size=+1>EPTour</font></font></tt></b><font color="#000000">
with tournament size in parentheses); and the </font><b><font color="#FF6600">steady-state
</font></b><font color="#000000">replacement
procedures, at the moment only based on fitnesses, replacement being either
</font><font color="#FF6600">deterministic</font><font color="#000000">
(new born replace worst parent, name </font><b><tt><font color="#009900"><font size=+1>SSGAWorst</font></font></tt></b><font color="#000000">),&nbsp;
or based on a tournament&nbsp; (name </font><b><tt><font color="#009900"><font size=+1>SSGADet</font></font></tt></b><font color="#000000">
for deterministic tournament, size in parentheses, and </font><b><tt><font color="#009900"><font size=+1>SSGAStoch</font></font></tt></b><font color="#000000">&nbsp;
for stochastic tournament, probability in parentheses). </font><font color="#FF0000">Default
is Comma</font><font color="#000000"> (which btw is also SGA </font><font color="#FF0000">generational
replacement</font><font color="#000000"> whenever there are as many offspring
as parents).</font>
<p><b><tt><font color="#009900"><font size=+1># --weakElitism=0 # -w :
Old best parent replaces new worst offspring *if necessary*</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
if true, weak elitism is added to the replacement procedure (i.e. if the
best fitness among the offspring is less than the best fitness, the best
parent replaces the worst offspring). </font><font color="#FF0000">Default
is false.</font>
<p>
<hr SIZE=5 WIDTH="30%">
<p><b><font size=+1><font color="#FF0000">Section </font><tt><font color="#3333FF">######
Output ######</font></tt></font></b>
<br><font color="#000000">This first section on Output contains parameters
related to screen text output.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --useEval=1 # Use nb of
eval. as counter (vs nb of gen.)</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
whether or not you want the nb of evluations to be displayed and used as
counter in statistics outputs and plots. </font><font color="#FF0000">Default
is true</font><font color="#000000">.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --printBestStat=1 # Print
Best/avg/stdev every gen.</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
toggles screen output of indicated statistics. </font><font color="#FF0000">Default
is true</font><font color="#000000">.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --printPop=0 # Print sorted
pop. every gen.</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
adds a dump of the whole population to the screen every generation. Is
likely to generate </font><b><font color="#FF6600">huge</font></b><font color="#000000">
output! </font><font color="#FF0000">Default is false.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --printFDC=1 # Print FDC
coeff. every gen.</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
adds Fitness Distance Correlation to output every generation. </font><font color="#FF0000">Default
is false.</font>
<p>
<hr SIZE=5 WIDTH="30%">
<p><b><font size=+1><font color="#FF0000">Section </font><tt><font color="#3333FF">######
Output - Disk ######</font></tt></font></b>
<br><font color="#000000">This second section on Output contains parameters
related to DISK output.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --resDir=Res # Directory
to store DISK outputs</font></font></tt></b>
<br><font color="#FF0000">String parameter: </font><font color="#000000">All
</font><font color="#FF6600">DISK
output</font><font color="#000000"> will be stored in a separate directory
-this is its name. If the directory does not exist, it is created. Note
that </font><font color="#FF6600">all graphical displays</font><font color="#000000">
will use that directory for their temporary files. Also </font><font color="#FF6600">all
job dump</font><font color="#000000"> (see section </font><b><font color="#3333FF">Persistence</font></b><font color="#000000">
below) store their files there too.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --eraseDir=0 # erase files
in dirName if any</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
in order not to mix up files from different runs, it is mandatory to ensure
that the directory where all files will be stored is empty. However, if
this parameter is not set and the directory already exists, an exception
is thrown and the program stops. It it is set, </font><b><font color="#FF6600">all
files in the result directory are erased</font></b><font color="#000000">.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --fileBestStat=0 # Output
Best/avg/stdev to a file</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
if present, the best, average and standard deviation statistics are stored
in file </font><b><tt><font color="#993300"><font size=+1>resDir/best.xg</font></font></tt></b><font color="#000000">.
