| |
- __builtin__.dict(__builtin__.object)
-
- CMAOptions
- __builtin__.object
-
- BaseDataLogger
-
- CMADataLogger
- BestSolution
- CMAAdaptSigmaBase
-
- CMAAdaptSigmaCSA
- CMAAdaptSigmaDistanceProportional
- CMAAdaptSigmaMedianImprovement
- CMAAdaptSigmaNone
- CMAAdaptSigmaTPA
- ElapsedTime
- GenoPheno
- MathHelperFunctions
- Misc
- NoiseHandler
- OOOptimizer
-
- CMAEvolutionStrategy
- Rotation
- Sections
- _abcoll.MutableMapping(_abcoll.Mapping)
-
- DerivedDictBase
-
- SolutionDict
-
- CMASolutionDict
- BoundaryHandlerBase(__builtin__.object)
-
- BoundNone
- BoundPenalty
- BoundTransform
class BaseDataLogger(__builtin__.object) |
|
"abstract" base class for a data logger that can be used with an `OOOptimizer`
Details: attribute `modulo` is used in ``OOOptimizer.optimize`` |
|
Methods defined here:
- add(self, optim=None, more_data=[])
- abstract method, add a "data point" from the state of `optim` into the
logger, the argument `optim` can be omitted if it was `register()`-ed before,
acts like an event handler
- data(self)
- return logged data in a dictionary (not implemented)
- disp(self)
- display some data trace (not implemented)
- plot(self)
- plot data (not implemented)
- register(self, optim)
- abstract method, register an optimizer `optim`, only needed if `add()` is
called without a value for the `optim` argument
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class BestSolution(__builtin__.object) |
|
container to keep track of the best solution seen |
|
Methods defined here:
- __init__(self, x=None, f=inf, evals=None)
- initialize the best solution with `x`, `f`, and `evals`.
Better solutions have smaller `f`-values.
- get(self)
- return ``(x, f, evals)``
- update(self, arx, xarchive=None, arf=None, evals=None)
- checks for better solutions in list `arx`.
Based on the smallest corresponding value in `arf`,
alternatively, `update` may be called with a `BestSolution`
instance like ``update(another_best_solution)`` in which case
the better solution becomes the current best.
`xarchive` is used to retrieve the genotype of a solution.
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class BoundNone(BoundaryHandlerBase) |
|
# ____________________________________________________________
# ____________________________________________________________ |
|
- Method resolution order:
- BoundNone
- BoundaryHandlerBase
- __builtin__.object
Methods defined here:
- __init__(self, bounds=None)
- is_in_bounds(self, x)
Methods inherited from BoundaryHandlerBase:
- __call__(self, solutions, *args, **kwargs)
- return penalty or list of penalties, by default zero(s).
This interface seems too specifically tailored to the derived
BoundPenalty class, it should maybe change.
- get_bounds(self, which, dimension)
- ``get_bounds('lower', 8)`` returns the lower bounds in 8-D
- has_bounds(self)
- return True, if any variable is bounded
- inverse(self, y, copy_if_changed=True, copy_always=False)
- repair(self, x, copy_if_changed=True, copy_always=False)
- projects infeasible values on the domain bound, might be
overwritten by derived class
- to_dim_times_two(self, bounds)
- return boundaries in format ``[[lb0, ub0], [lb1, ub1], ...]``,
as used by ``BoxConstraints...`` class.
- update(self, *args, **kwargs)
Data descriptors inherited from BoundaryHandlerBase:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class BoundPenalty(BoundaryHandlerBase) |
|
Computes the boundary penalty. Must be updated each iteration,
using the `update` method.
Details
-------
The penalty computes like ``sum(w[i] * (x[i]-xfeas[i])**2)``,
where `xfeas` is the closest feasible (in-bounds) solution from `x`.
The weight `w[i]` should be updated during each iteration using
the update method.
Example:
>>> import cma
>>> cma.fmin(cma.felli, 6 * [1], 1,
... {
... 'boundary_handling': 'BoundPenalty',
... 'bounds': [-1, 1],
... 'fixed_variables': {0: 0.012, 2:0.234}
... })
Reference: Hansen et al 2009, A Method for Handling Uncertainty...
IEEE TEC, with addendum, see
http://www.lri.fr/~hansen/TEC2009online.pdf |
|
- Method resolution order:
- BoundPenalty
- BoundaryHandlerBase
- __builtin__.object
Methods defined here:
- __call__(self, x, archive, gp)
- returns the boundary violation penalty for `x` ,where `x` is a
single solution or a list or array of solutions.
- __init__(self, bounds=None)
- Argument bounds can be `None` or ``bounds[0]`` and ``bounds[1]``
are lower and upper domain boundaries, each is either `None` or
a scalar or a list or array of appropriate size.
- feasible_ratio(self, solutions)
- counts for each coordinate the number of feasible values in
``solutions`` and returns an array of length ``len(solutions[0])``
with the ratios.
`solutions` is a list or array of repaired ``Solution``
instances,
- repair(self, x, copy_if_changed=True, copy_always=False)
- sets out-of-bounds components of ``x`` on the bounds.
- update(self, function_values, es)
- updates the weights for computing a boundary penalty.
Arguments
---------
`function_values`
all function values of recent population of solutions
`es`
`CMAEvolutionStrategy` object instance, in particular
mean and variances and the methods from the attribute
`gp` of type `GenoPheno` are used.
Methods inherited from BoundaryHandlerBase:
- get_bounds(self, which, dimension)
- ``get_bounds('lower', 8)`` returns the lower bounds in 8-D
- has_bounds(self)
- return True, if any variable is bounded
- inverse(self, y, copy_if_changed=True, copy_always=False)
- is_in_bounds(self, x)
- not yet tested
- to_dim_times_two(self, bounds)
- return boundaries in format ``[[lb0, ub0], [lb1, ub1], ...]``,
as used by ``BoxConstraints...`` class.
Data descriptors inherited from BoundaryHandlerBase:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class BoundTransform(BoundaryHandlerBase) |
|
Handles boundary by a smooth, piecewise linear and quadratic
transformation into the feasible domain.
>>> import cma
>>> veq = cma.Mh.vequals_approximately
>>> b = cma.BoundTransform([None, 1])
>>> assert b.bounds == [[None], [1]]
>>> assert veq(b.repair([0, 1, 1.2]), array([ 0., 0.975, 0.975]))
>>> assert b.is_in_bounds([0, 0.5, 1])
>>> assert veq(b.transform([0, 1, 2]), [ 0. , 0.975, 0.2 ])
>>> o=cma.fmin(cma.fcts.sphere, 6 * [-2], 0.5, options={
... 'boundary_handling': 'BoundTransform ',
... 'bounds': [[], 5 * [-1] + [inf]] })
>>> assert o[1] < 5 + 1e-8
>>> import numpy as np
>>> b = cma.BoundTransform([-np.random.rand(120), np.random.rand(120)])
>>> for i in range(100):
... x = (-i-1) * np.random.rand(120) + i * np.random.randn(120)
... x_to_b = b.repair(x)
... x2 = b.inverse(x_to_b)
... x2_to_b = b.repair(x2)
... x3 = b.inverse(x2_to_b)
... x3_to_b = b.repair(x3)
... assert veq(x_to_b, x2_to_b)
... assert veq(x2, x3)
... assert veq(x2_to_b, x3_to_b)
Details: this class uses ``class BoxConstraintsLinQuadTransformation`` |
|
- Method resolution order:
- BoundTransform
- BoundaryHandlerBase
- __builtin__.object
Methods defined here:
- __init__(self, bounds=None)
- Argument bounds can be `None` or ``bounds[0]`` and ``bounds[1]``
are lower and upper domain boundaries, each is either `None` or
a scalar or a list or array of appropriate size.
- inverse(self, x, copy_if_changed=True, copy_always=False)
- inverse transform of ``x`` from the bounded domain.
- repair(self, x, copy_if_changed=True, copy_always=False)
- transforms ``x`` into the bounded domain.
``copy_always`` option might disappear.
- transform(self, x)
Methods inherited from BoundaryHandlerBase:
- __call__(self, solutions, *args, **kwargs)
- return penalty or list of penalties, by default zero(s).
This interface seems too specifically tailored to the derived
BoundPenalty class, it should maybe change.
- get_bounds(self, which, dimension)
- ``get_bounds('lower', 8)`` returns the lower bounds in 8-D
- has_bounds(self)
- return True, if any variable is bounded
- is_in_bounds(self, x)
- not yet tested
- to_dim_times_two(self, bounds)
- return boundaries in format ``[[lb0, ub0], [lb1, ub1], ...]``,
as used by ``BoxConstraints...`` class.
- update(self, *args, **kwargs)
Data descriptors inherited from BoundaryHandlerBase:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class CMAAdaptSigmaBase(__builtin__.object) |
|
step-size adaptation base class, implementing hsig functionality
via an isotropic evolution path. |
|
Methods defined here:
- __init__(self, *args, **kwargs)
- hsig(self, es)
- return "OK-signal" for rank-one update, `True` (OK) or `False`
(stall rank-one update), based on the length of an evolution path
- initialize_base(self, es)
- set parameters and state variable based on dimension,
mueff and possibly further options.
- update(self, es, **kwargs)
- update ``es.sigma``
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class CMAAdaptSigmaCSA(CMAAdaptSigmaBase) |
| |
- Method resolution order:
- CMAAdaptSigmaCSA
- CMAAdaptSigmaBase
- __builtin__.object
Methods defined here:
- __init__(self)
- postpone initialization to a method call where dimension and mueff should be known.
- initialize(self, es)
- set parameters and state variable based on dimension,
mueff and possibly further options.
- update(self, es, **kwargs)
Methods inherited from CMAAdaptSigmaBase:
- hsig(self, es)
- return "OK-signal" for rank-one update, `True` (OK) or `False`
(stall rank-one update), based on the length of an evolution path
- initialize_base(self, es)
- set parameters and state variable based on dimension,
mueff and possibly further options.
Data descriptors inherited from CMAAdaptSigmaBase:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class CMAAdaptSigmaMedianImprovement(CMAAdaptSigmaBase) |
|
Compares median fitness against a fitness percentile of the previous iteration,
see Ait ElHara et al, GECCO 2013. |
|
- Method resolution order:
- CMAAdaptSigmaMedianImprovement
- CMAAdaptSigmaBase
- __builtin__.object
Methods defined here:
- __init__(self)
- initialize(self, es)
- update(self, es, **kwargs)
Methods inherited from CMAAdaptSigmaBase:
- hsig(self, es)
- return "OK-signal" for rank-one update, `True` (OK) or `False`
(stall rank-one update), based on the length of an evolution path
- initialize_base(self, es)
- set parameters and state variable based on dimension,
mueff and possibly further options.
