"""Module containing tools that are useful when benchmarking algorithms
"""
from math import hypot, sqrt
from functools import wraps
from itertools import repeat
try:
import numpy
numpy_imported = True
except ImportError:
numpy_imported = False
try:
import scipy.spatial
scipy_imported = True
except ImportError:
scipy_imported = False
try:
# try importing the C version
from ..tools._hypervolume import hv
except ImportError:
# fallback on python version
from ..tools._hypervolume import pyhv as hv
[docs]class translate(object):
"""Decorator for evaluation functions, it translates the objective
function by *vector* which should be the same length as the individual
size. When called the decorated function should take as first argument the
individual to be evaluated. The inverse translation vector is actually
applied to the individual and the resulting list is given to the
evaluation function. Thus, the evaluation function shall not be expecting
an individual as it will receive a plain list.
This decorator adds a :func:`translate` method to the decorated function.
"""
def __init__(self, vector):
self.vector = vector
def __call__(self, func):
# wraps is used to combine stacked decorators that would add functions
@wraps(func)
def wrapper(individual, *args, **kargs):
# A subtraction is applied since the translation is applied to the
# individual and not the function
return func([v - t for v, t in zip(individual, self.vector)],
*args, **kargs)
wrapper.translate = self.translate
return wrapper
[docs] def translate(self, vector):
"""Set the current translation to *vector*. After decorating the
evaluation function, this function will be available directly from
the function object. ::
@translate([0.25, 0.5, ..., 0.1])
def evaluate(individual):
return sum(individual),
# This will cancel the translation
evaluate.translate([0.0, 0.0, ..., 0.0])
"""
self.vector = vector
[docs]class rotate(object):
"""Decorator for evaluation functions, it rotates the objective function
by *matrix* which should be a valid orthogonal NxN rotation matrix, with N
the length of an individual. When called the decorated function should
take as first argument the individual to be evaluated. The inverse
rotation matrix is actually applied to the individual and the resulting
list is given to the evaluation function. Thus, the evaluation function
shall not be expecting an individual as it will receive a plain list
(numpy.array). The multiplication is done using numpy.
This decorator adds a :func:`rotate` method to the decorated function.
.. note::
A random orthogonal matrix Q can be created via QR decomposition. ::
A = numpy.random.random((n,n))
Q, _ = numpy.linalg.qr(A)
"""
def __init__(self, matrix):
if not numpy_imported:
raise RuntimeError("Numpy is required for using the rotation "
"decorator")
# The inverse is taken since the rotation is applied to the individual
# and not the function which is the inverse
self.matrix = numpy.linalg.inv(matrix)
def __call__(self, func):
# wraps is used to combine stacked decorators that would add functions
@wraps(func)
def wrapper(individual, *args, **kargs):
return func(numpy.dot(self.matrix, individual), *args, **kargs)
wrapper.rotate = self.rotate
return wrapper
[docs] def rotate(self, matrix):
"""Set the current rotation to *matrix*. After decorating the
evaluation function, this function will be available directly from
the function object. ::
# Create a random orthogonal matrix
A = numpy.random.random((n,n))
Q, _ = numpy.linalg.qr(A)
@rotate(Q)
def evaluate(individual):
return sum(individual),
# This will reset rotation to identity
evaluate.rotate(numpy.identity(n))
"""
self.matrix = numpy.linalg.inv(matrix)
[docs]class noise(object):
"""Decorator for evaluation functions, it evaluates the objective function
and adds noise by calling the function(s) provided in the *noise*
argument. The noise functions are called without any argument, consider
using the :class:`~deap.base.Toolbox` or Python's
:func:`functools.partial` to provide any required argument. If a single
function is provided it is applied to all objectives of the evaluation
function. If a list of noise functions is provided, it must be of length
equal to the number of objectives. The noise argument also accept
:obj:`None`, which will leave the objective without noise.
This decorator adds a :func:`noise` method to the decorated
function.
"""
def __init__(self, noise):
try:
self.rand_funcs = tuple(noise)
except TypeError:
self.rand_funcs = repeat(noise)
def __call__(self, func):
# wraps is used to combine stacked decorators that would add functions
@wraps(func)
def wrapper(individual, *args, **kargs):
result = func(individual, *args, **kargs)
noisy = list()
for r, f in zip(result, self.rand_funcs):
if f is None:
noisy.append(r)
else:
noisy.append(r + f())
return tuple(noisy)
wrapper.noise = self.noise
return wrapper
[docs] def noise(self, noise):
"""Set the current noise to *noise*. After decorating the
evaluation function, this function will be available directly from
the function object. ::
prand = functools.partial(random.gauss, mu=0.0, sigma=1.0)
@noise(prand)
def evaluate(individual):
return sum(individual),
# This will remove noise from the evaluation function
evaluate.noise(None)
"""
try:
self.rand_funcs = tuple(noise)
except TypeError:
self.rand_funcs = repeat(noise)
[docs]class scale(object):
"""Decorator for evaluation functions, it scales the objective function by
*factor* which should be the same length as the individual size. When
called the decorated function should take as first argument the individual
to be evaluated. The inverse factor vector is actually applied to the
individual and the resulting list is given to the evaluation function.