Each line contains the generation number, eventualy the evaluation count
(depending on parameter </font><b><tt><font color="#3333FF"><font size=+1>useEval</font></font></tt></b><font color="#000000">
then the statistics. </font><font color="#FF0000">Default is false.</font>
<br>&nbsp;
<p>
<hr SIZE=5 WIDTH="30%">
<p><b><font size=+1><font color="#FF0000">Section </font><tt><font color="#3333FF">######
Output - Graphical ######</font></tt></font></b>
<br><font color="#000000">This last section on Output contains parameters
related to graphical output (only available in Unix through gnuplot at
the moment).</font>
<p><b><tt><font color="#3333FF"><font size=+1># --plotBestStat=0 # Plot
Best/avg Stat</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
toggles gnuplot output of best and average plots (Linux only at the moment).
</font><font color="#FF0000">Default
is false.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --plotFDCStat=0 # Plot
FDC scatter plot</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
toggles the Fitness Distance Correlation plot (Fitness vs distance to best).
</font><font color="#FF0000">Default
is false.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --plotHisto=0 # Plot histogram
of fitnesses</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
if on, gnuplot is used to plot the sorted population (fitness vs rank).
Gives a graphical idea of the diversity. </font><font color="#FF0000">Default
is false.</font>
<p>
<hr SIZE=5 WIDTH="30%">
<p><b><font size=+1><font color="#FF0000">Section </font><tt><font color="#3333FF">######
Persistence ######</font></tt></font></b>
<br><font color="#000000">This section contains parameters handling job
dump and restart mechanism.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --Load= # -L : A save file
to restart from</font></font></tt></b>
<br><font color="#FF0000">String parameter:</font><font color="#000000">
if present, the initial population (and the RNG) is read from indicated
file. That file </font><b><font color="#FF0000">must</font></b><font color="#000000">
come from a previous save (or must be in same format!), i.e. must contain
a popualtion, the RNG and all parameters. If no other parameter is modified,
using a previously saved population and RNG will give exactly the same
results than having run that previous run longer. And a way to be sure
to re-use the same parameters is to ... use that very save file as parameter
file, as it contains all actual parameters in the right format.</font>
<br><font color="#000000">Note that if not enough individuals are read,
the remaining are randomly initialized. </font><font color="#FF0000">No
default value</font><font color="#000000">.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --recomputeFitness=0 #
-r : Recompute the fitness after re-loading the pop.?</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
in case some individuals are read from a file, their fitness is read too.
If this one is true, it is nevertheless recomputed. </font><font color="#FF0000">Default
is false</font><font color="#000000"> i.e. use fitnes that's in the file.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --saveFrequency=0 # Save
every F generation (0 = only final state, absent = never)</font></font></tt></b>
<br><font color="#FF0000">Integer parameter:</font><font color="#000000">
interval between two dump to disk of the whole population (+RNG + parameters),
in a file named genNN.sav in the </font><b><tt><font color="#993300"><font size=+1>dirRes</font></font></tt></b><font color="#000000">
directory, where NN is the generation number. If this prameter is present
(even with 0 or negative value), the final population will always be saved,
whatever the reason for stopping. Hence the only way to avoid all saves
is to omit the parameter (there is </font><font color="#FF0000">no default
value</font><font color="#000000">).</font>
<p><b><tt><font color="#3333FF"><font size=+1># --saveTimeInterval=0 #
Save every T seconds (0 or absent = never)</font></font></tt></b>
<br><font color="#FF0000">Integer parameter:</font><font color="#000000">
time interval between two population (+RNG + parameters) dumps to disks.
Files are names timeNN.sav. See pervious parameter description for ore
details. </font><font color="#FF0000">No default value.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --status=t-eoGA.status
# Status file</font></font></tt></b>
<br><font color="#FF0000">String parameter:</font><font color="#000000">
name of the status file (that contains all parameters in the input format).
There is no way to avoid creating that file except recompiling ... or giving
the name /dev/null (Unix). Default value is </font><font color="#FF0000">ProgramName.status</font>
<p>
<hr SIZE=5 WIDTH="30%">
<p><b><font size=+1><font color="#FF0000">Section </font><tt><font color="#3333FF">######
Stopping criterion ######</font></tt></font></b>
<br><font color="#000000">This section allows to decide when the algorithm
will stop.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --maxGen=100 # -G : Maximum
number of generations (0 = none)</font></font></tt></b>
<br><font color="#000000">Integer parameter: maximum number of generations.