Data descriptors inherited from CMAAdaptSigmaBase:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class CMAAdaptSigmaNone(CMAAdaptSigmaBase) |
| |
- Method resolution order:
- CMAAdaptSigmaNone
- CMAAdaptSigmaBase
- __builtin__.object
Methods defined here:
- update(self, es, **kwargs)
- no update, ``es.sigma`` remains constant.
:param es: ``CMAEvolutionStrategy`` class instance
:param kwargs: whatever else is needed to update ``es.sigma``
Methods inherited from CMAAdaptSigmaBase:
- __init__(self, *args, **kwargs)
- hsig(self, es)
- return "OK-signal" for rank-one update, `True` (OK) or `False`
(stall rank-one update), based on the length of an evolution path
- initialize_base(self, es)
- set parameters and state variable based on dimension,
mueff and possibly further options.
Data descriptors inherited from CMAAdaptSigmaBase:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class CMAAdaptSigmaTPA(CMAAdaptSigmaBase) |
|
two point adaptation for step-size sigma. Relies on a specific
sampling of the first two offspring, whose objective function
value ranks are used to decide on the step-size change.
Example
=======
>>> import cma
>>> cma.CMAOptions('adapt').pprint()
>>> es = cma.CMAEvolutionStrategy(10 * [0.2], 0.1, {'AdaptSigma': cma.CMAAdaptSigmaTPA, 'ftarget': 1e-8})
>>> es.optimize(cma.fcts.rosen)
>>> assert 'ftarget' in es.stop()
>>> assert es.result()[1] <= 1e-8
>>> assert es.result()[2] < 6500 # typically < 5500
References: loosely based on Hansen 2008, CMA-ES with Two-Point
Step-Size Adaptation, more tightly based on an upcoming paper by
Hansen et al. |
|
- Method resolution order:
- CMAAdaptSigmaTPA
- CMAAdaptSigmaBase
- __builtin__.object
Methods defined here:
- __init__(self, dimension=None, opts=None)
- initialize(self, N=None, opts=None)
- update(self, es, function_values, **kwargs)
- the first and second value in ``function_values``
must reflect two mirrored solutions sampled
in direction / in opposite direction of
the previous mean shift, respectively.
Methods inherited from CMAAdaptSigmaBase:
- hsig(self, es)
- return "OK-signal" for rank-one update, `True` (OK) or `False`
(stall rank-one update), based on the length of an evolution path
- initialize_base(self, es)
- set parameters and state variable based on dimension,
mueff and possibly further options.
Data descriptors inherited from CMAAdaptSigmaBase:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class CMADataLogger(BaseDataLogger) |
|
data logger for class `CMAEvolutionStrategy`. The logger is
identified by its name prefix and (over-)writes or reads according
data files. Therefore, the logger must be considered as *global* variable
with unpredictable side effects, if two loggers with the same name
and on the same working folder are used at the same time.
Examples
========
::
import cma
es = cma.CMAEvolutionStrategy(...)
logger = cma.CMADataLogger().register(es)
while not es.stop():
...
logger.add() # add can also take an argument
logger.plot() # or a short cut can be used:
cma.plot() # plot data from logger with default name
logger2 = cma.CMADataLogger('just_another_filename_prefix').load()
logger2.plot()
logger2.disp()
::
import cma
from matplotlib.pylab import *
res = cma.fmin(cma.Fcts.sphere, rand(10), 1e-0)
logger = res[-1] # the CMADataLogger
logger.load() # by "default" data are on disk
semilogy(logger.f[:,0], logger.f[:,5]) # plot f versus iteration, see file header
show()
Details
=======
After loading data, the logger has the attributes `xmean`, `xrecent`,
`std`, `f`, `D` and `corrspec` corresponding to ``xmean``,
``xrecentbest``, ``stddev``, ``fit``, ``axlen`` and ``axlencorr``
filename trails.
:See: `disp()`, `plot()` |
|
- Method resolution order:
- CMADataLogger
- BaseDataLogger
- __builtin__.object
Methods defined here:
- __init__(self, name_prefix=u'outcmaes', modulo=1, append=False)
- initialize logging of data from a `CMAEvolutionStrategy`
instance, default ``modulo=1`` means logging with each call
- add(self, es=None, more_data=[], modulo=None)
- append some logging data from `CMAEvolutionStrategy` class instance `es`,
if ``number_of_times_called % modulo`` equals to zero, never if ``modulo==0``.
The sequence ``more_data`` must always have the same length.
When used for a different optimizer class, this function can be
(easily?) adapted by changing the assignments under INTERFACE
in the implemention.
- closefig(self)
- data(self)
- return dictionary with data.
If data entries are None or incomplete, consider calling
``.load().data()`` to (re-)load the data from files first.
- disp(self, idx=100)
- displays selected data from (files written by) the class `CMADataLogger`.
Arguments
---------
`idx`
indices corresponding to rows in the data file;
if idx is a scalar (int), the first two, then every idx-th,
and the last three rows are displayed. Too large index values are removed.
Example
-------
>>> import cma, numpy as np
>>> res = cma.fmin(cma.fcts.elli, 7 * [0.1], 1, {'verb_disp':1e9}) # generate data
>>> assert res[1] < 1e-9
>>> assert res[2] < 4400
>>> l = cma.CMADataLogger() # == res[-1], logger with default name, "points to" above data
>>> l.disp([0,-1]) # first and last
>>> l.disp(20) # some first/last and every 20-th line
>>> l.disp(np.r_[0:999999:100, -1]) # every 100-th and last
>>> l.disp(np.r_[0, -10:0]) # first and ten last
>>> cma.disp(l.name_prefix, np.r_[0::100, -10:]) # the same as l.disp(...)
Details
-------
The data line with the best f-value is displayed as last line.
:See: `disp()`
- disp_header(self)
- downsampling(self, factor=10, first=3, switch=True, verbose=True)
- rude downsampling of a `CMADataLogger` data file by `factor`,
keeping also the first `first` entries. This function is a
stump and subject to future changes. Return self.
Arguments
---------
- `factor` -- downsampling factor
- `first` -- keep first `first` entries
- `switch` -- switch the new logger to the downsampled logger
original_name+'down'
Details
-------
``self.name_prefix+'down'`` files are written
Example
-------
::
import cma
cma.downsampling() # takes outcmaes* files
cma.plot('outcmaesdown')
- initialize(self, modulo=None)
- reset logger, overwrite original files, `modulo`: log only every modulo call
- load(self, filenameprefix=None)
- load (or reload) data from output files, `load()` is called in
`plot()` and `disp()`.
Argument `filenameprefix` is the filename prefix of data to be
loaded (six files), by default ``'outcmaes'``.
Return self with (added) attributes `xrecent`, `xmean`,
`f`, `D`, `std`, 'corrspec'
- plot(self, fig=None, iabscissa=1, iteridx=None, plot_mean=False, foffset=1e-19, x_opt=None, fontsize=9)
- plot data from a `CMADataLogger` (using the files written
by the logger).
Arguments
---------
`fig`
figure number, by default 325
`iabscissa`
``0==plot`` versus iteration count,
``1==plot`` versus function evaluation number
`iteridx`
iteration indices to plot
Return `CMADataLogger` itself.
Examples
--------
::
import cma
logger = cma.CMADataLogger() # with default name
# try to plot the "default logging" data (e.g.
# from previous fmin calls, which is essentially what
# also cma.plot() does)
logger.plot()
cma.savefig('fig325.png') # save current figure
logger.closefig()
Dependencies: matlabplotlib/pyplot.
- plot_all(self, fig=None, iabscissa=1, iteridx=None, foffset=1e-19, x_opt=None, fontsize=9)
- plot data from a `CMADataLogger` (using the files written by the logger).
Arguments
---------
`fig`
figure number, by default 425
`iabscissa`
``0==plot`` versus iteration count,
``1==plot`` versus function evaluation number
`iteridx`
iteration indices to plot
Return `CMADataLogger` itself.
Examples
--------
::
import cma
logger = cma.CMADataLogger() # with default name
# try to plot the "default logging" data (e.g.
# from previous fmin calls, which is essentially what
# also cma.plot() does)
logger.plot_all()
cma.savefig('fig425.png') # save current figure
logger.closefig()
Dependencies: matlabplotlib/pyplot.
- plot_axes_scaling(self, iabscissa=1)
- plot_correlations(self, iabscissa=1)
- spectrum of correlation matrix and largest correlation
- plot_divers(self, iabscissa=1, foffset=1e-19)
- plot fitness, sigma, axis ratio...
:param iabscissa: 0 means vs evaluations, 1 means vs iterations
:param foffset: added to f-value
:See: `plot()`
- plot_mean(self, iabscissa=1, x_opt=None, annotations=None)
- plot_stds(self, iabscissa=1)
- plot_xrecent(self, iabscissa=1, x_opt=None, annotations=None)
- register(self, es, append=None, modulo=None)
- register a `CMAEvolutionStrategy` instance for logging,
``append=True`` appends to previous data logged under the same name,
by default previous data are overwritten.
- save_to(self, nameprefix, switch=False)
- saves logger data to a different set of files, for
``switch=True`` also the loggers name prefix is switched to
the new value
- select_data(self, iteration_indices)
- keep only data of `iteration_indices`
Data and other attributes defined here:
- default_prefix = u'outcmaes'
Data descriptors inherited from BaseDataLogger:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class CMAEvolutionStrategy(OOOptimizer) |
|
CMA-ES stochastic optimizer class with ask-and-tell interface.
Calling Sequences
=================
es = CMAEvolutionStrategy(x0, sigma0)
es = CMAEvolutionStrategy(x0, sigma0, opts)
es = CMAEvolutionStrategy(x0, sigma0).optimize(objective_fct)
res = CMAEvolutionStrategy(x0, sigma0,
opts).optimize(objective_fct).result()
Arguments
=========
`x0`
initial solution, starting point. `x0` is given as "phenotype"
which means, if::
opts = {'transformation': [transform, inverse]}
is given and ``inverse is None``, the initial mean is not
consistent with `x0` in that ``transform(mean)`` does not
equal to `x0` unless ``transform(mean)`` equals ``mean``.
`sigma0`
initial standard deviation. The problem variables should
have been scaled, such that a single standard deviation
on all variables is useful and the optimum is expected to
lie within about `x0` +- ``3*sigma0``. See also options
`scaling_of_variables`. Often one wants to check for
solutions close to the initial point. This allows,
for example, for an easier check of consistency of the
objective function and its interfacing with the optimizer.
In this case, a much smaller `sigma0` is advisable.
`opts`
options, a dictionary with optional settings,
see class `CMAOptions`.
