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differentialevolution
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<h2><font color="#000080">
DIFFERENTIAL EVOLUTION
</font></h2>
<h3><font color="#000080">
Preamble
</font></h3>
I have put a lot of effort into this contribution to Matlab Central. As I
used the code successfully for myself for quite some time, I am sure that it can
be rather valuable for the one or the other. If you find any errors or bugs,
if you have problems in using the function or if you find the documentation
insufficiently detailed:
<h4><font color="#660000">
Please contact me and give me the chance to help you before giving a bad
rating on Matlab Central!
</font></h4>
Contact details at the bottom of this page.
<h3><font color="#000080">Introduction
</font></h3>
This contribution provides functions for finding an optimum parameter set
using the <a href="http://en.wikipedia.org/wiki/Evolutionary_algorithm">
Evolutionary Algorithm</a> of <b>Differential Evolution</b>. Simply
speaking: If you have some complicated function of which you are unable to
compute a derivative, and you want to find the parameter set minimizing the
output of the function, using this package is one possible way to go.<br><br>
The core of the optimization is the Differential Evolution algorithm. For an
introduction to the algorithm, see the <a href="http://www.icsi.berkeley.edu/~storn/code.html#basi">
basics section</a> on the <a href="http://www.icsi.berkeley.edu/~storn/code.html">
<b>Differential Evolution homepage</b></a> of Rainer Storn. You will also find a demo
applet and code for different programming languages there. For in-depth documentation and
publications, check out the <a href="http://www.icsi.berkeley.edu/~storn/litera.html">
Literature Section</a>. Even several <a href="http://www.icsi.berkeley.edu/~storn/code.html#link">
books about Differential Evolution</a> are available.<br><br>
This package provides much more than the code available on the referenced
homepage. Here is a list of some features:
<ul>
<li>Optimization can run in parallel on multiple cores/computers.
<li>Extensive and configurable progress information during optimization.
<li>Intermediate results are stored for later review of optimization progress.
<li>Progress information can be sent by E-mail.
<li>Optimization toolbox is not needed.
<li>Quick start with demo functions.
<li>Intermediate results are displayed after the optimization.
<li>Different end conditions can be chosen (maximum time, value to reach etc.).
<li>Each parameter value can be constrained to an interval.
<li>Each parameter value can be quantized (for example for parameters of integer nature).
<li>Code can easily be extended to use the evolutionary algorithm of your choice.
</ul>
I have developed this package for an own project. A single evaluation of my
objective function took between 30 seconds and one minute and the parameter
space was galactically large. If your objective function needs only milliseconds to
evaluate and your optimization is expected to finish in seconds or minutes,
you can still use this package. However, much of its power (parallel processing,
progress notifications) will not be of much use.
<h3><font color="#000080">Quick start
</font></h3>
To get into the usage of the package quickly, check out the demo functions
<font face="Courier New" color="#000080">demo1.m</font> and
<font face="Courier New" color="#000080">demo2.m</font>. Modify those files
to start your first optimization. Essentially you only have to define
which parameters to optimize and provide a handle to your objective function.
You can learn about everything else later.
Your objective function can be called in different ways:
<ul>
<li>With a scalar or column vector as the only input argument.
<li>With a structure containing the current parameters as only input argument.
<li>With one or more fixed arguments first, then a parameter vector or structure as last argument.
</ul>
If your objective function has an argument list that does not comply with
one of these possibilities, you have to write a small wrapper function which
brings the arguments into the correct order and calls your objective function.
In any case, your objective function has to return a <b>finite scalar</b>
(not NaN or Inf) as the first output argument.<br><br>
The definition of the parameters to optimize is expected as a cell array. The
first column of the cell array has to contain the parameter names. In the second
column, you have to provide the parameter ranges. For a scalar parameter, the
range is expected as a two-element row vector. For vector-valued parameters, you
have to give the ranges of the elements as a two-column matrix with ranges in
rows. The third column contains the parameter quantization steps as a
scalar or a column vector (set to zero for no quantization). The fourth column
(optional) can contain the initial values of the parameters. If your objective
function shall be called with a column parameter vector instead of a structure
as input, define only one single parameter with an empty string as parameter name.
See the help text ("help differentialevolution") and the demos for
more details and examples.<br><br>
<h3><font color="#000080">Parallel processing on multiple cores
</font></h3>
This package allows to work in parallel on multiple cores in order to increase
the speed of the optimization. One process acts as the master and all other
processes act as slaves. The only requirements for parallel processing are:
<ul>
<li>All involved processes have to have read- and write-access to a common directory,
for example on a network share.
<li>All involved processes have to have access to identical code versions of the
objective function.
</ul>
For parallel processing, the main function differentialevolution.m has to be started in
one Matlab process. In all other processes, the function differentialevolutionslave.m
has to be started. The master process will save files including the parameter
sets to evaluate into the common directory.
The slave processes load the parameter files, evaluate the objective function and
save the obtainted results into other files. After each iteration, the master process
collects the evaluated results and feeds the slave processes with data files
again. If there are no results found, the master process will evaluate the
parameter sets himself. This way, the slaves can never cause the master to
get stuck.<br><br>
The <a href="http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=13775&objectType=file">
Multicore package</a> on Matlab Central actually emanated from this function
and works quite similar.
<h3><font color="#000080">Functions contained in this package
</font></h3>
In the following, the most important functions contained in this package are
listed. Every file contains its own help comments which you can access by
typing "help functionname" on the Matlab command line.
<br><br><b><font color="#000080">differentialevolution.m
</font></b><br>
The main function to call after preparing the input arguments.