A value of 0 disables that stopping criterion. </font><font color="#FF0000">Default
is 100.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --steadyGen=100 # -s :
Number of generations with no improvement</font></font></tt></b>
<br><font color="#FF0000">Integer parameter:</font><font color="#000000">
stops whenever that number of generations is passed without any improvement
of the best fitness in the population, provided the following minimum number
of generations has been done. </font><font color="#FF0000">No default value.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --minGen=0 # -g : Minimum
number of generations</font></font></tt></b>
<br><font color="#000000">Integer parameter: the above steadyGen parameter
starts its job only after that minimum nuber of generations is passed.
</font><font color="#FF0000">No
default value.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --maxEval=0 # -E : Maximum
number of evaluations (0 = none)</font></font></tt></b>
<br><font color="#FF0000">Integer parameter:</font><font color="#000000">
maximum number of generations.
</font><font color="#FF0000">No default
value.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --targetFitness=0 # -T
: Stop when fitness reaches</font></font></tt></b>
<br><font color="#FF0000">Real-valued parameter:</font><font color="#000000">
the algorithm stops whenever the best fitness reaches that target. </font><font color="#FF0000">No
default value.</font>
<p><b><tt><font color="#3333FF"><font size=+1># --CtrlC=0 # -C : Terminate
current generation upon Ctrl C</font></font></tt></b>
<br><font color="#FF0000">Boolean parameter:</font><font color="#000000">
if true, Ctrl C only stops after the current generation as completed (eventually
dumping population to a file if some saver is active). THis very useful
feature is only available in Unix at the moment. </font><font color="#FF0000">Default
is false.</font>
<br>
<hr ALIGN=LEFT SIZE=5 WIDTH="100%">
<p><a NAME="binary"></a><b><font color="#000099"><font size=+1>User's guide:</font></font><font color="#FF0000">
Bistring specific parameters</font></b>
<br>The following describes the specific parameters that are available
in program BitEA to evolve genotypes that are <b><font color="#FF6600">bitstrings</font></b>.
<br>The two representation-dependent sections are concerned repectively
with genotype initilization and variation operators.
<p>
<hr SIZE=5 WIDTH="30%">
<p><b><font size=+1><font color="#FF0000">Section </font><tt><font color="#CC33CC">######&nbsp;&nbsp;&nbsp;
Genotype Initialization&nbsp;&nbsp;&nbsp; ######</font></tt></font></b>
<br><font color="#000000">This section should allow input if all necessary
parameters for genitype initialization</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --ChromSize=10 # -n : The
length of the bitstrings</font></font></tt></b>
<br><font color="#FF0000">Integer parameter:</font><font color="#000000">
The bitstring initilization only requires the length of the chromosome.</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">This section allows to tune the way the variation
operators will be applied to the individuals (in the strict limit of SGA
model at the moment, see below).</font>
<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># --onePointRate=1 # -1 :
Relative rate for one point crossover</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
Rate of aplication of the 1-point crossover </font><b><font color="#FF6600">relatively</font></b><font color="#000000">
to 2-point and uniform below (see </font><b><tt><font color="#CC33CC"><font size=+1>pCross</font></font></tt></b><font color="#000000">
parameter). </font><font color="#FF0000">Default is 1</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --twoPointRate=1 # -2 :
Relative rate for two point crossover</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
Rate of aplication of the 2-point crossover </font><b><font color="#FF6600">relatively</font></b><font color="#000000">
to 1-point above and uniform below (see </font><b><tt><font color="#CC33CC"><font size=+1>pCross</font></font></tt></b><font color="#000000">
parameter). </font><font color="#FF0000">Default is 1</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --uRate=2 # -U : Relative
rate for uniform crossover</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
Rate of aplication of the 1-point crossover </font><b><font color="#FF6600">relatively</font></b><font color="#000000">
