import cma
import numpy as np
from pymoo.algorithms.base.local import LocalSearch
from pymoo.core.population import Population
from pymoo.core.termination import NoTermination
from pymoo.docs import parse_doc_string
from pymoo.termination.max_eval import MaximumFunctionCallTermination
from pymoo.termination.max_gen import MaximumGenerationTermination
from pymoo.util.display.column import Column
from pymoo.util.display.single import SingleObjectiveOutput
from pymoo.util.normalization import ZeroToOneNormalization, NoNormalization
from pymoo.util.optimum import filter_optimum
from pymoo.vendor.vendor_cmaes import my_fmin
# =========================================================================================================
# Implementation
# =========================================================================================================
class CMAESOutput(SingleObjectiveOutput):
def __init__(self):
super().__init__()
self.sigma = Column("sigma")
self.min_std = Column("min_std", width=8)
self.max_std = Column("max_std", width=8)
self.axis = Column("axis", width=8)
self.run = Column("run", width=4)
self.fpop = Column("fpop", width=8)
self.n_pop = Column("n_pop", width=5)
def initialize(self, algorithm):
super().initialize(algorithm)
if algorithm.restarts > 0:
self.columns += [self.run, self.fpop, self.n_pop]
self.columns += [self.sigma, self.min_std, self.max_std, self.axis]
def update(self, algorithm):
super().update(algorithm)
if not algorithm.es.gi_frame:
return
fmin = algorithm.es.gi_frame.f_locals
cma = fmin["es"]
self.sigma.set(cma.sigma)
val = cma.sigma_vec * cma.dC ** 0.5
self.min_std.set((cma.sigma * min(val)))
self.max_std.set((cma.sigma * max(val)))
if algorithm.restarts > 0:
self.run.set(int(fmin["irun"] - fmin["runs_with_small"]) + 1)
self.fpop.set(algorithm.pop.get("F").min())
self.n_pop.set(int(cma.opts['popsize']))
axis = (cma.D.max() / cma.D.min()
if not cma.opts['CMA_diagonal'] or cma.countiter > cma.opts['CMA_diagonal']
else max(cma.sigma_vec * 1) / min(cma.sigma_vec * 1))
self.axis.set(axis)
[docs]
class CMAES(LocalSearch):
def __init__(self,
x0=None,
sigma=0.1,
normalize=True,
parallelize=True,
maxfevals=np.inf,
tolfun=1e-11,
tolx=1e-11,
restarts=0,
restart_from_best='False',
incpopsize=2,
eval_initial_x=False,
noise_handler=None,
noise_change_sigma_exponent=1,
noise_kappa_exponent=0,
bipop=False,
cmaes_verbose=-9,
verb_log=0,
output=CMAESOutput(),
pop_size=None,
**kwargs
):
"""
Parameters
----------
x0 : list or `numpy.ndarray`
initial guess of minimum solution
before the application of the geno-phenotype transformation
according to the ``transformation`` option. It can also be
a string holding a Python expression that is evaluated
to yield the initial guess - this is important in case
restarts are performed so that they start from different
places. Otherwise ``x0`` can also be a `cma.CMAEvolutionStrategy`
object instance, in that case ``sigma0`` can be ``None``.
sigma : float
Initial standard deviation in each coordinate.
``sigma0`` should be about 1/4th of the search domain width
(where the optimum is to be expected). The variables in
``objective_function`` should be scaled such that they
presumably have similar sensitivity.
See also `ScaleCoordinates`.
parallelize : bool
Whether the objective function should be called for each single evaluation or batch wise.
restarts : int, default 0
Number of restarts with increasing population size, see also
parameter ``incpopsize``, implementing the IPOP-CMA-ES restart
strategy, see also parameter ``bipop``; to restart from
different points (recommended), pass ``x0`` as a string.
restart_from_best : bool, default false
Which point to restart from
incpopsize : int
Multiplier for increasing the population size ``popsize`` before each restart
eval_initial_x : bool
Evaluate initial solution, for ``None`` only with elitist option
noise_handler : class
A ``NoiseHandler`` class or instance or ``None``. Example:
``cma.fmin(f, 6 * [1], 1, noise_handler=cma.NoiseHandler(6))``
see ``help(cma.NoiseHandler)``.
