CMA-ES, Covariance Matrix Adaptation Evolution Strategy for non-linear numerical optimization in Python
A stochastic numerical optimization algorithm for difficult (non-convex, ill-conditioned, multi-modal, rugged, noisy) optimization problems in continuous search spaces, implemented in Python.
Typical domain of application are bound-constrained or unconstrained objective functions with:
The CMA-ES is quite reliable, however for small budgets (fewer function evaluations than, say, 100 times dimension) or in very small dimensions better (i.e. faster) methods are available.
The pycma module provides two independent implementations of the
CMA-ES algorithm in the classes cma.CMAEvolutionStrategy and
cma.purecma.CMAES.
There are several ways of installation:
In the terminal command line type::
python -m pip install cma
Typing just pip instead of python -m pip may be sufficient. Or,
alternatively::
easy_install cma
The package will be downloaded and installed automatically. To
upgrade an existing installation, 'cma' must be replaced by
'-U cma' in both cases. If you never heard of pip, see here__.
__ http://www.pip-installer.org
Download and unpack the cma-...tar.gz file and type::
pip install -e cma
or::
python setup.py install
in the cma-... folder (under Windows just
"setup.py install").
Under Windows one may also download the MS Windows installer.
Installation might require root privileges. In this case, try
the --user option of pip or prepended with sudo.
The folder cma from the tar archive can also be used without
any installation (just import needs to find it).
In a Python shell::
>>> import cma
>>> help(cma)
<output omitted>
>>> es = cma.CMAEvolutionStrategy(8 * [0], 0.5)
(5_w,10)-aCMA-ES (mu_w=3.2,w_1=45%) in dimension 8 (seed=468976, Tue May 6 19:14:06 2014)
>>> help(es) # the same as help(cma.CMAEvolutionStrategy)
<output omitted>
>>> es.optimize(cma.ff.rosen)
Iterat #Fevals function value axis ratio sigma minstd maxstd min:sec
1 10 1.042661803766204e+02 1.0e+00 4.50e-01 4e-01 5e-01 0:0.0
2 20 7.322331708590002e+01 1.2e+00 3.89e-01 4e-01 4e-01 0:0.0
3 30 6.048150359372417e+01 1.2e+00 3.47e-01 3e-01 3e-01 0:0.0
100 1000 3.165939452385367e+00 1.1e+01 7.08e-02 2e-02 7e-02 0:0.2
200 2000 4.157333035296804e-01 1.9e+01 8.10e-02 9e-03 5e-02 0:0.4
300 3000 2.413696640005903e-04 4.3e+01 9.57e-03 3e-04 7e-03 0:0.5
400 4000 1.271582136805314e-11 7.6e+01 9.70e-06 8e-08 3e-06 0:0.7
439 4390 1.062554035878040e-14 9.4e+01 5.31e-07 3e-09 8e-08 0:0.8
>>> es.result_pretty() # pretty print result
termination on tolfun=1e-11
final/bestever f-value = 3.729752e-15 3.729752e-15
mean solution: [ 1. 1. 1. 1. 0.99999999 0.99999998
0.99999995 0.99999991]
std deviation: [ 2.84303359e-09 2.74700402e-09 3.28154576e-09 5.92961588e-09
1.07700123e-08 2.12590385e-08 4.09374304e-08 8.16649754e-08]
optimizes the 8-dimensional Rosenbrock function with initial solution all
zeros and initial sigma = 0.5.
Pretty much the same can be achieved a little less "elaborate" with::
>>> import cma
>>> xopt, es = cma.fmin2(cma.ff.rosen, 8 * [0], 0.5)
<output omitted>
And a little more elaborate exposing the ask-and-tell interface::
>>> import cma
>>> es = cma.CMAEvolutionStrategy(12 * [0], 0.5)
>>> while not es.stop():
... solutions = es.ask()
... es.tell(solutions, [cma.ff.rosen(x) for x in solutions])
... es.logger.add() # write data to disc to be plotted
... es.disp()
<output omitted>
>>> es.result_pretty()
<output omitted>
>>> cma.plot() # shortcut for es.logger.plot()
.. figure:: http://www.cmap.polytechnique.fr/~nikolaus.hansen/rosen12.png :alt: CMA-ES on Rosenbrock function in dimension 8 :target: https://cma-es.github.io/cmaes_sourcecode_page.html#example :align: center
A single run on the 12-dimensional Rosenbrock function.
The CMAOptions class manages options for CMAEvolutionStrategy,
e.g. verbosity options can be found like::
>>> import cma
>>> cma.s.pprint(cma.CMAOptions('erb'))
{'verb_log': '1 #v verbosity: write data to files every verb_log iteration, writing can be time critical on fast to evaluate functions'
'verbose': '1 #v verbosity e.v. of initial/final message, -1 is very quiet, not yet implemented'
'verb_plot': '0 #v in fmin(): plot() is called every verb_plot iteration'
'verb_disp': '100 #v verbosity: display console output every verb_disp iteration'
'verb_filenameprefix': 'outcmaes # output filenames prefix'
'verb_append': '0 # initial evaluation counter, if append, do not overwrite output files'
'verb_time': 'True #v output timings on console'}
Options are passed like::
>>> import cma
>>> es = cma.CMAEvolutionStrategy(8 * [0], 0.5,
{'verb_disp': 1}) # display each iteration
The full package API documentation:
version 3+_ (recent)version 1.x_.. _version 3+: https://cma-es.github.io/apidocs-pycma/
.. _version 1.x: http://www.cmap.polytechnique.fr/~nikolaus.hansen/html-pythoncma/
See also
Github page hosting this code_ and its FAQ_ (under development)General CMA-ES source code page_ with practical hintsCMA-ES on Wikipedia_.. _Github page hosting this code: https://github.com/CMA-ES/pycma
.. _FAQ: https://github.com/CMA-ES/pycma/issues?q=is:issue+label:FAQ
.. _General CMA-ES source code page: https://cma-es.github.io/cmaes_sourcecode_page.html
.. _CMA-ES on Wikipedia: http://en.wikipedia.org/wiki/CMA-ES
cma.purecma): numpy -- array processing for numbers, strings, records, and objectsmatplotlib -- Python plotting package (includes pylab)Use pip install numpy etc. for installation. The cma.purecma submodule can be used without any dependencies installed.
License: BSD