Main interface / usage
======================
The interface is inherited from the generic `OOOptimizer`
class (see also there). An object instance is generated from
es = cma.CMAEvolutionStrategy(8 * [0.5], 0.2)
The least verbose interface is via the optimize method::
es.optimize(objective_func)
res = es.result()
More verbosely, the optimization is done using the
methods ``stop``, ``ask``, and ``tell``::
while not es.stop():
solutions = es.ask()
es.tell(solutions, [cma.fcts.rosen(s) for s in solutions])
es.disp()
es.result_pretty()
where ``ask`` delivers new candidate solutions and ``tell`` updates
the ``optim`` instance by passing the respective function values
(the objective function ``cma.fcts.rosen`` can be replaced by any
properly defined objective function, see ``cma.fcts`` for more
examples).
To change an option, for example a termination condition to
continue the optimization, call
es.opts.set({'tolfacupx': 1e4})
The class `CMAEvolutionStrategy` also provides::
(solutions, func_values) = es.ask_and_eval(objective_func)
and an entire optimization can also be written like::
while not es.stop():
es.tell(*es.ask_and_eval(objective_func))
Besides for termination criteria, in CMA-ES only the ranks of the
`func_values` are relevant.
Attributes and Properties
=========================
- `inputargs` -- passed input arguments
- `inopts` -- passed options
- `opts` -- actually used options, some of them can be changed any
time via ``opts.set``, see class `CMAOptions`
- `popsize` -- population size lambda, number of candidate
solutions returned by `ask()`
- `logger` -- a `CMADataLogger` instance utilized by `optimize`
Examples
========
Super-short example, with output shown:
>>> import cma
>>> # construct an object instance in 4-D, sigma0=1:
>>> es = cma.CMAEvolutionStrategy(4 * [1], 1, {'seed':234})
(4_w,8)-CMA-ES (mu_w=2.6,w_1=52%) in dimension 4 (seed=234)
>>>
>>> # optimize the ellipsoid function
>>> es.optimize(cma.fcts.elli, verb_disp=1)
Iterat #Fevals function value axis ratio sigma minstd maxstd min:sec
1 8 2.093015112685775e+04 1.0e+00 9.27e-01 9e-01 9e-01 0:0.0
2 16 4.964814235917688e+04 1.1e+00 9.54e-01 9e-01 1e+00 0:0.0
3 24 2.876682459926845e+05 1.2e+00 1.02e+00 9e-01 1e+00 0:0.0
100 800 6.809045875281943e-01 1.3e+02 1.41e-02 1e-04 1e-02 0:0.2
200 1600 2.473662150861846e-10 8.0e+02 3.08e-05 1e-08 8e-06 0:0.5
233 1864 2.766344961865341e-14 8.6e+02 7.99e-07 8e-11 7e-08 0:0.6
>>>
>>> cma.pprint(es.result())
(array([ -1.98546755e-09, -1.10214235e-09, 6.43822409e-11,
-1.68621326e-11]),
4.5119610261406537e-16,
1666,
1672,
209,
array([ -9.13545269e-09, -1.45520541e-09, -6.47755631e-11,
-1.00643523e-11]),
array([ 3.20258681e-08, 3.15614974e-09, 2.75282215e-10,
3.27482983e-11]))
>>> assert es.result()[1] < 1e-9
>>> help(es.result)
Help on method result in module cma:
result(self) method of cma.CMAEvolutionStrategy instance
return ``(xbest, f(xbest), evaluations_xbest, evaluations, iterations, pheno(xmean), effective_stds)``
The optimization loop can also be written explicitly.
>>> import cma
>>> es = cma.CMAEvolutionStrategy(4 * [1], 1)
>>> while not es.stop():
... X = es.ask()
... es.tell(X, [cma.fcts.elli(x) for x in X])
... es.disp()
<output omitted>
achieving the same result as above.
An example with lower bounds (at zero) and handling infeasible
solutions:
>>> import cma
>>> import numpy as np
>>> es = cma.CMAEvolutionStrategy(10 * [0.2], 0.5, {'bounds': [0, np.inf]})
>>> while not es.stop():
... fit, X = [], []
... while len(X) < es.popsize:
... curr_fit = None
... while curr_fit in (None, np.NaN):
... x = es.ask(1)[0]
... curr_fit = cma.fcts.somenan(x, cma.fcts.elli) # might return np.NaN
... X.append(x)
... fit.append(curr_fit)
... es.tell(X, fit)
... es.logger.add()
... es.disp()
<output omitted>
>>>
>>> assert es.result()[1] < 1e-9
>>> assert es.result()[2] < 9000 # by internal termination
>>> # es.logger.plot() # will plot data
>>> # cma.show() # display plot window
An example with user-defined transformation, in this case to realize
a lower bound of 2.
>>> es = cma.CMAEvolutionStrategy(5 * [3], 1,
... {"transformation": [lambda x: x**2+2, None]})
>>> es.optimize(cma.fcts.rosen)
<output omitted>
>>> assert cma.fcts.rosen(es.result()[0]) < 1e-6 + 5.530760944396627e+02
>>> assert es.result()[2] < 3300
The inverse transformation is (only) necessary if the `BoundPenalty`
boundary handler is used at the same time.
The ``CMAEvolutionStrategy`` class also provides a default logger
(cave: files are overwritten when the logger is used with the same
filename prefix):
>>> import cma
>>> es = cma.CMAEvolutionStrategy(4 * [0.2], 0.5, {'verb_disp': 0})
>>> es.logger.disp_header() # to understand the print of disp
Iterat Nfevals function value axis ratio maxstd minstd
>>> while not es.stop():
... X = es.ask()
... es.tell(X, [cma.fcts.sphere(x) for x in X])
... es.logger.add() # log current iteration
... es.logger.disp([-1]) # display info for last iteration
1 8 2.72769793021748e+03 1.0e+00 4.05e-01 3.99e-01
2 16 6.58755537926063e+03 1.1e+00 4.00e-01 3.39e-01
<output ommitted>
193 1544 3.15195320957214e-15 1.2e+03 3.70e-08 3.45e-11
>>> es.logger.disp_header()
Iterat Nfevals function value axis ratio maxstd minstd
>>> # es.logger.plot() # will make a plot
Example implementing restarts with increasing popsize (IPOP), output
is not displayed:
>>> import cma, numpy as np
>>>
>>> # restart with increasing population size (IPOP)
>>> bestever = cma.BestSolution()
>>> for lam in 10 * 2**np.arange(8): # 10, 20, 40, 80, ..., 10 * 2**7
... es = cma.CMAEvolutionStrategy('6 - 8 * np.random.rand(9)', # 9-D
... 5, # initial std sigma0
... {'popsize': lam, # options
... 'verb_append': bestever.evalsall})
... logger = cma.CMADataLogger().register(es, append=bestever.evalsall)
... while not es.stop():
... X = es.ask() # get list of new solutions
... fit = [cma.fcts.rastrigin(x) for x in X] # evaluate each solution
... es.tell(X, fit) # besides for termination only the ranking in fit is used
...
... # display some output
... logger.add() # add a "data point" to the log, writing in files
... es.disp() # uses option verb_disp with default 100
...
... print('termination:', es.stop())
... cma.pprint(es.best.__dict__)
...
... bestever.update(es.best)
...
... # show a plot
... # logger.plot();
... if bestever.f < 1e-8: # global optimum was hit
... break
<output omitted>
>>> assert es.result()[1] < 1e-8
On the Rastrigin function, usually after five restarts the global
optimum is located.
Using the ``multiprocessing`` module, we can evaluate the function in
parallel with a simple modification of the example (however
multiprocessing seems not always reliable)::
try:
import multiprocessing as mp
import cma
es = cma.CMAEvolutionStrategy(22 * [0.0], 1.0, {'maxiter':10})
pool = mp.Pool(es.popsize)
while not es.stop():
X = es.ask()
f_values = pool.map_async(cma.felli, X).get()
# use chunksize parameter as es.popsize/len(pool)?
es.tell(X, f_values)
es.disp()
es.logger.add()
except ImportError:
pass
The final example shows how to resume:
>>> import cma, pickle
>>>
>>> es = cma.CMAEvolutionStrategy(12 * [0.1], # a new instance, 12-D
... 0.5) # initial std sigma0
>>> es.optimize(cma.fcts.rosen, iterations=100)
>>> pickle.dump(es, open('saved-cma-object.pkl', 'wb'))
>>> print('saved')
>>> del es # let's start fresh
>>>
>>> es = pickle.load(open('saved-cma-object.pkl', 'rb'))
>>> print('resumed')
>>> es.optimize(cma.fcts.rosen, verb_disp=200)
>>> assert es.result()[2] < 15000
>>> cma.pprint(es.result())
Details
=======
The following two enhancements are implemented, the latter is turned
on by default only for very small population size.
*Active CMA* is implemented with option ``CMA_active`` and
conducts an update of the covariance matrix with negative weights.
The negative update is implemented, such that positive definiteness
is guarantied. The update is applied after the default update and
only before the covariance matrix is decomposed, which limits the
additional computational burden to be at most a factor of three
(typically smaller). A typical speed up factor (number of
f-evaluations) is between 1.1 and two.
References: Jastrebski and Arnold, CEC 2006, Glasmachers et al, GECCO 2010.
*Selective mirroring* is implemented with option ``CMA_mirrors``
in the method ``get_mirror()``. Only the method `ask_and_eval()`
(used by `fmin`) will then sample selectively mirrored vectors. In
selective mirroring, only the worst solutions are mirrored. With
the default small number of mirrors, *pairwise selection* (where at
most one of the two mirrors contribute to the update of the
distribution mean) is implicitly guarantied under selective
mirroring and therefore not explicitly implemented.
References: Brockhoff et al, PPSN 2010, Auger et al, GECCO 2011.
:See: `fmin()`, `OOOptimizer`, `CMAOptions`, `plot()`, `ask()`,
`tell()`, `ask_and_eval()` |
|
- Method resolution order:
- CMAEvolutionStrategy
- OOOptimizer
- __builtin__.object
Methods defined here:
- __init__(self, x0, sigma0, inopts={})
- see class `CMAEvolutionStrategy`
- ask(self, number=None, xmean=None, sigma_fac=1, gradf=None, args=())
- get new candidate solutions, sampled from a multi-variate
normal distribution and transformed to f-representation
(phenotype) to be evaluated.
Arguments
---------
`number`
number of returned solutions, by default the
population size ``popsize`` (AKA ``lambda``).
`xmean`
distribution mean, phenotyp?
`sigma_fac`
multiplier for internal sample width (standard
deviation)
`gradf`
gradient, ``len(gradf(x)) == len(x)``, if
``gradf is not None`` the third solution in the
returned list is "sampled" in supposedly Newton
direction ``dot(C, gradf(xmean, *args))``.
