"""
This file include the following optimizer:
1. differential_evolution:
The differential evolution global optimization algorithm
https://github.com/scipy/scipy/blob/70e61dee181de23fdd8d893eaa9491100e2218d7/scipy/optimize/_differentialevolution.py
modified by:
https://github.com/DebangLi/one-pixel-attack-pytorch/blob/master/differential_evolution.py
2. Basic Adam Optimizer
"""
from __future__ import division, print_function, absolute_import
import numpy as np
from scipy.optimize import OptimizeResult, minimize
from scipy.optimize.optimize import _status_message
from scipy._lib._util import check_random_state
from scipy._lib.six import xrange, string_types
import warnings
__all__ = ['differential_evolution', 'AdamOptimizer']
_MACHEPS = np.finfo(np.float64).eps
def differential_evolution(func, bounds, args=(), strategy='best1bin',
maxiter=1000, popsize=15, tol=0.01,
mutation=(0.5, 1), recombination=0.7, seed=None,
callback=None, disp=False, polish=True,
init='latinhypercube', atol=0):
"""Finds the global minimum of a multivariate function.
Differential Evolution is stochastic in nature (does not use gradient
methods) to find the minimium, and can search large areas of candidate
space, but often requires larger numbers of function evaluations than
conventional gradient based techniques.
The algorithm is due to Storn and Price [1]_.
Parameters
----------
func : callable
The objective function to be minimized. Must be in the form
``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array
and ``args`` is a tuple of any additional fixed parameters needed to
completely specify the function.
bounds : sequence
Bounds for variables. ``(min, max)`` pairs for each element in ``x``,
defining the lower and upper bounds for the optimizing argument of
`func`. It is required to have ``len(bounds) == len(x)``.
``len(bounds)`` is used to determine the number of parameters in ``x``.
args : tuple, optional
Any additional fixed parameters needed to
completely specify the objective function.
strategy : str, optional
The differential evolution strategy to use. Should be one of:
- 'best1bin'
- 'best1exp'
- 'rand1exp'
- 'randtobest1exp'
- 'currenttobest1exp'
- 'best2exp'
- 'rand2exp'
- 'randtobest1bin'
- 'currenttobest1bin'
- 'best2bin'
- 'rand2bin'
- 'rand1bin'
The default is 'best1bin'.
maxiter : int, optional
The maximum number of generations over which the entire population is
evolved. The maximum number of function evaluations (with no polishing)
is: ``(maxiter + 1) * popsize * len(x)``
popsize : int, optional
A multiplier for setting the total population size. The population has
``popsize * len(x)`` individuals (unless the initial population is
supplied via the `init` keyword).
tol : float, optional
Relative tolerance for convergence, the solving stops when
``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``,
where and `atol` and `tol` are the absolute and relative tolerance
respectively.
mutation : float or tuple(float, float), optional
The mutation constant. In the literature this is also known as
differential weight, being denoted by F.
If specified as a float it should be in the range [0, 2].
If specified as a tuple ``(min, max)`` dithering is employed. Dithering
randomly changes the mutation constant on a generation by generation
basis. The mutation constant for that generation is taken from
``U[min, max)``. Dithering can help speed convergence significantly.
Increasing the mutation constant increases the search radius, but will
slow down convergence.
recombination : float, optional
The recombination constant, should be in the range [0, 1]. In the
literature this is also known as the crossover probability, being
denoted by CR. Increasing this value allows a larger number of mutants
to progress into the next generation, but at the risk of population
stability.
seed : int or `np.random.RandomState`, optional
If `seed` is not specified the `np.RandomState` singleton is used.
If `seed` is an int, a new `np.random.RandomState` instance is used,
seeded with seed.
If `seed` is already a `np.random.RandomState instance`, then that
`np.random.RandomState` instance is used.
Specify `seed` for repeatable minimizations.
disp : bool, optional
Display status messages
callback : callable, `callback(xk, convergence=val)`, optional
A function to follow the progress of the minimization. ``xk`` is
the current value of ``x0``. ``val`` represents the fractional
value of the population convergence. When ``val`` is greater than one
the function halts. If callback returns `True`, then the minimization
is halted (any polishing is still carried out).
polish : bool, optional
If True (default), then `scipy.optimize.minimize` with the `L-BFGS-B`
method is used to polish the best population member at the end, which
can improve the minimization slightly.
init : str or array-like, optional
Specify which type of population initialization is performed. Should be
one of:
- 'latinhypercube'
- 'random'
- array specifying the initial population. The array should have
shape ``(M, len(x))``, where len(x) is the number of parameters.
