/usr/lib/python3/dist-packages/deap/benchmarks/tools.py is in python3-deap 1.0.2.post2-2.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 | """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
except ImportError:
numpy = False
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
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
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:
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
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)
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
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)
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 aplied 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
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 aplied 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
wheter 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 = itertools.repeat(bounds)
if type == "mirror":
self.bound = self._mirror
elif type == "wrap":
self.bound = self._wrap
elif type == "clip":
self.bound = self._clip
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
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)
|