noise_change_sigma_exponent : int
Exponent for the sigma increment provided by the noise handler for
additional noise treatment. 0 means no sigma change.
noise_kappa_exponent : int
Instead of applying reevaluations, the "number of evaluations"
is (ab)used as init_simplex_scale factor kappa (experimental).
bipop : bool
If `True`, run as BIPOP-CMA-ES; BIPOP is a special restart
strategy switching between two population sizings - small
(like the default CMA, but with more focused search) and
large (progressively increased as in IPOP). This makes the
algorithm perform well both on functions with many regularly
or irregularly arranged local optima (the latter by frequently
restarting with small populations). For the `bipop` parameter
to actually take effect, also select non-zero number of
(IPOP) restarts; the recommended setting is ``restarts<=9``
and `x0` passed as a string using `numpy.rand` to generate
initial solutions. Note that small-population restarts
do not count into the total restart count.
AdaptSigma : True
Or False or any CMAAdaptSigmaBase class e.g. CMAAdaptSigmaTPA, CMAAdaptSigmaCSA
CMA_active : True
Negative update, conducted after the original update
CMA_activefac : 1
Learning rate multiplier for active update
CMA_cmean : 1
Learning rate for the mean value
CMA_const_trace : False
Normalize trace, 1, True, "arithm", "geom", "aeig", "geig" are valid
CMA_diagonal : 0*100*N/popsize**0.5
Number of iterations with diagonal covariance matrix, True for always
CMA_eigenmethod : np.linalg.eigh or cma.utilities.math.eig or pygsl.eigen.eigenvectors
CMA_elitist : False or "initial" or True
Elitism likely impairs global search performance
CMA_injections_threshold_keep_len : 0
Keep length if Mahalanobis length is below the given relative threshold
CMA_mirrors : popsize < 6
Values <0.5 are interpreted as fraction, values >1 as numbers (rounded), otherwise about 0.16 is used
CMA_mirrormethod : int, default 2, 0=unconditional, 1=selective, 2=selective with delay
CMA_mu : None
Parents selection parameter, default is popsize // 2
CMA_on : 1
Multiplier for all covariance matrix updates
CMA_sampler : None
A class or instance that implements the interface of
`cma.interfaces.StatisticalModelSamplerWithZeroMeanBaseClass`
CMA_sampler_options : dict
Options passed to `CMA_sampler` class init as keyword arguments
CMA_rankmu : 1.0
Multiplier for rank-mu update learning rate of covariance matrix
CMA_rankone : 1.0
Multiplier for rank-one update learning rate of covariance matrix
CMA_recombination_weights : None
A list, see class RecombinationWeights, overwrites CMA_mu and popsize options
CMA_dampsvec_fac : np.Inf
Tentative and subject to changes, 0.5 would be a "default" damping for sigma vector update
CMA_dampsvec_fade : 0.1
Tentative fading out parameter for sigma vector update
CMA_teststds : None
Factors for non-isotropic initial distr. of C, mainly for test purpose, see CMA_stds for production
CMA_stds : None
Multipliers for sigma0 in each coordinate, not represented in C,
makes scaling_of_variables obsolete
CSA_dampfac : 1
Positive multiplier for step-size damping, 0.3 is close to optimal on the sphere
CSA_damp_mueff_exponent : 0.5
Zero would mean no dependency of damping on mueff, useful with CSA_disregard_length option
CSA_disregard_length : False
True is untested, also changes respective parameters
CSA_clip_length_value : None
Poorly tested, [0, 0] means const length N**0.5, [-1, 1] allows a variation of +- N/(N+2), etc.