`init` is clipped to `bounds` before use.
The default is 'latinhypercube'. Latin Hypercube sampling tries to
maximize coverage of the available parameter space. 'random'
initializes the population randomly - this has the drawback that
clustering can occur, preventing the whole of parameter space being
covered. Use of an array to specify a population subset could be used,
for example, to create a tight bunch of initial guesses in an location
where the solution is known to exist, thereby reducing time for
convergence.
atol : float, optional
Absolute tolerance for convergence, the solving stops when
``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``,
where and `atol` and `tol` are the absolute and relative tolerance
respectively.
Returns
-------
res : OptimizeResult
The optimization result represented as a `OptimizeResult` object.
Important attributes are: ``x`` the solution array, ``success`` a
Boolean flag indicating if the optimizer exited successfully and
``message`` which describes the cause of the termination. See
`OptimizeResult` for a description of other attributes. If `polish`
was employed, and a lower minimum was obtained by the polishing, then
OptimizeResult also contains the ``jac`` attribute.
Notes
-----
Differential evolution is a stochastic population based method that is
useful for global optimization problems. At each pass through the population
the algorithm mutates each candidate solution by mixing with other candidate
solutions to create a trial candidate. There are several strategies [2]_ for
creating trial candidates, which suit some problems more than others. The
'best1bin' strategy is a good starting point for many systems. In this
strategy two members of the population are randomly chosen. Their difference
is used to mutate the best member (the `best` in `best1bin`), :math:`b_0`,
so far:
.. math::
b' = b_0 + mutation * (population[rand0] - population[rand1])
A trial vector is then constructed. Starting with a randomly chosen 'i'th
parameter the trial is sequentially filled (in modulo) with parameters from
`b'` or the original candidate. The choice of whether to use `b'` or the
original candidate is made with a binomial distribution (the 'bin' in
'best1bin') - a random number in [0, 1) is generated. If this number is
less than the `recombination` constant then the parameter is loaded from
`b'`, otherwise it is loaded from the original candidate. The final
parameter is always loaded from `b'`. Once the trial candidate is built
its fitness is assessed. If the trial is better than the original candidate
then it takes its place. If it is also better than the best overall
candidate it also replaces that.
To improve your chances of finding a global minimum use higher `popsize`
values, with higher `mutation` and (dithering), but lower `recombination`
values. This has the effect of widening the search radius, but slowing
convergence.
.. versionadded:: 0.15.0
Examples
--------
Let us consider the problem of minimizing the Rosenbrock function. This
function is implemented in `rosen` in `scipy.optimize`.
>>> from scipy.optimize import rosen, differential_evolution
>>> bounds = [(0,2), (0, 2), (0, 2), (0, 2), (0, 2)]
>>> result = differential_evolution(rosen, bounds)
>>> result.x, result.fun
(array([1., 1., 1., 1., 1.]), 1.9216496320061384e-19)
Next find the minimum of the Ackley function
(http://en.wikipedia.org/wiki/Test_functions_for_optimization).
>>> from scipy.optimize import differential_evolution
>>> import numpy as np
>>> def ackley(x):
... arg1 = -0.2 * np.sqrt(0.5 * (x[0] ** 2 + x[1] ** 2))
... arg2 = 0.5 * (np.cos(2. * np.pi * x[0]) + np.cos(2. * np.pi * x[1]))
... return -20. * np.exp(arg1) - np.exp(arg2) + 20. + np.e
>>> bounds = [(-5, 5), (-5, 5)]
>>> result = differential_evolution(ackley, bounds)
>>> result.x, result.fun
(array([ 0., 0.]), 4.4408920985006262e-16)
References
----------
.. [1] Storn, R and Price, K, Differential Evolution - a Simple and
Efficient Heuristic for Global Optimization over Continuous Spaces,
Journal of Global Optimization, 1997, 11, 341 - 359.