`args`
additional arguments passed to gradf
Return
------
A list of N-dimensional candidate solutions to be evaluated
Example
-------
>>> import cma
>>> es = cma.CMAEvolutionStrategy([0,0,0,0], 0.3)
>>> while not es.stop() and es.best.f > 1e-6: # my_desired_target_f_value
... X = es.ask() # get list of new solutions
... fit = [cma.fcts.rosen(x) for x in X] # call function rosen with each solution
... es.tell(X, fit) # feed values
:See: `ask_and_eval`, `ask_geno`, `tell`
- ask_and_eval(self, func, args=(), gradf=None, number=None, xmean=None, sigma_fac=1, evaluations=1, aggregation=<function median>, kappa=1)
- samples `number` solutions and evaluates them on `func`, where
each solution `s` is resampled until ``self.is_feasible(s, func(s)) is True``.
Arguments
---------
`func`
objective function, ``func(x)`` returns a scalar
`args`
additional parameters for `func`
`gradf`
gradient of objective function, ``g = gradf(x, *args)``
must satisfy ``len(g) == len(x)``
`number`
number of solutions to be sampled, by default
population size ``popsize`` (AKA lambda)
`xmean`
mean for sampling the solutions, by default ``self.mean``.
`sigma_fac`
multiplier for sampling width, standard deviation, for example
to get a small perturbation of solution `xmean`
`evaluations`
number of evaluations for each sampled solution
`aggregation`
function that aggregates `evaluations` values to
as single value.
`kappa`
multiplier used for the evaluation of the solutions, in
that ``func(m + kappa*(x - m))`` is the f-value for x.
Return
------
``(X, fit)``, where
X -- list of solutions
fit -- list of respective function values
Details
-------
While ``not self.is_feasible(x, func(x))``new solutions are sampled. By
default ``self.is_feasible == cma.feasible == lambda x, f: f not in (None, np.NaN)``.
The argument to `func` can be freely modified within `func`.
Depending on the ``CMA_mirrors`` option, some solutions are not sampled
independently but as mirrors of other bad solutions. This is a simple
derandomization that can save 10-30% of the evaluations in particular
with small populations, for example on the cigar function.
Example
-------
>>> import cma
>>> x0, sigma0 = 8*[10], 1 # 8-D
>>> es = cma.CMAEvolutionStrategy(x0, sigma0)
>>> while not es.stop():
... X, fit = es.ask_and_eval(cma.fcts.elli) # handles NaN with resampling
... es.tell(X, fit) # pass on fitness values
... es.disp(20) # print every 20-th iteration
>>> print('terminated on ' + str(es.stop()))
<output omitted>
A single iteration step can be expressed in one line, such that
an entire optimization after initialization becomes
::
while not es.stop():
es.tell(*es.ask_and_eval(cma.fcts.elli))
- ask_geno(self, number=None, xmean=None, sigma_fac=1)
- get new candidate solutions in genotyp, sampled from a
multi-variate normal distribution.
Arguments are
`number`
number of returned solutions, by default the
population size `popsize` (AKA lambda).
`xmean`
distribution mean
`sigma_fac`
multiplier for internal sample width (standard
deviation)
`ask_geno` returns a list of N-dimensional candidate solutions
in genotyp representation and is called by `ask`.
Details: updates the sample distribution and might change
the geno-pheno transformation during this update.
:See: `ask`, `ask_and_eval`
- clip_or_fit_solutions(self, pop, idx)
- make sure that solutions fit to sample distribution, this interface will probably change.
In particular the frequency of long vectors appearing in pop[idx] - self.mean is limited.
- copy_constructor(self, es)
- correlation_matrix(self)
- # ____________________________________________________________
# ____________________________________________________________
- decompose_C(self)
- eigen-decompose self.C and update self.dC, self.C, self.B.
Known bugs: this might give a runtime error with
CMA_diagonal / separable option on.
- disp(self, modulo=None)
- prints some single-line infos according to `disp_annotation()`,
if ``iteration_counter % modulo == 0``
- disp_annotation(self)
- print annotation for `disp()`
- eval_mean(self, func, args=())
- evaluate the distribution mean, this is not (yet) effective
in terms of termination or display
- feedForResume(self, X, function_values)
- Given all "previous" candidate solutions and their respective
function values, the state of a `CMAEvolutionStrategy` object
can be reconstructed from this history. This is the purpose of
function `feedForResume`.
Arguments
---------
`X`
(all) solution points in chronological order, phenotypic
representation. The number of points must be a multiple
of popsize.
`function_values`
respective objective function values
Details
-------
`feedForResume` can be called repeatedly with only parts of
the history. The part must have the length of a multiple
of the population size.
`feedForResume` feeds the history in popsize-chunks into `tell`.
The state of the random number generator might not be
reconstructed, but this would be only relevant for the future.
Example
-------
::
import cma
# prepare
(x0, sigma0) = ... # initial values from previous trial
X = ... # list of generated solutions from a previous trial
f = ... # respective list of f-values
# resume
es = cma.CMAEvolutionStrategy(x0, sigma0)
es.feedForResume(X, f)
# continue with func as objective function
while not es.stop():
X = es.ask()
es.tell(X, [func(x) for x in X])
Credits to Dirk Bueche and Fabrice Marchal for the feeding idea.
:See: class `CMAEvolutionStrategy` for a simple dump/load to resume
- get_mirror(self, x, preserve_length=False)
- return ``pheno(self.mean - (geno(x) - self.mean))``.
>>> import cma
>>> es = cma.CMAEvolutionStrategy(cma.np.random.randn(3), 1)
>>> x = cma.np.random.randn(3)
>>> assert cma.Mh.vequals_approximately(es.mean - (x - es.mean), es.get_mirror(x, preserve_length=True))
>>> x = es.ask(1)[0]
>>> vals = (es.get_mirror(x) - es.mean) / (x - es.mean)
>>> assert cma.Mh.equals_approximately(sum(vals), len(vals) * vals[0])
TODO: this implementation is yet experimental.
TODO: this implementation includes geno-pheno transformation,
however in general GP-transformation should be separated from
specific code.
Selectively mirrored sampling improves to a moderate extend but
overadditively with active CMA for quite understandable reasons.
Optimal number of mirrors are suprisingly small: 1,2,3 for
maxlam=7,13,20 where 3,6,10 are the respective maximal possible
mirrors that must be clearly suboptimal.
- get_selective_mirrors(self, number=None, pop_sorted=None)
- get mirror genotypic directions of the `number` worst
solution, based on ``pop_sorted`` attribute (from last
iteration).
Details:
Takes the last ``number=sp.lam_mirr`` entries in
``pop_sorted=self.pop_sorted`` as solutions to be mirrored.
- inject(self, solutions)
- inject a genotypic solution. The solution is used as direction
relative to the distribution mean to compute a new candidate
solution returned in method `ask_geno` which in turn is used in
method `ask`.
>>> import cma
>>> es = cma.CMAEvolutionStrategy(4 * [1], 2)
>>> while not es.stop():
... es.inject([4 * [0.0]])
... X = es.ask()
... break
>>> assert X[0][0] == X[0][1]
- mahalanobis_norm(self, dx)
- compute the Mahalanobis norm that is induced by the adapted
sample distribution, covariance matrix ``C`` times ``sigma**2``,
including ``sigma_vec``. The expected Mahalanobis distance to
the sample mean is about ``sqrt(dimension)``.
Argument
--------
A *genotype* difference `dx`.
Example
-------
>>> import cma, numpy
>>> es = cma.CMAEvolutionStrategy(numpy.ones(10), 1)
>>> xx = numpy.random.randn(2, 10)
>>> d = es.mahalanobis_norm(es.gp.geno(xx[0]-xx[1]))
`d` is the distance "in" the true sample distribution,
sampled points have a typical distance of ``sqrt(2*es.N)``,
where ``es.N`` is the dimension, and an expected distance of
close to ``sqrt(N)`` to the sample mean. In the example,
`d` is the Euclidean distance, because C = I and sigma = 1.
- multiplyC(self, alpha)
- multiply C with a scalar and update all related internal variables (dC, D,...)
- plot(self)
- prepare_injection_directions(self)
- provide genotypic directions for TPA and selective mirroring,
with no specific length normalization, to be used in the
coming iteration.
Details:
This method is called in the end of `tell`. The result is
assigned to ``self.pop_injection_directions`` and used in
`ask_geno`.
TODO: should be rather appended?
- random_rescale_to_mahalanobis(self, x)
- change `x` like for injection, all on genotypic level
- random_rescaling_factor_to_mahalanobis_size(self, y)
- ``self.mean + self.random_rescaling_factor_to_mahalanobis_size(y)``
is guarantied to appear like from the sample distribution.
- readProperties(self)
- reads dynamic parameters from property file (not implemented)
- repair_genotype(self, x, copy_if_changed=False)
- make sure that solutions fit to the sample distribution, this interface will probably change.
In particular the frequency of x - self.mean being long is limited.
- result(self)
- return::
(xbest, f(xbest), evaluations_xbest, evaluations, iterations,
pheno(xmean), effective_stds)
- result_pretty(self, number_of_runs=0, time_str=None, fbestever=None)
- pretty print result.
Returns ``self.result()``
- stop(self, check=True)
- return a dictionary with the termination status.
With ``check==False``, the termination conditions are not checked
and the status might not reflect the current situation.
- tell(self, solutions, function_values, check_points=None, copy=False)
- pass objective function values to prepare for next
iteration. This core procedure of the CMA-ES algorithm updates
all state variables, in particular the two evolution paths, the
distribution mean, the covariance matrix and a step-size.
Arguments
---------
`solutions`
list or array of candidate solution points (of
type `numpy.ndarray`), most presumably before
delivered by method `ask()` or `ask_and_eval()`.
`function_values`
list or array of objective function values
corresponding to the respective points. Beside for termination
decisions, only the ranking of values in `function_values`
is used.
`check_points`
If ``check_points is None``, only solutions that are not generated
by `ask()` are possibly clipped (recommended). ``False`` does not clip
any solution (not recommended).
If ``True``, clips solutions that realize long steps (i.e. also
those that are unlikely to be generated with `ask()`). `check_points`
can be a list of indices to be checked in solutions.
`copy`
``solutions`` can be modified in this routine, if ``copy is False``
Details
-------
`tell()` updates the parameters of the multivariate
normal search distribution, namely covariance matrix and
step-size and updates also the attributes ``countiter`` and
``countevals``. To check the points for consistency is quadratic
in the dimension (like sampling points).
Bugs
----
The effect of changing the solutions delivered by `ask()`
depends on whether boundary handling is applied. With boundary
handling, modifications are disregarded. This is necessary to
apply the default boundary handling that uses unrepaired
solutions but might change in future.
Example
-------
::
import cma
func = cma.fcts.elli # choose objective function
es = cma.CMAEvolutionStrategy(cma.np.random.rand(10), 1)
while not es.stop():
X = es.ask()
es.tell(X, [func(x) for x in X])
es.result() # where the result can be found
:See: class `CMAEvolutionStrategy`, `ask()`, `ask_and_eval()`, `fmin()`
- updateBD(self)
- update internal variables for sampling the distribution with the
current covariance matrix C. This method is O(N^3), if C is not diagonal.