to 1- and 2-point above (see </font><b><tt><font color="#CC33CC"><font size=+1>pCross</font></font></tt></b><font color="#000000">
parameter). </font><font color="#FF0000">Default is 2</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --pMutPerBit=0.01 # -b
: Probability of flipping 1 bit in bit-flip mutation</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
When </font><b><tt><font color="#CC33CC"><font size=+1>bit-flip mutation</font></font></tt></b><font color="#000000">
is applied, each bit is flipped independently with probability&nbsp; </font><b><tt><font color="#CC33CC"><font size=+1>pMutPerBit</font></font></tt></b><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --bitFlipRate=0.01 # -s
: Relative rate for bit-flip mutation</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
Rate of aplication of the bit-flip mutation </font><b><font color="#FF6600">relatively</font></b><font color="#000000">
to one-Bit mutation below (see </font><b><tt><font color="#CC33CC"><font size=+1>pMut</font></font></tt></b><font color="#000000">
above). </font><font color="#FF0000">Default is 0.01</font><font color="#000000">
(if all relative rates are equal, the choice is uniform among available
operators).</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --oneBitRate=0.01 # -d
: Relative rate for deterministic bit-flip mutation</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
Rate of aplication of the one-bit mutation </font><b><font color="#FF6600">relatively</font></b><font color="#000000">
to bit-flip mutation below (see </font><b><tt><font color="#CC33CC"><font size=+1>pMut</font></font></tt></b><font color="#000000">
above). One-bit mutation flips one and only one bit, uniformly chosen in
the individual. </font><font color="#FF0000">Default is 0.01</font><font color="#000000">
(if all relative rates are equal, the choice is uniform among available
operators).</font>
<br>&nbsp;
<p>
<hr ALIGN=LEFT SIZE=5 WIDTH="100%">
<p><a NAME="real"></a><b><font color="#000099"><font size=+1>User's guide:</font></font><font color="#FF0000">
Real-valued specific parameters</font></b>
<br>The following describes the specific parameters that are available
in programs <b><tt><font color="#993300"><font size=+1>RealEA</font></font></tt></b>
and <b><tt><font color="#993300"><font size=+1>ESEA</font></font></tt></b>
to evolve genotypes that are <b><font color="#FF6600">vector&lt;double></font></b>.
<br><b><tt><font color="#993300"><font size=+1>RealEA</font></font></tt></b>&nbsp;
implements what can be called a "real-coded GA", where everything is identical
to the bitstring case above (except initialization and operators that are
specific to vector&lt;double> of course) and <b><tt><font color="#993300"><font size=+1>ESEA</font></font></tt></b>
implements the full Evolution-Strategy self-adaptive mutation mechanism
- together with specific ES crossover operators. The initialization section
for both programs are identical, but the operator sections are totally
different. See <a href="#ES">next paragraph</a> for a description of ES
specific parameters.
<p>
<hr SIZE=5 WIDTH="30%">
<p><b><font size=+1><font color="#FF0000">Section </font><tt><font color="#CC33CC">######&nbsp;&nbsp;&nbsp;
Genotype Initialization&nbsp;&nbsp;&nbsp; ######</font></tt></font></b>
<br><font color="#000000">This section should allow input if all necessary
parameters for genitype initialization</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --vecSize=10 # -n : The
number of variables</font></font></tt></b>
<br><font color="#FF0000">Integer parameter:</font><font color="#000000">
The initilization requires the length of the vector&lt;double>.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --initBounds=(0,1) # -B
: Bounds for uniform initialization</font></font></tt></b>
<br><font color="#FF0000">Special string parameter:</font><font color="#000000">
Bounds for uniform initialization of the real variables. At the moment
only the same bounds for all variables can be chosen, and the format is
(min,max) without any white space.&nbsp; This argument is mandatory, and
</font><font color="#FF0000">default is (0,1)</font><font color="#000000">.</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --sigmaInit=0.3 # -s :
Initial value for Sigma(s)</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
The initial value for all standard-deviation mutation strategy parameters.