.. [2] http://www1.icsi.berkeley.edu/~storn/code.html
.. [3] http://en.wikipedia.org/wiki/Differential_evolution
"""
solver = DifferentialEvolutionSolver(func, bounds, args=args,
strategy=strategy, maxiter=maxiter,
popsize=popsize, tol=tol,
mutation=mutation,
recombination=recombination,
seed=seed, polish=polish,
callback=callback,
disp=disp, init=init, atol=atol)
return solver.solve()
class DifferentialEvolutionSolver(object):
"""This class implements the differential evolution solver
Parameters
----------
func : callable
The objective function to be minimized. Must be in the form
``f(x, *args)``, where ``x`` is the argument in the form of a 1-D array
and ``args`` is a tuple of any additional fixed parameters needed to
completely specify the function.
bounds : sequence
Bounds for variables. ``(min, max)`` pairs for each element in ``x``,
defining the lower and upper bounds for the optimizing argument of
`func`. It is required to have ``len(bounds) == len(x)``.
``len(bounds)`` is used to determine the number of parameters in ``x``.
args : tuple, optional
Any additional fixed parameters needed to
completely specify the objective function.
strategy : str, optional
The differential evolution strategy to use. Should be one of:
- 'best1bin'
- 'best1exp'
- 'rand1exp'
- 'randtobest1exp'
- 'currenttobest1exp'
- 'best2exp'
- 'rand2exp'
- 'randtobest1bin'
- 'currenttobest1bin'
- 'best2bin'
- 'rand2bin'
- 'rand1bin'
The default is 'best1bin'
maxiter : int, optional
The maximum number of generations over which the entire population is
evolved. The maximum number of function evaluations (with no polishing)
is: ``(maxiter + 1) * popsize * len(x)``
popsize : int, optional
A multiplier for setting the total population size. The population has
``popsize * len(x)`` individuals (unless the initial population is
supplied via the `init` keyword).
tol : float, optional
Relative tolerance for convergence, the solving stops when
``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``,
where and `atol` and `tol` are the absolute and relative tolerance
respectively.
mutation : float or tuple(float, float), optional
The mutation constant. In the literature this is also known as
differential weight, being denoted by F.
If specified as a float it should be in the range [0, 2].
If specified as a tuple ``(min, max)`` dithering is employed. Dithering
randomly changes the mutation constant on a generation by generation
basis. The mutation constant for that generation is taken from
U[min, max). Dithering can help speed convergence significantly.
Increasing the mutation constant increases the search radius, but will
slow down convergence.
recombination : float, optional
The recombination constant, should be in the range [0, 1]. In the
literature this is also known as the crossover probability, being
denoted by CR. Increasing this value allows a larger number of mutants
to progress into the next generation, but at the risk of population
stability.
seed : int or `np.random.RandomState`, optional
If `seed` is not specified the `np.random.RandomState` singleton is
used.
If `seed` is an int, a new `np.random.RandomState` instance is used,
seeded with `seed`.
If `seed` is already a `np.random.RandomState` instance, then that
`np.random.RandomState` instance is used.
Specify `seed` for repeatable minimizations.
disp : bool, optional
Display status messages
callback : callable, `callback(xk, convergence=val)`, optional
A function to follow the progress of the minimization. ``xk`` is
the current value of ``x0``. ``val`` represents the fractional
value of the population convergence. When ``val`` is greater than one
the function halts. If callback returns `True`, then the minimization
is halted (any polishing is still carried out).
polish : bool, optional
If True, then `scipy.optimize.minimize` with the `L-BFGS-B` method
is used to polish the best population member at the end. This requires
a few more function evaluations.
maxfun : int, optional
Set the maximum number of function evaluations. However, it probably
makes more sense to set `maxiter` instead.
init : str or array-like, optional
Specify which type of population initialization is performed. Should be
one of:
- 'latinhypercube'
- 'random'
- array specifying the initial population. The array should have
shape ``(M, len(x))``, where len(x) is the number of parameters.
`init` is clipped to `bounds` before use.
The default is 'latinhypercube'. Latin Hypercube sampling tries to
maximize coverage of the available parameter space. 'random'
initializes the population randomly - this has the drawback that
clustering can occur, preventing the whole of parameter space being
covered. Use of an array to specify a population could be used, for
example, to create a tight bunch of initial guesses in an location
where the solution is known to exist, thereby reducing time for
convergence.
atol : float, optional
Absolute tolerance for convergence, the solving stops when
``np.std(pop) <= atol + tol * np.abs(np.mean(population_energies))``,
where and `atol` and `tol` are the absolute and relative tolerance
respectively.