- update_exponential(self, Z, eta, BDpair=None)
- exponential update of C that guarantees positive definiteness, that is,
instead of the assignment ``C = C + eta * Z``,
we have ``C = C**.5 * exp(eta * C**-.5 * Z * C**-.5) * C**.5``.
Parameter `Z` should have expectation zero, e.g. sum(w[i] * z[i] * z[i].T) - C
if E z z.T = C.
Parameter `eta` is the learning rate, for ``eta == 0`` nothing is updated.
This function conducts two eigendecompositions, assuming that
B and D are not up to date, unless `BDpair` is given. Given BDpair,
B is the eigensystem and D is the vector of sqrt(eigenvalues), one
eigendecomposition is omitted.
Reference: Glasmachers et al 2010, Exponential Natural Evolution Strategies
Data descriptors defined here:
- popsize
- number of samples by default returned by` ask()`
Methods inherited from OOOptimizer:
- initialize(self)
- (re-)set to the initial state
- optimize(self, objective_fct, iterations=None, min_iterations=1, args=(), verb_disp=None, logger=None, call_back=None)
- find minimizer of `objective_fct`.
CAVEAT: the return value for `optimize` has changed to ``self``.
Arguments
---------
`objective_fct`
function be to minimized
`iterations`
number of (maximal) iterations, while ``not self.stop()``
`min_iterations`
minimal number of iterations, even if ``not self.stop()``
`args`
arguments passed to `objective_fct`
`verb_disp`
print to screen every `verb_disp` iteration, if ``None``
the value from ``self.logger`` is "inherited", if
available.
``logger``
a `BaseDataLogger` instance, which must be compatible
with the type of ``self``.
``call_back``
call back function called like ``call_back(self)`` or
a list of call back functions.
``return self``, that is, the `OOOptimizer` instance.
Example
-------
>>> import cma
>>> es = cma.CMAEvolutionStrategy(7 * [0.1], 0.5
... ).optimize(cma.fcts.rosen, verb_disp=100)
(4_w,9)-CMA-ES (mu_w=2.8,w_1=49%) in dimension 7 (seed=630721393)
Iterat #Fevals function value axis ratio sigma minstd maxstd min:sec
1 9 3.163954777181882e+01 1.0e+00 4.12e-01 4e-01 4e-01 0:0.0
2 18 3.299006223906629e+01 1.0e+00 3.60e-01 3e-01 4e-01 0:0.0
3 27 1.389129389866704e+01 1.1e+00 3.18e-01 3e-01 3e-01 0:0.0
100 900 2.494847340045985e+00 8.6e+00 5.03e-02 2e-02 5e-02 0:0.3
200 1800 3.428234862999135e-01 1.7e+01 3.77e-02 6e-03 3e-02 0:0.5
300 2700 3.216640032470860e-04 5.6e+01 6.62e-03 4e-04 9e-03 0:0.8
400 3600 6.155215286199821e-12 6.6e+01 7.44e-06 1e-07 4e-06 0:1.1
438 3942 1.187372505161762e-14 6.0e+01 3.27e-07 4e-09 9e-08 0:1.2
438 3942 1.187372505161762e-14 6.0e+01 3.27e-07 4e-09 9e-08 0:1.2
('termination by', {'tolfun': 1e-11})
('best f-value =', 1.1189867885201275e-14)
('solution =', array([ 1. , 1. , 1. , 0.99999999, 0.99999998,
0.99999996, 0.99999992]))
>>> print(es.result()[0])
array([ 1. 1. 1. 0.99999999 0.99999998 0.99999996
0.99999992])
Data descriptors inherited from OOOptimizer:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class CMAOptions(__builtin__.dict) |
|
``CMAOptions()`` returns a dictionary with the available options
and their default values for class ``CMAEvolutionStrategy``.
``CMAOptions('pop')`` returns a subset of recognized options that
contain 'pop' in there keyword name or (default) value or description.
``CMAOptions(opts)`` returns the subset of recognized options in
``dict(opts)``.
Option values can be "written" in a string and, when passed to fmin
or CMAEvolutionStrategy, are evaluated using "N" and "popsize" as
known values for dimension and population size (sample size, number
of new solutions per iteration). All default option values are such
a string.
Details
-------
``CMAOptions`` entries starting with ``tol`` are termination
"tolerances".
For `tolstagnation`, the median over the first and the second half
of at least `tolstagnation` iterations are compared for both, the
per-iteration best and per-iteration median function value.
Example
-------
::
import cma
cma.CMAOptions('tol')
is a shortcut for cma.CMAOptions().match('tol') that returns all options
that contain 'tol' in their name or description.
To set an option::
import cma
opts = cma.CMAOptions()
opts.set('tolfun', 1e-12)
opts['tolx'] = 1e-11
:See: `fmin`(), `CMAEvolutionStrategy`, `_CMAParameters` |
|
- Method resolution order:
- CMAOptions
- __builtin__.dict
- __builtin__.object
Methods defined here:
- __call__(self, key, default=None, loc=None)
- evaluate and return the value of option `key` on the fly, or
returns those options whose name or description contains `key`,
case disregarded.
Details
-------
Keys that contain `filename` are not evaluated.
For ``loc==None``, `self` is used as environment
but this does not define ``N``.
:See: `eval()`, `evalall()`
- __init__(self, s=None, unchecked=False)
- return an `CMAOptions` instance, either with the default
options, if ``s is None``, or with all options whose name or
description contains `s`, if `s` is a string (case is
disregarded), or with entries from dictionary `s` as options,
not complemented with default options or settings
Returns: see above.
- check(self, options=None)
- check for ambiguous keys and move attributes into dict
- check_attributes(self, opts=None)
- check for attributes and moves them into the dictionary
- check_values(self, options=None)
- complement(self)
- add all missing options with their default values
- corrected_key(self, key)
- return the matching valid key, if ``key.lower()`` is a unique
starting sequence to identify the valid key, ``else None``
- eval(self, key, default=None, loc=None, correct_key=True)
- Evaluates and sets the specified option value in
environment `loc`. Many options need ``N`` to be defined in
`loc`, some need `popsize`.
Details
-------
Keys that contain 'filename' are not evaluated.
For `loc` is None, the self-dict is used as environment
:See: `evalall()`, `__call__`
- evalall(self, loc=None, defaults=None)
- Evaluates all option values in environment `loc`.
:See: `eval()`
- init(self, dict_or_str, val=None, warn=True)
- initialize one or several options.
Arguments
---------
`dict_or_str`
a dictionary if ``val is None``, otherwise a key.
If `val` is provided `dict_or_str` must be a valid key.
`val`
value for key
Details
-------
Only known keys are accepted. Known keys are in `CMAOptions.defaults()`
- match(self, s=u'')
- return all options that match, in the name or the description,
with string `s`, case is disregarded.
Example: ``cma.CMAOptions().match('verb')`` returns the verbosity
options.
- pp(self)
- pprint(self, linebreak=80)
- print_ = pprint(self, linebreak=80)
- printme = pprint(self, linebreak=80)
- set(self, dic, val=None, force=False)
- set can assign versatile options from
`CMAOptions.versatile_options()` with a new value, use `init()`
for the others.
Arguments
---------
`dic`
either a dictionary or a key. In the latter
case, `val` must be provided
`val`
value for `key`, approximate match is sufficient
`force`
force setting of non-versatile options, use with caution
This method will be most probably used with the ``opts`` attribute of
a `CMAEvolutionStrategy` instance.
- settable(self)
- return the subset of those options that are settable at any
time.
Settable options are in `versatile_options()`, but the
list might be incomplete.
Static methods defined here:
- defaults()
- return a dictionary with default option values and description
- merge(self, dict_=None)
- not is use so far, see check()
- versatile_options()
- return list of options that can be changed at any time (not
only be initialized), however the list might not be entirely up
to date.
The string ' #v ' in the default value indicates a 'versatile'
option that can be changed any time.
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
Methods inherited from __builtin__.dict:
- __cmp__(...)
- x.__cmp__(y) <==> cmp(x,y)
- __contains__(...)
- D.__contains__(k) -> True if D has a key k, else False
- __delitem__(...)
- x.__delitem__(y) <==> del x[y]
- __eq__(...)
- x.__eq__(y) <==> x==y
- __ge__(...)
- x.__ge__(y) <==> x>=y
- __getattribute__(...)
- x.__getattribute__('name') <==> x.name
- __getitem__(...)
- x.__getitem__(y) <==> x[y]
- __gt__(...)
- x.__gt__(y) <==> x>y
- __iter__(...)
- x.__iter__() <==> iter(x)
- __le__(...)
- x.__le__(y) <==> x<=y
- __len__(...)
- x.__len__() <==> len(x)
- __lt__(...)
- x.__lt__(y) <==> x<y
- __ne__(...)
- x.__ne__(y) <==> x!=y
- __repr__(...)
- x.__repr__() <==> repr(x)
- __setitem__(...)
- x.__setitem__(i, y) <==> x[i]=y
- __sizeof__(...)
- D.__sizeof__() -> size of D in memory, in bytes
- clear(...)
- D.clear() -> None. Remove all items from D.
- copy(...)
- D.copy() -> a shallow copy of D
- fromkeys(...)
- dict.fromkeys(S[,v]) -> New dict with keys from S and values equal to v.
v defaults to None.
- get(...)
- D.get(k[,d]) -> D[k] if k in D, else d. d defaults to None.
- has_key(...)
- D.has_key(k) -> True if D has a key k, else False
- items(...)
- D.items() -> list of D's (key, value) pairs, as 2-tuples
- iteritems(...)
- D.iteritems() -> an iterator over the (key, value) items of D
- iterkeys(...)
- D.iterkeys() -> an iterator over the keys of D
- itervalues(...)
- D.itervalues() -> an iterator over the values of D
- keys(...)
- D.keys() -> list of D's keys
- pop(...)
- D.pop(k[,d]) -> v, remove specified key and return the corresponding value.
If key is not found, d is returned if given, otherwise KeyError is raised
- popitem(...)
- D.popitem() -> (k, v), remove and return some (key, value) pair as a
2-tuple; but raise KeyError if D is empty.
- setdefault(...)
- D.setdefault(k[,d]) -> D.get(k,d), also set D[k]=d if k not in D
- update(...)
- D.update([E, ]**F) -> None. Update D from dict/iterable E and F.
If E present and has a .keys() method, does: for k in E: D[k] = E[k]
If E present and lacks .keys() method, does: for (k, v) in E: D[k] = v
In either case, this is followed by: for k in F: D[k] = F[k]
- values(...)