Thus, the evaluation function shall not be expecting an individual as it
will receive a plain list.
This decorator adds a :func:`scale` method to the decorated function.
"""
def __init__(self, factor):
# Factor is inverted since it is applied to the individual and not the
# objective function
self.factor = tuple(1.0 / f for f in factor)
def __call__(self, func):
# wraps is used to combine stacked decorators that would add functions
@wraps(func)
def wrapper(individual, *args, **kargs):
return func([v * f for v, f in zip(individual, self.factor)],
*args, **kargs)
wrapper.scale = self.scale
return wrapper
[docs] def scale(self, factor):
"""Set the current scale to *factor*. After decorating the
evaluation function, this function will be available directly from
the function object. ::
@scale([0.25, 2.0, ..., 0.1])
def evaluate(individual):
return sum(individual),
# This will cancel the scaling
evaluate.scale([1.0, 1.0, ..., 1.0])
"""
# Factor is inverted since it is applied to the individual and not the
# objective function
self.factor = tuple(1.0 / f for f in factor)
class bound(object):
"""Decorator for crossover and mutation functions, it changes the
individuals after the modification is done to bring it back in the allowed
*bounds*. The *bounds* are functions taking individual and returning
whether of not the variable is allowed. You can provide one or multiple such
functions. In the former case, the function is used on all dimensions and
in the latter case, the number of functions must be greater or equal to
the number of dimension of the individuals.
The *type* determines how the attributes are brought back into the valid
range
This decorator adds a :func:`bound` method to the decorated function.
"""
def _clip(self, individual):
return individual
def _wrap(self, individual):
return individual
def _mirror(self, individual):
return individual
def __call__(self, func):
@wraps(func)
def wrapper(*args, **kargs):
individuals = func(*args, **kargs)
return self.bound(individuals)
wrapper.bound = self.bound
return wrapper
def __init__(self, bounds, type):
try:
self.bounds = tuple(bounds)
except TypeError:
self.bounds = repeat(bounds)
if type == "mirror":
self.bound = self._mirror
elif type == "wrap":
self.bound = self._wrap
elif type == "clip":
self.bound = self._clip
[docs]def diversity(first_front, first, last):
"""Given a Pareto front `first_front` and the two extreme points of the
optimal Pareto front, this function returns a metric of the diversity
of the front as explained in the original NSGA-II article by K. Deb.
The smaller the value is, the better the front is.
"""
df = hypot(first_front[0].fitness.values[0] - first[0],
first_front[0].fitness.values[1] - first[1])
dl = hypot(first_front[-1].fitness.values[0] - last[0],
first_front[-1].fitness.values[1] - last[1])
dt = [hypot(first.fitness.values[0] - second.fitness.values[0],
first.fitness.values[1] - second.fitness.values[1])
for first, second in zip(first_front[:-1], first_front[1:])]
if len(first_front) == 1:
return df + dl
dm = sum(dt) / len(dt)
di = sum(abs(d_i - dm) for d_i in dt)
delta = (df + dl + di) / (df + dl + len(dt) * dm)
return delta
[docs]def convergence(first_front, optimal_front):
"""Given a Pareto front `first_front` and the optimal Pareto front,
this function returns a metric of convergence
of the front as explained in the original NSGA-II article by K. Deb.
The smaller the value is, the closer the front is to the optimal one.
"""
distances = []
for ind in first_front:
distances.append(float("inf"))
for opt_ind in optimal_front:
dist = 0.
for i in range(len(opt_ind)):
dist += (ind.fitness.values[i] - opt_ind[i])**2
if dist < distances[-1]:
distances[-1] = dist
distances[-1] = sqrt(distances[-1])
return sum(distances) / len(distances)
def hypervolume(front, ref=None):
"""Return the hypervolume of a *front*. If the *ref* point is not
given, the worst value for each objective +1 is used.
:param front: The population (usually a list of undominated individuals)
on which to compute the hypervolume.
:param ref: A point of the same dimensionality as the individuals in *front*.
"""
# Must use wvalues * -1 since hypervolume use implicit minimization
wobj = numpy.array([ind.fitness.wvalues for ind in front]) * -1
if ref is None:
ref = numpy.max(wobj, axis=0) + 1
return hv.hypervolume(wobj, ref)
def igd(A, Z):
"""Inverse generational distance.
"""
if not scipy_imported:
raise ImportError("idg requires scipy module")
distances = scipy.spatial.distance.cdist(A, Z)
return numpy.average(numpy.min(distances, axis=0))