"""
# Dispatch of mutation strategy method (binomial or exponential).
_binomial = {'best1bin': '_best1',
'randtobest1bin': '_randtobest1',
'currenttobest1bin': '_currenttobest1',
'best2bin': '_best2',
'rand2bin': '_rand2',
'rand1bin': '_rand1'}
_exponential = {'best1exp': '_best1',
'rand1exp': '_rand1',
'randtobest1exp': '_randtobest1',
'currenttobest1exp': '_currenttobest1',
'best2exp': '_best2',
'rand2exp': '_rand2'}
__init_error_msg = ("The population initialization method must be one of "
"'latinhypercube' or 'random', or an array of shape "
"(M, N) where N is the number of parameters and M>5")
def __init__(self, func, bounds, args=(),
strategy='best1bin', maxiter=1000, popsize=15,
tol=0.01, mutation=(0.5, 1), recombination=0.7, seed=None,
maxfun=np.inf, callback=None, disp=False, polish=True,
init='latinhypercube', atol=0):
if strategy in self._binomial:
self.mutation_func = getattr(self, self._binomial[strategy])
elif strategy in self._exponential:
self.mutation_func = getattr(self, self._exponential[strategy])
else:
raise ValueError("Please select a valid mutation strategy")
self.strategy = strategy
self.callback = callback
self.polish = polish
# relative and absolute tolerances for convergence
self.tol, self.atol = tol, atol
# Mutation constant should be in [0, 2). If specified as a sequence
# then dithering is performed.
self.scale = mutation
if (not np.all(np.isfinite(mutation)) or
np.any(np.array(mutation) >= 2) or
np.any(np.array(mutation) < 0)):
raise ValueError('The mutation constant must be a float in '
'U[0, 2), or specified as a tuple(min, max)'
' where min < max and min, max are in U[0, 2).')
self.dither = None
if hasattr(mutation, '__iter__') and len(mutation) > 1:
self.dither = [mutation[0], mutation[1]]
self.dither.sort()
self.cross_over_probability = recombination
self.func = func
self.args = args
# convert tuple of lower and upper bounds to limits
# [(low_0, high_0), ..., (low_n, high_n]
# -> [[low_0, ..., low_n], [high_0, ..., high_n]]
self.limits = np.array(bounds, dtype='float').T
if (np.size(self.limits, 0) != 2 or not
np.all(np.isfinite(self.limits))):
raise ValueError('bounds should be a sequence containing '
'real valued (min, max) pairs for each value'
' in x')
if maxiter is None: # the default used to be None
maxiter = 1000
self.maxiter = maxiter
if maxfun is None: # the default used to be None
maxfun = np.inf
self.maxfun = maxfun
# population is scaled to between [0, 1].
# We have to scale between parameter <-> population
# save these arguments for _scale_parameter and
# _unscale_parameter. This is an optimization
self.__scale_arg1 = 0.5 * (self.limits[0] + self.limits[1])
self.__scale_arg2 = np.fabs(self.limits[0] - self.limits[1])
self.parameter_count = np.size(self.limits, 1)
self.random_number_generator = check_random_state(seed)
# default population initialization is a latin hypercube design, but
# there are other population initializations possible.
# the minimum is 5 because 'best2bin' requires a population that's at
# least 5 long
self.num_population_members = max(5, popsize * self.parameter_count)
self.population_shape = (self.num_population_members,
self.parameter_count)
self._nfev = 0
if isinstance(init, string_types):
if init == 'latinhypercube':
self.init_population_lhs()
elif init == 'random':
self.init_population_random()
else:
raise ValueError(self.__init_error_msg)
else:
self.init_population_array(init)
self.disp = disp
def init_population_lhs(self):
"""
Initializes the population with Latin Hypercube Sampling.
Latin Hypercube Sampling ensures that each parameter is uniformly
sampled over its range.