- D.values() -> list of D's values
- viewitems(...)
- D.viewitems() -> a set-like object providing a view on D's items
- viewkeys(...)
- D.viewkeys() -> a set-like object providing a view on D's keys
- viewvalues(...)
- D.viewvalues() -> an object providing a view on D's values
Data and other attributes inherited from __builtin__.dict:
- __hash__ = None
- __new__ = <built-in method __new__ of type object>
- T.__new__(S, ...) -> a new object with type S, a subtype of T
|
class CMASolutionDict(SolutionDict) |
| |
- Method resolution order:
- CMASolutionDict
- SolutionDict
- DerivedDictBase
- _abcoll.MutableMapping
- _abcoll.Mapping
- _abcoll.Sized
- _abcoll.Iterable
- _abcoll.Container
- __builtin__.object
Methods defined here:
- __init__(self, *args, **kwargs)
- insert(self, key, geno=None, iteration=None, fitness=None, value=None)
- insert an entry with key ``key`` and value
``value if value is not None else {'geno':key}`` and
``self[key]['kwarg'] = kwarg if kwarg is not None`` for the further kwargs.
Data and other attributes defined here:
- __abstractmethods__ = frozenset([])
Methods inherited from SolutionDict:
- __delitem__(self, key)
- remove only most current key-entry
- __getitem__(self, key)
- defines self[key]
- __setitem__(self, key, value)
- defines self[key] = value
- key(self, x)
- truncate(self, max_len, min_iter)
Methods inherited from DerivedDictBase:
- __contains__(self, key)
- __iter__(self)
- __len__(self)
Methods inherited from _abcoll.MutableMapping:
- clear(self)
- D.clear() -> None. Remove all items from D.
- pop(self, key, default=<object object>)
- D.pop(k[,d]) -> v, remove specified key and return the corresponding value.
If key is not found, d is returned if given, otherwise KeyError is raised.
- popitem(self)
- D.popitem() -> (k, v), remove and return some (key, value) pair
as a 2-tuple; but raise KeyError if D is empty.
- setdefault(self, key, default=None)
- D.setdefault(k[,d]) -> D.get(k,d), also set D[k]=d if k not in D
- update(*args, **kwds)
- D.update([E, ]**F) -> None. Update D from mapping/iterable E and F.
If E present and has a .keys() method, does: for k in E: D[k] = E[k]
If E present and lacks .keys() method, does: for (k, v) in E: D[k] = v
In either case, this is followed by: for k, v in F.items(): D[k] = v
Methods inherited from _abcoll.Mapping:
- __eq__(self, other)
- __ne__(self, other)
- get(self, key, default=None)
- D.get(k[,d]) -> D[k] if k in D, else d. d defaults to None.
- items(self)
- D.items() -> list of D's (key, value) pairs, as 2-tuples
- iteritems(self)
- D.iteritems() -> an iterator over the (key, value) items of D
- iterkeys(self)
- D.iterkeys() -> an iterator over the keys of D
- itervalues(self)
- D.itervalues() -> an iterator over the values of D
- keys(self)
- D.keys() -> list of D's keys
- values(self)
- D.values() -> list of D's values
Data and other attributes inherited from _abcoll.Mapping:
- __hash__ = None
Class methods inherited from _abcoll.Sized:
- __subclasshook__(cls, C) from abc.ABCMeta
Data descriptors inherited from _abcoll.Sized:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
Data and other attributes inherited from _abcoll.Sized:
- __metaclass__ = <class 'abc.ABCMeta'>
- Metaclass for defining Abstract Base Classes (ABCs).
Use this metaclass to create an ABC. An ABC can be subclassed
directly, and then acts as a mix-in class. You can also register
unrelated concrete classes (even built-in classes) and unrelated
ABCs as 'virtual subclasses' -- these and their descendants will
be considered subclasses of the registering ABC by the built-in
issubclass() function, but the registering ABC won't show up in
their MRO (Method Resolution Order) nor will method
implementations defined by the registering ABC be callable (not
even via super()).
|
class DerivedDictBase(_abcoll.MutableMapping) |
|
for conveniently adding "features" to a dictionary. The actual
dictionary is in ``self.data``. Copy-paste
and modify setitem, getitem, and delitem, if necessary.
Details: This is the clean way to subclass build-in dict. |
|
- Method resolution order:
- DerivedDictBase
- _abcoll.MutableMapping
- _abcoll.Mapping
- _abcoll.Sized
- _abcoll.Iterable
- _abcoll.Container
- __builtin__.object
Methods defined here:
- __contains__(self, key)
- __delitem__(self, key)
- __getitem__(self, key)
- defines self[key]
- __init__(self, *args, **kwargs)
- __iter__(self)
- __len__(self)
- __setitem__(self, key, value)
- defines self[key] = value
Data and other attributes defined here:
- __abstractmethods__ = frozenset([])
Methods inherited from _abcoll.MutableMapping:
- clear(self)
- D.clear() -> None. Remove all items from D.
- pop(self, key, default=<object object>)
- D.pop(k[,d]) -> v, remove specified key and return the corresponding value.
If key is not found, d is returned if given, otherwise KeyError is raised.
- popitem(self)
- D.popitem() -> (k, v), remove and return some (key, value) pair
as a 2-tuple; but raise KeyError if D is empty.
- setdefault(self, key, default=None)
- D.setdefault(k[,d]) -> D.get(k,d), also set D[k]=d if k not in D
- update(*args, **kwds)
- D.update([E, ]**F) -> None. Update D from mapping/iterable E and F.
If E present and has a .keys() method, does: for k in E: D[k] = E[k]
If E present and lacks .keys() method, does: for (k, v) in E: D[k] = v
In either case, this is followed by: for k, v in F.items(): D[k] = v
Methods inherited from _abcoll.Mapping:
- __eq__(self, other)
- __ne__(self, other)
- get(self, key, default=None)
- D.get(k[,d]) -> D[k] if k in D, else d. d defaults to None.
- items(self)
- D.items() -> list of D's (key, value) pairs, as 2-tuples
- iteritems(self)
- D.iteritems() -> an iterator over the (key, value) items of D
- iterkeys(self)
- D.iterkeys() -> an iterator over the keys of D
- itervalues(self)
- D.itervalues() -> an iterator over the values of D
- keys(self)
- D.keys() -> list of D's keys
- values(self)
- D.values() -> list of D's values
Data and other attributes inherited from _abcoll.Mapping:
- __hash__ = None
Class methods inherited from _abcoll.Sized:
- __subclasshook__(cls, C) from abc.ABCMeta
Data descriptors inherited from _abcoll.Sized:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
Data and other attributes inherited from _abcoll.Sized:
- __metaclass__ = <class 'abc.ABCMeta'>
- Metaclass for defining Abstract Base Classes (ABCs).
Use this metaclass to create an ABC. An ABC can be subclassed
directly, and then acts as a mix-in class. You can also register
unrelated concrete classes (even built-in classes) and unrelated
ABCs as 'virtual subclasses' -- these and their descendants will
be considered subclasses of the registering ABC by the built-in
issubclass() function, but the registering ABC won't show up in
their MRO (Method Resolution Order) nor will method
implementations defined by the registering ABC be callable (not
even via super()).
|
class ElapsedTime(__builtin__.object) |
|
using ``time.clock`` with overflow handling to measure CPU time.
Example:
>>> clock = ElapsedTime() # clock starts here
>>> t1 = clock() # get elapsed CPU time
Details: 32-bit C overflows after int(2**32/1e6) == 4294s about 72 min |
|
Methods defined here:
- __call__(self)
- __init__(self)
- reset = __init__(self)
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class GenoPheno(__builtin__.object) |
|
Genotype-phenotype transformation.
Method `pheno` provides the transformation from geno- to phenotype,
that is from the internal representation to the representation used
in the objective function. Method `geno` provides the "inverse" pheno-
to genotype transformation. The geno-phenotype transformation comprises,
in this order:
- insert fixed variables (with the phenotypic and therefore quite
possibly "wrong" values)
- affine linear transformation (first scaling then shift)
- user-defined transformation
- repair (e.g. into feasible domain due to boundaries)
- assign fixed variables their original phenotypic value
By default all transformations are the identity. The repair is only applied,
if the transformation is given as argument to the method `pheno`.
``geno`` is only necessary, if solutions have been injected. |
|
Methods defined here:
- __init__(self, dim, scaling=None, typical_x=None, fixed_values=None, tf=None)
- return `GenoPheno` instance with phenotypic dimension `dim`.
Keyword Arguments
-----------------
`scaling`
the diagonal of a scaling transformation matrix, multipliers
in the genotyp-phenotyp transformation, see `typical_x`
`typical_x`
``pheno = scaling*geno + typical_x``
`fixed_values`
a dictionary of variable indices and values, like ``{0:2.0, 2:1.1}``,
that are not subject to change, negative indices are ignored
(they act like incommenting the index), values are phenotypic
values.
`tf`
list of two user-defined transformation functions, or `None`.
``tf[0]`` is a function that transforms the internal representation
as used by the optimizer into a solution as used by the
objective function. ``tf[1]`` does the back-transformation.
For example::
tf_0 = lambda x: [xi**2 for xi in x]
tf_1 = lambda x: [abs(xi)**0.5 fox xi in x]
or "equivalently" without the `lambda` construct::
def tf_0(x):
return [xi**2 for xi in x]
def tf_1(x):
return [abs(xi)**0.5 fox xi in x]
``tf=[tf_0, tf_1]`` is a reasonable way to guaranty that only positive
values are used in the objective function.
Details
-------
If ``tf_0`` is not the identity and ``tf_1`` is ommitted,
the genotype of ``x0`` cannot be computed consistently and
"injection" of phenotypic solutions is likely to lead to
unexpected results.
- geno(self, y, from_bounds=None, copy_if_changed=True, copy_always=False, repair=None, archive=None)
- maps the phenotypic input argument into the genotypic space,
that is, computes essentially the inverse of ``pheno``.
By default a copy is made only to prevent to modify ``y``.
The inverse of the user-defined transformation (if any)
is only needed if external solutions are injected, it is not
applied to the initial solution x0.
Details
=======
``geno`` searches first in ``archive`` for the genotype of
``y`` and returns the found value, typically unrepaired.
Otherwise, first ``from_bounds`` is applied, to revert a
projection into the bound domain (if necessary) and ``pheno``
is reverted. ``repair`` is applied last, and is usually the
method ``CMAEvolutionStrategy.repair_genotype`` that limits the
Mahalanobis norm of ``geno(y) - mean``.
- pheno(self, x, into_bounds=None, copy=True, copy_always=False, archive=None, iteration=None)
- maps the genotypic input argument into the phenotypic space,
see help for class `GenoPheno`
Details
-------
If ``copy``, values from ``x`` are copied if changed under the transformation.
