Source code for deap.benchmarks.tools

"""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))