"""
rng = self.random_number_generator
# Each parameter range needs to be sampled uniformly. The scaled
# parameter range ([0, 1)) needs to be split into
# `self.num_population_members` segments, each of which has the following
# size:
segsize = 1.0 / self.num_population_members
# Within each segment we sample from a uniform random distribution.
# We need to do this sampling for each parameter.
samples = (segsize * rng.random_sample(self.population_shape)
# Offset each segment to cover the entire parameter range [0, 1)
+ np.linspace(0., 1., self.num_population_members,
endpoint=False)[:, np.newaxis])
# Create an array for population of candidate solutions.
self.population = np.zeros_like(samples)
# Initialize population of candidate solutions by permutation of the
# random samples.
for j in range(self.parameter_count):
order = rng.permutation(range(self.num_population_members))
self.population[:, j] = samples[order, j]
# reset population energies
self.population_energies = (np.ones(self.num_population_members) *
np.inf)
# reset number of function evaluations counter
self._nfev = 0
def init_population_random(self):
"""
Initialises the population at random. This type of initialization
can possess clustering, Latin Hypercube sampling is generally better.
"""
rng = self.random_number_generator
self.population = rng.random_sample(self.population_shape)
# reset population energies
self.population_energies = (np.ones(self.num_population_members) *
np.inf)
# reset number of function evaluations counter
self._nfev = 0
def init_population_array(self, init):
"""
Initialises the population with a user specified population.
Parameters
----------
init : np.ndarray
Array specifying subset of the initial population. The array should
have shape (M, len(x)), where len(x) is the number of parameters.
The population is clipped to the lower and upper `bounds`.
"""
# make sure you're using a float array
popn = np.asfarray(init)
if (np.size(popn, 0) < 5 or
popn.shape[1] != self.parameter_count or
len(popn.shape) != 2):
raise ValueError("The population supplied needs to have shape"
" (M, len(x)), where M > 4.")
# scale values and clip to bounds, assigning to population
self.population = np.clip(self._unscale_parameters(popn), 0, 1)
self.num_population_members = np.size(self.population, 0)
self.population_shape = (self.num_population_members,
self.parameter_count)
# reset population energies
self.population_energies = (np.ones(self.num_population_members) *
np.inf)
# reset number of function evaluations counter
self._nfev = 0
@property
def x(self):
"""
The best solution from the solver
Returns
-------
x : ndarray
The best solution from the solver.
"""
return self._scale_parameters(self.population[0])
@property
def convergence(self):
"""
The standard deviation of the population energies divided by their
mean.
"""
return (np.std(self.population_energies) /
np.abs(np.mean(self.population_energies) + _MACHEPS))
def solve(self):
"""
Runs the DifferentialEvolutionSolver.
Returns
-------
res : OptimizeResult
The optimization result represented as a ``OptimizeResult`` object.
Important attributes are: ``x`` the solution array, ``success`` a
Boolean flag indicating if the optimizer exited successfully and
``message`` which describes the cause of the termination. See
`OptimizeResult` for a description of other attributes. If `polish`
was employed, and a lower minimum was obtained by the polishing,
then OptimizeResult also contains the ``jac`` attribute.
"""
nit, warning_flag = 0, False
status_message = _status_message['success']
# The population may have just been initialized (all entries are
# np.inf). If it has you have to calculate the initial energies.
# Although this is also done in the evolve generator it's possible
# that someone can set maxiter=0, at which point we still want the
# initial energies to be calculated (the following loop isn't run).
if np.all(np.isinf(self.population_energies)):
self._calculate_population_energies()
# do the optimisation.
for nit in xrange(1, self.maxiter + 1):
# evolve the population by a generation
try:
next(self)
except StopIteration:
warning_flag = True
status_message = _status_message['maxfev']
break
if self.disp:
print("differential_evolution step %d: f(x)= %g"
% (nit,
self.population_energies[0]))
# should the solver terminate?
convergence = self.convergence
if (self.callback and
self.callback(self._scale_parameters(self.population[0]),
convergence=self.tol / convergence) is True):
warning_flag = True
status_message = ('callback function requested stop early '
'by returning True')
break
intol = (np.std(self.population_energies) <=
self.atol +
self.tol * np.abs(np.mean(self.population_energies)))
if warning_flag or intol:
break
else:
status_message = _status_message['maxiter']
warning_flag = True
DE_result = OptimizeResult(
x=self.x,
fun=self.population_energies[0],
nfev=self._nfev,
nit=nit,
message=status_message,
success=(warning_flag is not True))
if self.polish:
result = minimize(self.func,
np.copy(DE_result.x),
method='L-BFGS-B',
bounds=self.limits.T,
args=self.args)
self._nfev += result.nfev
DE_result.nfev = self._nfev
if result.fun < DE_result.fun:
DE_result.fun = result.fun
DE_result.x = result.x
DE_result.jac = result.jac
# to keep internal state consistent
self.population_energies[0] = result.fun
self.population[0] = self._unscale_parameters(result.x)
return DE_result
def _calculate_population_energies(self):
"""
Calculate the energies of all the population members at the same time.