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
Mh = class MathHelperFunctions(__builtin__.object) |
|
static convenience math helper functions, if the function name
is preceded with an "a", a numpy array is returned |
|
Static methods defined here:
- aclamp(x, upper)
- amax(vec, vec_or_scalar)
- amin(vec_or_scalar, vec_or_scalar2)
- aminmax(val, min_val, max_val)
- apos(x, lower=0)
- clips argument (scalar or array) from below at lower
- cauchy_with_variance_one()
- equals_approximately(a, b, eps=1e-12)
- expms(A, eig=<function eigh>)
- matrix exponential for a symmetric matrix
- max(vec, vec_or_scalar)
- min(a, b)
- minmax(val, min_val, max_val)
- norm(vec, expo=2)
- prctile(data, p_vals=[0, 25, 50, 75, 100], sorted_=False)
- ``prctile(data, 50)`` returns the median, but p_vals can
also be a sequence.
Provides for small samples better values than matplotlib.mlab.prctile,
however also slower.
- sround(nb)
- return stochastic round: floor(nb) + (rand()<remainder(nb))
- standard_finite_cauchy(size=1)
- vequals_approximately(a, b, eps=1e-12)
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class Misc(__builtin__.object) |
| |
Static methods defined here:
- eig(C)
- eigendecomposition of a symmetric matrix, much slower than
`numpy.linalg.eigh`, return ``(EVals, Basis)``, the eigenvalues
and an orthonormal basis of the corresponding eigenvectors, where
``Basis[i]``
the i-th row of ``Basis``
columns of ``Basis``, ``[Basis[j][i] for j in range(len(Basis))]``
the i-th eigenvector with eigenvalue ``EVals[i]``
- likelihood(x, m=None, Cinv=None, sigma=1, detC=None)
- return likelihood of x for the normal density N(m, sigma**2 * Cinv**-1)
- loglikelihood(self, x, previous=False)
- return log-likelihood of `x` regarding the current sample distribution
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
Data and other attributes defined here:
- MathHelperFunctions = <class 'cma.MathHelperFunctions'>
- static convenience math helper functions, if the function name
is preceded with an "a", a numpy array is returned
|
class NoiseHandler(__builtin__.object) |
|
Noise handling according to [Hansen et al 2009, A Method for
Handling Uncertainty in Evolutionary Optimization...]
The interface of this class is yet versatile and subject to changes.
The noise handling follows closely [Hansen et al 2009] in the
measurement part, but the implemented treatment is slightly
different: for ``noiseS > 0``, ``evaluations`` (time) and sigma are
increased by ``alpha``. For ``noiseS < 0``, ``evaluations`` (time)
is decreased by ``alpha**(1/4)``.
The (second) parameter ``evaluations`` defines the maximal number
of evaluations for a single fitness computation. If it is a list,
the smallest element defines the minimal number and if the list has
three elements, the median value is the start value for
``evaluations``.
``NoiseHandler`` serves to control the noise via steps-size
increase and number of re-evaluations, for example via ``fmin`` or
with ``ask_and_eval()``.
Examples
--------
Minimal example together with `fmin` on a non-noisy function:
>>> import cma
>>> cma.fmin(cma.felli, 7 * [1], 1, noise_handler=cma.NoiseHandler(7))
in dimension 7 (which needs to be given tice). More verbose example
in the optimization loop with a noisy function defined in ``func``:
>>> import cma, numpy as np
>>> func = lambda x: cma.fcts.sphere(x) * (1 + 4 * np.random.randn() / len(x)) # cma.Fcts.noisysphere
>>> es = cma.CMAEvolutionStrategy(np.ones(10), 1)
>>> nh = cma.NoiseHandler(es.N, maxevals=[1, 1, 30])
>>> while not es.stop():
... X, fit_vals = es.ask_and_eval(func, evaluations=nh.evaluations)
... es.tell(X, fit_vals) # prepare for next iteration
... es.sigma *= nh(X, fit_vals, func, es.ask) # see method __call__
... es.countevals += nh.evaluations_just_done # this is a hack, not important though
... es.logger.add(more_data = [nh.evaluations, nh.noiseS]) # add a data point
... es.disp()
... # nh.maxevals = ... it might be useful to start with smaller values and then increase
>>> print(es.stop())
>>> print(es.result()[-2]) # take mean value, the best solution is totally off
>>> assert sum(es.result()[-2]**2) < 1e-9
>>> print(X[np.argmin(fit_vals)]) # not bad, but probably worse than the mean
>>> # es.logger.plot()
The command ``logger.plot()`` will plot the logged data.
The noise options of `fmin()` control a `NoiseHandler` instance
similar to this example. The command ``cma.CMAOptions('noise')``
lists in effect the parameters of `__init__` apart from
``aggregate``.
Details
-------
The parameters reevals, theta, c_s, and alpha_t are set differently
than in the original publication, see method `__init__()`. For a
very small population size, say popsize <= 5, the measurement
technique based on rank changes is likely to fail.
Missing Features
----------------
In case no noise is found, ``self.lam_reeval`` should be adaptive
and get at least as low as 1 (however the possible savings from this
are rather limited). Another option might be to decide during the
first call by a quantitative analysis of fitness values whether
``lam_reeval`` is set to zero. More generally, an automatic noise
mode detection might also set the covariance matrix learning rates
to smaller values.
:See: `fmin()`, `CMAEvolutionStrategy.ask_and_eval()` |
|
Methods defined here:
- __call__(self, X, fit, func, ask=None, args=())
- proceed with noise measurement, set anew attributes ``evaluations``
(proposed number of evaluations to "treat" noise) and ``evaluations_just_done``
and return a factor for increasing sigma.
Parameters
----------
`X`
a list/sequence/vector of solutions
`fit`
the respective list of function values
`func`
the objective function, ``fit[i]`` corresponds to ``func(X[i], *args)``
`ask`
a method to generate a new, slightly disturbed solution. The argument
is (only) mandatory if ``epsilon`` is not zero, see `__init__()`.
`args`
optional additional arguments to `func`
Details
-------
Calls the methods ``reeval()``, ``update_measure()`` and ``treat()`` in this order.
``self.evaluations`` is adapted within the method `treat()`.
- __init__(self, N, maxevals=[1, 1, 1], aggregate=<function median>, reevals=None, epsilon=1e-07, parallel=False)
- parameters are
`N`
dimension, (only) necessary to adjust the internal
"alpha"-parameters
`maxevals`
maximal value for ``self.evaluations``, where
``self.evaluations`` function calls are aggregated for
noise treatment. With ``maxevals == 0`` the noise
handler is (temporarily) "switched off". If `maxevals`
is a list, min value and (for >2 elements) median are
used to define minimal and initial value of
``self.evaluations``. Choosing ``maxevals > 1`` is only
reasonable, if also the original ``fit`` values (that
are passed to `__call__`) are computed by aggregation of
``self.evaluations`` values (otherwise the values are
not comparable), as it is done within `fmin()`.
`aggregate`
function to aggregate single f-values to a 'fitness', e.g.
``np.median``.
`reevals`
number of solutions to be reevaluated for noise
measurement, can be a float, by default set to ``2 +
popsize/20``, where ``popsize = len(fit)`` in
``__call__``. zero switches noise handling off.
`epsilon`
multiplier for perturbation of the reevaluated solutions
`parallel`
a single f-call with all resampled solutions
:See: `fmin()`, `CMAOptions`, `CMAEvolutionStrategy.ask_and_eval()`
- get_evaluations(self)
- return ``self.evaluations``, the number of evalutions to get a single fitness measurement
- indices(self, fit)
- return the set of indices to be reevaluated for noise
measurement.
Given the first values are the earliest, this is a useful policy also
with a time changing objective.
- reeval(self, X, fit, func, ask, args=())
- store two fitness lists, `fit` and ``fitre`` reevaluating some
solutions in `X`.
``self.evaluations`` evaluations are done for each reevaluated
fitness value.
See `__call__()`, where `reeval()` is called.
- treat(self)
- adapt self.evaluations depending on the current measurement value
and return ``sigma_fac in (1.0, self.alphasigma)``
- update_measure(self)
- updated noise level measure using two fitness lists ``self.fit`` and
``self.fitre``, return ``self.noiseS, all_individual_measures``.
Assumes that `self.idx` contains the indices where the fitness
lists differ
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
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class OOOptimizer(__builtin__.object) |
|
"abstract" base class for an Object Oriented Optimizer interface.
Relevant methods are `__init__`, `ask`, `tell`, `stop`, `result`,
and `optimize`. Only `optimize` is fully implemented in this base
class.
Examples
--------
All examples minimize the function `elli`, the output is not shown.
(A preferred environment to execute all examples is ``ipython`` in
``%pylab`` mode.)
First we need::
from cma import CMAEvolutionStrategy
# CMAEvolutionStrategy derives from the OOOptimizer class
felli = lambda x: sum(1e3**((i-1.)/(len(x)-1.)*x[i])**2 for i in range(len(x)))
The shortest example uses the inherited method
`OOOptimizer.optimize()`::
es = CMAEvolutionStrategy(8 * [0.1], 0.5).optimize(felli)
The input parameters to `CMAEvolutionStrategy` are specific to this
inherited class. The remaining functionality is based on interface
defined by `OOOptimizer`. We might have a look at the result::
print(es.result()[0]) # best solution and
print(es.result()[1]) # its function value
In order to display more exciting output we do::
es.logger.plot() # if matplotlib is available
Virtually the same example can be written with an explicit loop
instead of using `optimize()`. This gives the necessary insight into
the `OOOptimizer` class interface and entire control over the
iteration loop::
optim = CMAEvolutionStrategy(9 * [0.5], 0.3)
# a new CMAEvolutionStrategy instance
# this loop resembles optimize()
while not optim.stop(): # iterate
X = optim.ask() # get candidate solutions
f = [felli(x) for x in X] # evaluate solutions
# in case do something else that needs to be done
optim.tell(X, f) # do all the real "update" work
optim.disp(20) # display info every 20th iteration
optim.logger.add() # log another "data line"
# final output
print('termination by', optim.stop())
print('best f-value =', optim.result()[1])
print('best solution =', optim.result()[0])
optim.logger.plot() # if matplotlib is available
Details
-------
Most of the work is done in the method `tell(...)`. The method
`result()` returns more useful output. |
|
Methods defined here:
- __init__(self, xstart, **more_args)
- ``xstart`` is a mandatory argument
- ask(self, gradf=None, **more_args)
- abstract method, AKA "get" or "sample_distribution", deliver
new candidate solution(s), a list of "vectors"
- disp(self, modulo=None)
- abstract method, display some iteration infos if
``self.iteration_counter % modulo == 0``
- initialize(self)
- (re-)set to the initial state
- optimize(self, objective_fct, iterations=None, min_iterations=1, args=(), verb_disp=None, logger=None, call_back=None)
- find minimizer of `objective_fct`.
