CMA-ES, Covariance Matrix Adaptation Evolution Strategy for non-linear numerical optimization in Python
Project description
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:
search space dimension between, say, 5 and (a few) 100,
no gradients available,
at least, say, 100 times dimension function evaluations needed to get satisfactory solutions,
non-separable, ill-conditioned, or rugged/multi-modal landscapes.
The CMA-ES is quite reliable, however for small budgets (fewer than, say, 100 times dimension function evaluations) or in very small dimensions better (i.e. faster) methods are available.
Installation
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.
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).
Usage Example
In a Python shell:
>>> import cma >>> 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.fcts.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 >>> res = cma.fmin(cma.fcts.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.fcts.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()
The CMAOptions class manages options for CMAEvolutionStrategy, e.g. verbosity options can be found like:
>>> import cma >>> from cma import pprint as pp # several imports per line are considered as bad style >>> pp(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
Documentations
Read the full package documentation:
See also
General CMA-ES source code page with practical hints
Dependencies
required: numpy – array processing for numbers, strings, records, and objects
optional (highly recommended): matplotlib – Python plotting package (includes pylab)
Use pip install numpy etc. for installation. For a Python implementation of CMA-ES with lesser dependencies see here.
License: BSD
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