Useless when no self-adaptive mutation mechanism is used.</font><font color="#000000"></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">This section allows to tune the way the variation
operators will be applied to the individuals (in the strict limit of SGA
model at the moment, see below).</font>
<p><b><tt><font color="#CC33CC"><font size=+1># --objectBounds=(0,1) #
-B : Bounds for variables (unbounded if absent)</font></font></tt></b>
<br><font color="#FF0000">Special string parameter:</font><font color="#000000">
Bounds for the variables to be met by all variation operators (see format
in </font><b><tt><font color="#CC33CC"><font size=+1>initBounds</font></font></tt></b><font color="#000000">
above). If this parameter is </font><b><font color="#FF6600">absent, unbounded
variables</font></b><font color="#000000"> are assumed (but they still
need some </font><b><tt><font color="#CC33CC"><font size=+1>initBounds</font></font></tt></b><font color="#000000">
for initialization). For the arithmetic crossovers below, and when parameter
alpha is greater than 0, those bounds result in restricting the values
of possible combination factors. For the uniform mutation, the interval
of uniform choice of the variables is restricted by those bounds. Finally,
in the case of Gaussian mutation, the probability distribution is folded
back into the boundeds as many times as necesssary. </font><font color="#FF0000">No
default (i.e. unbounded variables).</font><b><tt><font color="#CC33CC"><font size=+1></font></font></tt></b>
<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><font color="#000000"></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><b><tt><font color="#CC33CC"><font size=+1></font></font></tt></b>
<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><b><tt><font color="#CC33CC"><font size=+1></font></font></tt></b>
<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><b><tt><font color="#CC33CC"><font size=+1></font></font></tt></b>
<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><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><b><tt><font color="#CC33CC"><font size=+1></font></font></tt></b>
<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><b><tt><font color="#CC33CC"><font size=+1></font></font></tt></b>
<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><b><tt><font color="#CC33CC"><font size=+1></font></font></tt></b>
<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 color="#000099"><font size=+1>User's guide:</font></font><font color="#FF0000">
ES-real-valued specific parameters</font></b>
<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><font color="#000000"></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><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><b><tt><font color="#CC33CC"><font size=+1></font></font></tt></b>
<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><tt><font color="#CC33CC"><font size=+1></font></font></tt>
<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><font color="#000000"></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,</font></font></tt></b><font color="#000000">
</font><b><tt><font color="#CC33CC"><font size=+1>operator,</font></font></tt></b><font color="#000000">
</font><b><tt><font color="#CC33CC"><font size=+1>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><font color="#000000"></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><font color="#000000"></font>
<p><b><tt><font color="#CC33CC"><font size=+1># --crossObj=discrete # -O
: Recombination of object variables (discrete or intermediate)</font></font></tt></b>
<br><font color="#FF0000">String parameter:</font><font color="#000000">&nbsp;
There are two possible crossovers in plain ES. The </font><b><tt><font color="#CC33CC"><font size=+1>discrete</font></font></tt></b><font color="#000000">
crossover simpy exchanges variables among the parents. It is similar to
the plain uniform crossover for real variables. The&nbsp; crossover performs
a linear combination of parents;variables - it si similar to the hypercube
crossover described for&nbsp; with alpah parameter set to 0. This parameter
allso to choose the type of crossover that will be applied to the </font><b><font color="#FF6600">object
variables</font></b><font color="#000000"> (i.e. the origianl variables
of the problem). </font><font color="#FF0000">Default is discrete.</font><font color="#000000"></font>
<p><b><tt><font color="#CC33CC"><font size=+1># --crossStdev=intermediate
# -S : Recombination of mutation strategy parameters (intermediate or discrete)</font></font></tt></b>
<br><font color="#FF0000">String parameter:</font><font color="#000000">&nbsp;
This parameter allows to choose the type of crossover (see above) that
will be applied to the </font><b><font color="#FF6600">mutation strategy
parameters</font></b><font color="#000000"> that are part of the genotype.
</font><font color="#FF0000">Default is intermediate.</font><b><tt><font color="#CC33CC"><font size=+1></font></font></tt></b>
<p><b><tt><font color="#CC33CC"><font size=+1># --TauLoc=1 # -l : Local
Tau (before normalization)</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
The local factor for the mutation of the mutation strategy parameters (the
only one used when a single standard deviation is used). </font><font color="#FF0000">Default
is 1</font><font color="#000000">.</font><font color="#000000"></font>
<p><b><tt><font color="#CC33CC"><font size=+1># --TauGlob=1 # -g : Global
Tau (before normalization)</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
The global factor for the mutation of the mutation strategy parameters
(only useful when more than one standard deviation are used). </font><font color="#FF0000">Default
is 1</font><font color="#000000">.</font><font color="#000000"></font>
<p><b><tt><font color="#CC33CC"><font size=+1># --Beta=0.0873 # -b : Beta</font></font></tt></b>
<br><font color="#FF0000">Floating-point parameter:</font><font color="#000000">
The factor for the mutation of the rotation angles in the case of the full
correlated mutation. </font><font color="#FF0000">Default is 0.0873</font><font color="#000000">
(following Schwefel).</font><font color="#000000"></font>
<p>
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<font color="#000000"><a href="mailto:Marc.Schoenauer@polytechnique.fr">Marc
Schoenauer</a></font></address>
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