CAVEAT: the return value for `optimize` has changed to ``self``.
Arguments
---------
`objective_fct`
function be to minimized
`iterations`
number of (maximal) iterations, while ``not self.stop()``
`min_iterations`
minimal number of iterations, even if ``not self.stop()``
`args`
arguments passed to `objective_fct`
`verb_disp`
print to screen every `verb_disp` iteration, if ``None``
the value from ``self.logger`` is "inherited", if
available.
``logger``
a `BaseDataLogger` instance, which must be compatible
with the type of ``self``.
``call_back``
call back function called like ``call_back(self)`` or
a list of call back functions.
``return self``, that is, the `OOOptimizer` instance.
Example
-------
>>> import cma
>>> es = cma.CMAEvolutionStrategy(7 * [0.1], 0.5
... ).optimize(cma.fcts.rosen, verb_disp=100)
(4_w,9)-CMA-ES (mu_w=2.8,w_1=49%) in dimension 7 (seed=630721393)
Iterat #Fevals function value axis ratio sigma minstd maxstd min:sec
1 9 3.163954777181882e+01 1.0e+00 4.12e-01 4e-01 4e-01 0:0.0
2 18 3.299006223906629e+01 1.0e+00 3.60e-01 3e-01 4e-01 0:0.0
3 27 1.389129389866704e+01 1.1e+00 3.18e-01 3e-01 3e-01 0:0.0
100 900 2.494847340045985e+00 8.6e+00 5.03e-02 2e-02 5e-02 0:0.3
200 1800 3.428234862999135e-01 1.7e+01 3.77e-02 6e-03 3e-02 0:0.5
300 2700 3.216640032470860e-04 5.6e+01 6.62e-03 4e-04 9e-03 0:0.8
400 3600 6.155215286199821e-12 6.6e+01 7.44e-06 1e-07 4e-06 0:1.1
438 3942 1.187372505161762e-14 6.0e+01 3.27e-07 4e-09 9e-08 0:1.2
438 3942 1.187372505161762e-14 6.0e+01 3.27e-07 4e-09 9e-08 0:1.2
('termination by', {'tolfun': 1e-11})
('best f-value =', 1.1189867885201275e-14)
('solution =', array([ 1. , 1. , 1. , 0.99999999, 0.99999998,
0.99999996, 0.99999992]))
>>> print(es.result()[0])
array([ 1. 1. 1. 0.99999999 0.99999998 0.99999996
0.99999992])
- result(self)
- abstract method, return ``(x, f(x), ...)``, that is, the
minimizer, its function value, ...
- stop(self)
- abstract method, return satisfied termination conditions in
a dictionary like ``{'termination reason': value, ...}``,
for example ``{'tolfun': 1e-12}``, or the empty dictionary ``{}``.
The implementation of `stop()` should prevent an infinite
loop.
- tell(self, solutions, function_values)
- abstract method, AKA "update", pass f-values and prepare for
next iteration
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class Rotation(__builtin__.object) |
|
Rotation class that implements an orthogonal linear transformation,
one for each dimension.
By default reach ``Rotation`` instance provides a different "random"
but fixed rotation. This class is used to implement non-separable
test functions, most conveniently via `FFWrapper.RotatedFitness`.
Example:
>>> import cma, numpy as np
>>> R = cma.Rotation()
>>> R2 = cma.Rotation() # another rotation
>>> x = np.array((1,2,3))
>>> print(R(R(x), inverse=1))
[ 1. 2. 3.]
See: `FFWrapper.RotatedFitness` |
|
Methods defined here:
- __call__(self, x, inverse=False)
- Rotates the input array `x` with a fixed rotation matrix
(``self.dicMatrices['str(len(x))']``)
- __init__(self, seed=None)
- by default a random but fixed rotation, different for each instance
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
Data and other attributes defined here:
- dicMatrices = {}
|
class Sections(__builtin__.object) |
|
plot sections through an objective function.
A first rational thing to do, when facing an (expensive)
application. By default 6 points in each coordinate are evaluated.
This class is still experimental.
Examples
--------
>>> import cma, numpy as np
>>> s = cma.Sections(cma.Fcts.rosen, np.zeros(3)).do(plot=False)
>>> s.do(plot=False) # evaluate the same points again, i.e. check for noise
>> try:
... s.plot()
... except:
... print('plotting failed: matplotlib.pyplot package missing?')
Details
-------
Data are saved after each function call during `do()`. The filename
is attribute ``name`` and by default ``str(func)``, see `__init__()`.
A random (orthogonal) basis can be generated with
``cma.Rotation()(np.eye(3))``.
CAVEAT: The default name is unique in the function name, but it
should be unique in all parameters of `__init__()` but `plot_cmd`
and `load`. If, for example, a different basis is chosen, either
the name must be changed or the ``.pkl`` file containing the
previous data must first be renamed or deleted.
``s.res`` is a dictionary with an entry for each "coordinate" ``i``
and with an entry ``'x'``, the middle point. Each entry ``i`` is
again a dictionary with keys being different dx values and the
value being a sequence of f-values. For example ``s.res[2][0.1] ==
[0.01, 0.01]``, which is generated using the difference vector ``s
.basis[2]`` like
``s.res[2][dx] += func(s.res['x'] + dx * s.basis[2])``.
:See: `__init__()` |
|
Methods defined here:
- __init__(self, func, x, args=(), basis=None, name=None, plot_cmd=<function plot>, load=True)
- Parameters
----------
`func`
objective function
`x`
point in search space, middle point of the sections
`args`
arguments passed to `func`
`basis`
evaluated points are ``func(x + locations[j] * basis[i])
for i in len(basis) for j in len(locations)``,
see `do()`
`name`
filename where to save the result
`plot_cmd`
command used to plot the data, typically matplotlib pyplots `plot` or `semilogy`
`load`
load previous data from file ``str(func) + '.pkl'``
- do(self, repetitions=1, locations=array([-0.5, -0.3, -0.1, 0.1, 0.3, 0.5]), plot=True)
- generates, plots and saves function values ``func(y)``,
where ``y`` is 'close' to `x` (see `__init__()`). The data are stored in
the ``res`` attribute and the class instance is saved in a file
with (the weired) name ``str(func)``.
Parameters
----------
`repetitions`
for each point, only for noisy functions is >1 useful. For
``repetitions==0`` only already generated data are plotted.
`locations`
coordinated wise deviations from the middle point given in `__init__`
- flattened(self)
- return flattened data ``(x, f)`` such that for the sweep through
coordinate ``i`` we have for data point ``j`` that ``f[i][j] == func(x[i][j])``
- load(self, name=None)
- load from file
- plot(self, plot_cmd=None, tf=<function <lambda>>)
- plot the data we have, return ``self``
- save(self, name=None)
- save to file
Data descriptors defined here:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
|
class SolutionDict(DerivedDictBase) |
|
dictionary with computation of an hash key.
The hash key is generated from the inserted solution and a stack of
previously inserted same solutions is provided. Each entry is meant
to store additional information related to the solution.
>>> import cma, numpy as np
>>> d = cma.SolutionDict()
>>> x = np.array([1,2,4])
>>> d[x] = {'f': sum(x**2), 'iteration': 1}
>>> assert d[x]['iteration'] == 1
>>> assert d.get(x) == (d[x] if d.key(x) in d.keys() else None)
TODO: data_with_same_key behaves like a stack (see setitem and
delitem), but rather should behave like a queue?! A queue is less
consistent with the operation self[key] = ..., if
self.data_with_same_key[key] is not empty.
TODO: iteration key is used to clean up without error management |
|
- Method resolution order:
- SolutionDict
- DerivedDictBase
- _abcoll.MutableMapping
- _abcoll.Mapping
- _abcoll.Sized
- _abcoll.Iterable
- _abcoll.Container
- __builtin__.object
Methods defined here:
- __delitem__(self, key)
- remove only most current key-entry
- __getitem__(self, key)
- defines self[key]
- __init__(self, *args, **kwargs)
- __setitem__(self, key, value)
- defines self[key] = value
- key(self, x)
- truncate(self, max_len, min_iter)
Data and other attributes defined here:
- __abstractmethods__ = frozenset([])
Methods inherited from DerivedDictBase:
- __contains__(self, key)
- __iter__(self)
- __len__(self)
Methods inherited from _abcoll.MutableMapping:
- clear(self)
- D.clear() -> None. Remove all items from D.
- pop(self, key, default=<object object>)
- D.pop(k[,d]) -> v, remove specified key and return the corresponding value.
If key is not found, d is returned if given, otherwise KeyError is raised.
- popitem(self)
- D.popitem() -> (k, v), remove and return some (key, value) pair
as a 2-tuple; but raise KeyError if D is empty.
- setdefault(self, key, default=None)
- D.setdefault(k[,d]) -> D.get(k,d), also set D[k]=d if k not in D
- update(*args, **kwds)
- D.update([E, ]**F) -> None. Update D from mapping/iterable E and F.
If E present and has a .keys() method, does: for k in E: D[k] = E[k]
If E present and lacks .keys() method, does: for (k, v) in E: D[k] = v
In either case, this is followed by: for k, v in F.items(): D[k] = v
Methods inherited from _abcoll.Mapping:
- __eq__(self, other)
- __ne__(self, other)
- get(self, key, default=None)
- D.get(k[,d]) -> D[k] if k in D, else d. d defaults to None.
- items(self)
- D.items() -> list of D's (key, value) pairs, as 2-tuples
- iteritems(self)
- D.iteritems() -> an iterator over the (key, value) items of D
- iterkeys(self)
- D.iterkeys() -> an iterator over the keys of D
- itervalues(self)
- D.itervalues() -> an iterator over the values of D
- keys(self)
- D.keys() -> list of D's keys
- values(self)
- D.values() -> list of D's values
Data and other attributes inherited from _abcoll.Mapping:
- __hash__ = None
Class methods inherited from _abcoll.Sized:
- __subclasshook__(cls, C) from abc.ABCMeta
Data descriptors inherited from _abcoll.Sized:
- __dict__
- dictionary for instance variables (if defined)
- __weakref__
- list of weak references to the object (if defined)
Data and other attributes inherited from _abcoll.Sized:
- __metaclass__ = <class 'abc.ABCMeta'>
- Metaclass for defining Abstract Base Classes (ABCs).
Use this metaclass to create an ABC. An ABC can be subclassed
directly, and then acts as a mix-in class. You can also register
unrelated concrete classes (even built-in classes) and unrelated
ABCs as 'virtual subclasses' -- these and their descendants will
be considered subclasses of the registering ABC by the built-in
issubclass() function, but the registering ABC won't show up in
their MRO (Method Resolution Order) nor will method
implementations defined by the registering ABC be callable (not
even via super()).
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