CSA_squared : False
Use squared length for sigma-adaptation ',
BoundaryHandler : BoundTransform or BoundPenalty, unused when ``bounds in (None, [None, None])``
conditioncov_alleviate : [1e8, 1e12]
When to alleviate the condition in the coordinates and in main axes
eval_final_mean : True
Evaluate the final mean, which is a favorite return candidate
fixed_variables : None
Dictionary with index-value pairs like dict(0=1.1, 2=0.1) that are not optimized
ftarget : -inf
Target function value, minimization
integer_variables : []
Index list, invokes basic integer handling: prevent std dev to become too small in the given variables
maxfevals : inf
Maximum number of function evaluations
maxiter : 100 + 150 * (N+3)**2 // popsize**0.5
Maximum number of iterations
mean_shift_line_samples : False
Sample two new solutions colinear to previous mean shift
mindx : 0
Minimal std in any arbitrary direction, cave interference with tol
minstd : 0
Minimal std (scalar or vector) in any coordinate direction, cave interference with tol
maxstd : inf
Maximal std in any coordinate direction
pc_line_samples : False
One line sample along the evolution path pc
popsize : 4+int(3*np.log(N))
Population size, AKA lambda, number of new solution per iteration
randn
Randn(lam, N) must return an np.array of shape (lam, N), see also cma.utilities.math.randhss
signals_filename : None
cma_signals.in # read versatile options from this file which contains a single options dict,
e.g. ``dict("timeout"=0)`` to stop, string-values are evaluated, e.g. "np.inf" is valid
termination_callback : None
A function returning True for termination, called in `stop` with `self` as argument, could be abused
for side effects
timeout : inf
Stop if timeout seconds are exceeded, the string "2.5 * 60**2" evaluates to 2 hours and 30 minutes
tolconditioncov : 1e14
Stop if the condition of the covariance matrix is above `tolconditioncov`
tolfacupx : 1e3
Termination when step-size increases by tolfacupx (diverges). That is, the initial step-size was chosen
far too small and better solutions were found far away from the initial solution x0
tolupsigma : 1e20
Sigma/sigma0 > tolupsigma * max(eivenvals(C)**0.5) indicates "creeping behavior" with usually minor
improvements
tolfun : 1e-11
Termination criterion: tolerance in function value, quite useful
tolfunhist : 1e-12
Termination criterion: tolerance in function value history
tolstagnation : int(100 + 100 * N**1.5 / popsize)
Termination if no improvement over tolstagnation iterations
tolx : 1e-11
Termination criterion: tolerance in x-changes
typical_x : None
Used with scaling_of_variables',
updatecovwait : None
Number of iterations without distribution update, name is subject to future changes
cmaes_verbose : 3
Verbosity e.g. of initial/final message, -1 is very quiet, -9 maximally quiet, may not be fully implemented
verb_append : 0
Initial evaluation counter, if append, do not overwrite output files
verb_disp : 100
Verbosity: display console output every verb_disp iteration
verb_filenameprefix : str
CMADataLogger.default_prefix + Output path and filenames prefix
verb_log : 1
Verbosity: write data to files every verb_log iteration, writing can be time critical on fast to
evaluate functions
verb_plot : 0
In fmin(): plot() is called every verb_plot iteration
verb_time : True
Output timings on console
vv : dict
Versatile set or dictionary for hacking purposes, value found in self.opts["vv"]
kwargs : dict
A dictionary with additional options passed to the constructor
of class ``CMAEvolutionStrategy``, see ``cma.CMAOptions`` ()
for a list of available options.