Puts the best member in first place. Useful if the population has just
been initialised.
"""
##############
## CHANGES: self.func operates on the entire parameters array
##############
itersize = max(0, min(len(self.population), self.maxfun - self._nfev + 1))
candidates = self.population[:itersize]
parameters = np.array([self._scale_parameters(c) for c in candidates]) # TODO: vectorize
energies = self.func(parameters, *self.args)
self.population_energies = energies
self._nfev += itersize
# for index, candidate in enumerate(self.population):
# if self._nfev > self.maxfun:
# break
# parameters = self._scale_parameters(candidate)
# self.population_energies[index] = self.func(parameters,
# *self.args)
# self._nfev += 1
##############
##############
minval = np.argmin(self.population_energies)
# put the lowest energy into the best solution position.
lowest_energy = self.population_energies[minval]
self.population_energies[minval] = self.population_energies[0]
self.population_energies[0] = lowest_energy
self.population[[0, minval], :] = self.population[[minval, 0], :]
def __iter__(self):
return self
def __next__(self):
"""
Evolve the population by a single generation
Returns
-------
x : ndarray
The best solution from the solver.
fun : float
Value of objective function obtained from the best solution.
"""
# the population may have just been initialized (all entries are
# np.inf). If it has you have to calculate the initial energies
if np.all(np.isinf(self.population_energies)):
self._calculate_population_energies()
if self.dither is not None:
self.scale = (self.random_number_generator.rand()
* (self.dither[1] - self.dither[0]) + self.dither[0])
##############
## CHANGES: self.func operates on the entire parameters array
##############
itersize = max(0, min(self.num_population_members, self.maxfun - self._nfev + 1))
trials = np.array([self._mutate(c) for c in range(itersize)]) # TODO: vectorize
for trial in trials: self._ensure_constraint(trial)
parameters = np.array([self._scale_parameters(trial) for trial in trials])
energies = self.func(parameters, *self.args)
self._nfev += itersize
for candidate,(energy,trial) in enumerate(zip(energies, trials)):
# if the energy of the trial candidate is lower than the
# original population member then replace it
if energy < self.population_energies[candidate]:
self.population[candidate] = trial
self.population_energies[candidate] = energy
# if the trial candidate also has a lower energy than the
# best solution then replace that as well
if energy < self.population_energies[0]:
self.population_energies[0] = energy
self.population[0] = trial
# for candidate in range(self.num_population_members):
# if self._nfev > self.maxfun:
# raise StopIteration
# # create a trial solution
# trial = self._mutate(candidate)
# # ensuring that it's in the range [0, 1)
# self._ensure_constraint(trial)
# # scale from [0, 1) to the actual parameter value
# parameters = self._scale_parameters(trial)
# # determine the energy of the objective function
# energy = self.func(parameters, *self.args)
# self._nfev += 1
# # if the energy of the trial candidate is lower than the
# # original population member then replace it
# if energy < self.population_energies[candidate]:
# self.population[candidate] = trial
# self.population_energies[candidate] = energy
# # if the trial candidate also has a lower energy than the
# # best solution then replace that as well
# if energy < self.population_energies[0]:
# self.population_energies[0] = energy
# self.population[0] = trial
##############
##############
return self.x, self.population_energies[0]
def next(self):
"""
Evolve the population by a single generation
Returns
-------
x : ndarray
The best solution from the solver.
fun : float
Value of objective function obtained from the best solution.
"""
# next() is required for compatibility with Python2.7.
return self.__next__()
def _scale_parameters(self, trial):
"""
scale from a number between 0 and 1 to parameters.
"""
return self.__scale_arg1 + (trial - 0.5) * self.__scale_arg2
def _unscale_parameters(self, parameters):
"""
scale from parameters to a number between 0 and 1.