<br><br><b><font color="#000080">getdefaultparams.m
</font></b><br>
When starting to work with this package, you probably do not want to handle
with every existing parameter for function differentialevolution.m. You can
get a default parameter set by calling getdefaultparams.m.
<br><br><b><font color="#000080">differentialevolutionslave.m
</font></b><br>
When working in parallel on multiple cores/computers, this
function has to be started in every Matlab process that shall act as slave.
<br><br><b><font color="#000080">computenewpopulation.m
</font></b><br>
The core Differential Evolution algorithm resides in this functions. If you
like to use your own favorite evolutionary algorithm, you can put the code
into this function.
<br><br><b><font color="#000080">demo1.m, demo2.m
</font></b><br>
Demo functions you can modify for a quick start.
<br><br><b><font color="#000080">foxholes.m, rosenbrocksaddle.m
</font></b><br>
These two functions are used for the demos. They implement two functions that
are often cited in the context of optimization algorithms ("Shekel's
Foxholes" and "Rosenbrock's Saddle").
<br><br><b><font color="#000080">deletewithsemaphores.m, setfilesemaphore.m
</font></b><br>
These functions help to avoid simultaneous file access when working with
multiple cores.
<br><br><b><font color="#000080">sendmailblat.m, blat.exe
</font></b><br>
Function sendmailblat.m sends E-mail notifications using the freeware
executable blat.exe on Windows (see the <a href="http://www.blat.net/">Blat
homepage</a> for more information). There are alternatives for sending E-mails
from Matlab on Windows, but I don't see any need to change this.
<br><br><b><font color="#000080">existfile.m, existfile.c</font></b><br>
Test if a file exists. To use the faster mex-file, type
<font face="Courier New" color="#000080">"mex -setup"</font>,
select the builtin Lcc compiler and type
<font face="Courier New" color="#000080">"mex existfile.c"</font>
to compile the file. However, the package also works without using the mex-file.
<h3><font color="#000080">
Problems/open issues
</font></h3>
<b>Vector parameters</b><br><br>
In my own project, I always passed the current parameter set as a structure
to my objective function. Each field contained a scalar parameter value.
Before releasing this package on Matlab Central, I introduced the possibility to
work with vector-valued parameters, either passed as a single column vector or as
a structure with vector-valued fields to the objective function. However, I did
not have the time to test vector-valued parameters extensively. If you find
any bugs with this, please let me know.
<br><br><b>Parameter quantization</b><br><br>
The original Differential Evolution algorithm only know unbounded, continuous
parameters. In order to include parameters of integer nature into the optimization,
I have extended the algorithm in this way. Internally, all parameters are
continuous. Only before passing them to the objective function, the parameter
values are quantized.
<br><br><b>Hard parameter bounds</b><br><br>
In my own project, and I guess in most other optimization problems as well,
I always had an idea about the possible range for each optimal parameter. A hard
parameter range has to be given here for every parameter. Using -Inf or Inf as
lower or upper bound is <b>not</b> possible. A side effect of the hard bounds
is that parameter sets including boundary values can be evaluated with higher
probability under certain circumstances.
<br><br><b>Breaking using Ctrl-C</b><br><br>
When breaking the optimization using Ctrl-C, it might happen that you catch
Matlab just when writing to a file. When you start the optimization again and
the same file needs to be accessed again, the file is locked until you quit
and restart Matlab (at least on Windows). To avoid this, a 'time-over'-file
is saved in the current directory. After each function evaluation, the master
process checks if the file is still existing. If it was deleted, the
optimization is finished cheerfully.
<br><br><b>Shrinking slave support in parallel processing</b><br><br>
When processing in parallel, the master process feeds the slaves at the start
of each iteration and collects the results at the end. Further, as all parameter
sets that have been evaluated before are saved, not all parameter vectors in
the current population might need to be evaluated. If the population has already
converged very well, it can happen that there are less new parameter vectors
in the population than processes are working on the optimization problem. In
this case, some or all slaves are sleeping, as there is no more work to do.
<br><br><b>Parameter vectors in rows and columns</b><br><br>
I always save parameter vectors as column vectors. However, the core
Differential Evolution algorithm taken from the
<a href="http://www.icsi.berkeley.edu/~storn/code.html#matl">Differential
Evolution homepage</a> expects parameter vectors to be stored in rows.
Unfortunately, the code now contains a mixture of representations as rows
and columns. You will never get involved with this issue until you edit the
code. Parameter vectors are passed to your objective functions as column vectors.
If your objective function needs to get parameter vectors passed as row vectors,
you will have to write a small wrapper function that transposed the vectors
and calls the objective function in the right way.
<h3><font color="#000080">
Links
</font></h3>
<a href="http://www.icsi.berkeley.edu/~storn/code.html">Differential Evolution
homepage.</a><br>
<a href="http://en.wikipedia.org/wiki/Evolutionary_algorithm">Wikipedia</a> about
Evolutionary Algorithms.<br>
<a href="http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=18593">
Latest Version of this package</a> on Matlab Central.<br>
The <a href="http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=13775&objectType=file">
Multicore package</a> on Matlab Central.<br>
<a href="http://www.blat.net/">Blat homepage</a> (E-mails from the
command line on Windows).
<h3><font color="#000080">
Contact
</font></h3>
Dipl.-Ing. Markus Buehren<br>
Stuttgart, Germany<br>
<br>
<a href="mailto:mb_matlab@gmx.de?subject=differential evolution package">mb_matlab@gmx.de</a><br>
<a href="http://www.markusbuehren.de">http://www.markusbuehren.de</a><br>
<h3><font color="#000080">
Version
</font></h3>
Last modified 06.02.2008<br>
Latest version on <a href="http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=18593">Matlab Central</a>.
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