"""
if pop_size is not None:
parallelize = True
kwargs["popsize"] = pop_size
super().__init__(x0=x0, output=output, **kwargs)
self.termination = NoTermination()
self.es = None
self.cma = None
self.normalize = normalize
self.norm = None
self.sigma = sigma
self.restarts = restarts
self.restart_from_best = restart_from_best
self.incpopsize = incpopsize
self.eval_initial_x = eval_initial_x
self.noise_handler = noise_handler
self.noise_change_sigma_exponent = noise_change_sigma_exponent
self.noise_kappa_exponent = noise_kappa_exponent
self.bipop = bipop
self.options = dict(
verbose=cmaes_verbose,
verb_log=verb_log,
maxfevals=maxfevals,
tolfun=tolfun,
tolx=tolx,
**kwargs
)
self.send_array_to_yield = True
self.parallelize = parallelize
self.al = None
def _setup(self, problem, **kwargs):
xl, xu = problem.bounds()
if self.normalize:
self.norm, self.options['bounds'] = bounds_if_normalize(xl, xu)
else:
self.norm = NoNormalization()
self.options['bounds'] = [xl, xu]
seed = kwargs.get('seed', self.seed)
self.options['seed'] = seed
if isinstance(self.termination, MaximumGenerationTermination):
self.options['maxiter'] = self.termination.n_max_gen
elif isinstance(self.termination, MaximumFunctionCallTermination):
self.options['maxfevals'] = self.termination.n_max_evals
def _initialize_advance(self, **kwargs):
super()._initialize_advance(**kwargs)
kwargs = dict(
options=self.options,
parallel_objective=self.parallelize,
restarts=self.restarts,
restart_from_best=self.restart_from_best,
incpopsize=self.incpopsize,
eval_initial_x=self.eval_initial_x,
noise_handler=self.noise_handler,
noise_change_sigma_exponent=self.noise_change_sigma_exponent,
noise_kappa_exponent=self.noise_kappa_exponent,
bipop=self.bipop,
random_state=self.random_state)
x0 = self.norm.forward(self.x0.X)
self.es = my_fmin(x0, self.sigma, **kwargs)
# do this to allow the printout in the first generation
self.next_X = next(self.es)
def _infill(self):
X = np.array(self.next_X)
self.send_array_to_yield = X.ndim > 1
X = np.atleast_2d(X)
# evaluate the population
self.pop = Population.new("X", self.norm.backward(X))
return self.pop
def _advance(self, infills=None, **kwargs):
if infills is None:
self.termination.force_termination = True
else:
# set infeasible individual's objective values to np.nan - then CMAES can handle it
for ind in infills:
if not ind.feas:
ind.F[:] = np.inf
F = infills.get("f").tolist()
if not self.send_array_to_yield:
F = F[0]
try:
self.next_X = self.es.send(F)
except:
self.next_X = None
if self.next_X is None:
self.termination.force_termination = True
def _set_optimum(self):
pop = self.pop if self.opt is None else Population.merge(self.opt, self.pop)
self.opt = filter_optimum(pop, least_infeasible=True)
def __getstate__(self):
state = self.__dict__.copy()
state.pop("es", None)
return state
def __setstate__(self, state):
self.__dict__.update(state)
self.ers = None
class SimpleCMAES(LocalSearch):
def __init__(self, sigma=0.1, opts=None, normalize=True, **kwargs):
super().__init__(**kwargs)
self.termination = NoTermination()
self.es = None
self.sigma = sigma
self.normalize = normalize
self.norm = None
DEFAULTS = {"verb_disp": 0}
if opts is None:
opts = {}
for k, v in DEFAULTS.items():
if k not in kwargs:
opts[k] = v
self.opts = opts
def _setup(self, problem, **kwargs):
xl, xu = problem.bounds()
if self.normalize:
self.norm, self.opts['bounds'] = bounds_if_normalize(xl, xu)
else:
self.norm = NoNormalization()
self.opts['bounds'] = [xl, xu]
self.opts['seed'] = self.seed
def _initialize_advance(self, infills=None, **kwargs):
super()._initialize_advance(infills, **kwargs)
x = self.norm.forward(self.x0.X)
self.es = cma.CMAEvolutionStrategy(x, self.sigma, inopts=self.opts)
def _infill(self):
X = self.norm.backward(np.array(self.es.ask()))
return Population.new("X", X)
def _advance(self, infills=None, **kwargs):
X, F = infills.get("X", "F")
X = self.norm.forward(X)
self.es.tell(X, F[:, 0])
self.pop = infills
if self.es.stop():
self.termination.force_termination = True
def _set_optimum(self):
pop = self.pop if self.opt is None else Population.merge(self.opt, self.pop)
self.opt = filter_optimum(pop, least_infeasible=True)
class BIPOPCMAES(CMAES):
def __init__(self, restarts=4, **kwargs):
super().__init__(restarts=restarts, bipop=True, **kwargs)
def bounds_if_normalize(xl, xu):
norm = ZeroToOneNormalization(xl=xl, xu=xu)
_xl, _xu = np.zeros_like(xl), np.ones_like(xu)
if xl is not None:
_xl[np.isnan(xl)] = np.nan
if xu is not None:
_xu[np.isnan(xu)] = np.nan
return norm, [_xl, _xu]
parse_doc_string(CMAES.__init__)