"""
return (parameters - self.__scale_arg1) / self.__scale_arg2 + 0.5
def _ensure_constraint(self, trial):
"""
make sure the parameters lie between the limits
"""
for index in np.where((trial < 0) | (trial > 1))[0]:
trial[index] = self.random_number_generator.rand()
def _mutate(self, candidate):
"""
create a trial vector based on a mutation strategy
"""
trial = np.copy(self.population[candidate])
rng = self.random_number_generator
fill_point = rng.randint(0, self.parameter_count)
if self.strategy in ['currenttobest1exp', 'currenttobest1bin']:
bprime = self.mutation_func(candidate,
self._select_samples(candidate, 5))
else:
bprime = self.mutation_func(self._select_samples(candidate, 5))
if self.strategy in self._binomial:
crossovers = rng.rand(self.parameter_count)
crossovers = crossovers < self.cross_over_probability
# the last one is always from the bprime vector for binomial
# If you fill in modulo with a loop you have to set the last one to
# true. If you don't use a loop then you can have any random entry
# be True.
crossovers[fill_point] = True
trial = np.where(crossovers, bprime, trial)
return trial
elif self.strategy in self._exponential:
i = 0
while (i < self.parameter_count and
rng.rand() < self.cross_over_probability):
trial[fill_point] = bprime[fill_point]
fill_point = (fill_point + 1) % self.parameter_count
i += 1
return trial
def _best1(self, samples):
"""
best1bin, best1exp
"""
r0, r1 = samples[:2]
return (self.population[0] + self.scale *
(self.population[r0] - self.population[r1]))
def _rand1(self, samples):
"""
rand1bin, rand1exp
"""
r0, r1, r2 = samples[:3]
return (self.population[r0] + self.scale *
(self.population[r1] - self.population[r2]))
def _randtobest1(self, samples):
"""
randtobest1bin, randtobest1exp
"""
r0, r1, r2 = samples[:3]
bprime = np.copy(self.population[r0])
bprime += self.scale * (self.population[0] - bprime)
bprime += self.scale * (self.population[r1] -
self.population[r2])
return bprime
def _currenttobest1(self, candidate, samples):
"""
currenttobest1bin, currenttobest1exp
"""
r0, r1 = samples[:2]
bprime = (self.population[candidate] + self.scale *
(self.population[0] - self.population[candidate] +
self.population[r0] - self.population[r1]))
return bprime
def _best2(self, samples):
"""
best2bin, best2exp
"""
r0, r1, r2, r3 = samples[:4]
bprime = (self.population[0] + self.scale *
(self.population[r0] + self.population[r1] -
self.population[r2] - self.population[r3]))
return bprime
def _rand2(self, samples):
"""
rand2bin, rand2exp
"""
r0, r1, r2, r3, r4 = samples
bprime = (self.population[r0] + self.scale *
(self.population[r1] + self.population[r2] -
self.population[r3] - self.population[r4]))
return bprime
def _select_samples(self, candidate, number_samples):
"""
obtain random integers from range(self.num_population_members),
without replacement. You can't have the original candidate either.
"""
idxs = list(range(self.num_population_members))
idxs.remove(candidate)
self.random_number_generator.shuffle(idxs)
idxs = idxs[:number_samples]
return idxs
class AdamOptimizer:
"""Basic Adam optimizer implementation that can minimize w.r.t.
a single variable.
Parameters
----------
shape : tuple
shape of the variable w.r.t. which the loss should be minimized
"""
#TODO Add reference or rewrite the function.
def __init__(self, shape):
self.m = np.zeros(shape)
self.v = np.zeros(shape)
self.t = 0
def __call__(self, gradient, learning_rate, beta1=0.9, beta2=0.999, epsilon=1e-8):
"""Updates internal parameters of the optimizer and returns
the change that should be applied to the variable.
Parameters
----------
gradient : `np.ndarray`
the gradient of the loss w.r.t. to the variable
learning_rate: float
the learning rate in the current iteration
beta1: float
decay rate for calculating the exponentially
decaying average of past gradients
beta2: float
decay rate for calculating the exponentially
decaying average of past squared gradients
epsilon: float
small value to avoid division by zero
"""
self.t += 1
self.m = beta1 * self.m + (1 - beta1) * gradient
self.v = beta2 * self.v + (1 - beta2) * gradient ** 2
bias_correction_1 = 1 - beta1 ** self.t
bias_correction_2 = 1 - beta2 ** self.t
m_hat = self.m / bias_correction_1
v_hat = self.v / bias_correction_2
return -learning_rate * m_hat / (np.sqrt(v_hat) + epsilon)
