# This file is part of DEAP.
#
# DEAP is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as
# published by the Free Software Foundation, either version 3 of
# the License, or (at your option) any later version.
#
# DEAP is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with DEAP. If not, see .
"""
Re-implementation of the `Moving Peaks Benchmark
`_ by Jurgen Branke. With the
addition of the fluctuating number of peaks presented in *du Plessis and
Engelbrecht, 2013, Self-Adaptive Environment with Fluctuating Number of
Optima.*
"""
import math
import itertools
import random
from collections import Sequence
def cone(individual, position, height, width):
"""The cone peak function to be used with scenario 2 and 3.
:math:`f(\mathbf{x}) = h - w \sqrt{\sum_{i=1}^N (x_i - p_i)^2}`
"""
value = 0.0
for x, p in zip(individual, position):
value += (x - p)**2
return height - width * math.sqrt(value)
def sphere(individual, position, height, width):
value = 0.0
for x, p in zip(individual, position):
value += (x - p)**2
return height * value
def function1(individual, position, height, width):
"""The function1 peak function to be used with scenario 1.
:math:`f(\mathbf{x}) = \\frac{h}{1 + w \sqrt{\sum_{i=1}^N (x_i - p_i)^2}}`
"""
value = 0.0
for x, p in zip(individual, position):
value += (x - p)**2
return height / (1 + width * value)
class MovingPeaks:
"""The Moving Peaks Benchmark is a fitness function changing over time. It
consists of a number of peaks, changing in height, width and location. The
peaks function is given by *pfunc*, wich is either a function object or a
list of function objects (the default is :func:`function1`). The number of
peaks is determined by *npeaks* (which defaults to 5). This parameter can
be either a integer or a sequence. If it is set to an integer the number
of peaks won't change, while if set to a sequence of 3 elements, the
number of peaks will fluctuate between the first and third element of that
sequence, the second element is the inital number of peaks. When
fluctuating the number of peaks, the parameter *number_severity* must be
included, it represents the number of peak fraction that is allowed to
change. The dimensionality of the search domain is *dim*. A basis function
*bfunc* can also be given to act as static landscape (the default is no
basis function). The argument *random* serves to grant an independent
random number generator to the moving peaks so that the evolution is not
influenced by number drawn by this object (the default uses random
functions from the Python module :mod:`random`). Various other keyword
parameters listed in the table below are required to setup the benchmark,
default parameters are based on scenario 1 of this benchmark.
=================== ============================= =================== =================== ======================================================================================================================
Parameter :data:`SCENARIO_1` (Default) :data:`SCENARIO_2` :data:`SCENARIO_3` Details
=================== ============================= =================== =================== ======================================================================================================================
``pfunc`` :func:`function1` :func:`cone` :func:`cone` The peak function or a list of peak function.
``npeaks`` 5 10 50 Number of peaks. If an integer, the number of peaks won't change, if a sequence it will fluctuate [min, current, max].
``bfunc`` :obj:`None` :obj:`None` ``lambda x: 10`` Basis static function.
``min_coord`` 0.0 0.0 0.0 Minimum coordinate for the centre of the peaks.
``max_coord`` 100.0 100.0 100.0 Maximum coordinate for the centre of the peaks.
``min_height`` 30.0 30.0 30.0 Minimum height of the peaks.
``max_height`` 70.0 70.0 70.0 Maximum height of the peaks.
``uniform_height`` 50.0 50.0 0 Starting height for all peaks, if ``uniform_height <= 0`` the initial height is set randomly for each peak.
``min_width`` 0.0001 1.0 1.0 Minimum width of the peaks.
``max_width`` 0.2 12.0 12.0 Maximum width of the peaks
``uniform_width`` 0.1 0 0 Starting width for all peaks, if ``uniform_width <= 0`` the initial width is set randomly for each peak.
``lambda_`` 0.0 0.5 0.5 Correlation between changes.
``move_severity`` 1.0 1.5 1.0 The distance a single peak moves when peaks change.
``height_severity`` 7.0 7.0 1.0 The standard deviation of the change made to the height of a peak when peaks change.
``width_severity`` 0.01 1.0 0.5 The standard deviation of the change made to the width of a peak when peaks change.
``period`` 5000 5000 1000 Period between two changes.
=================== ============================= =================== =================== ======================================================================================================================
Dictionnaries :data:`SCENARIO_1`, :data:`SCENARIO_2` and
:data:`SCENARIO_3` of this module define the defaults for these
parameters. The scenario 3 requires a constant basis function
which can be given as a lambda function ``lambda x: constant``.
The following shows an example of scenario 1 with non uniform heights and
widths.
.. plot:: code/benchmarks/movingsc1.py
:width: 67 %
"""
def __init__(self, dim, random=random, **kargs):
# Scenario 1 is the default
sc = SCENARIO_1.copy()
sc.update(kargs)
pfunc = sc.get("pfunc")
npeaks = sc.get("npeaks")
self.dim = dim
self.minpeaks, self.maxpeaks = None, None
if hasattr(npeaks, "__getitem__"):
self.minpeaks, npeaks, self.maxpeaks = npeaks
self.number_severity = sc.get("number_severity")
try:
if len(pfunc) == npeaks:
self.peaks_function = pfunc
else:
self.peaks_function = self.random.sample(pfunc, npeaks)
self.pfunc_pool = tuple(pfunc)
except TypeError:
self.peaks_function = list(itertools.repeat(pfunc, npeaks))
self.pfunc_pool = (pfunc,)
self.random = random
self.basis_function = sc.get("bfunc")
self.min_coord = sc.get("min_coord")
self.max_coord = sc.get("max_coord")
self.min_height = sc.get("min_height")
self.max_height = sc.get("max_height")
uniform_height = sc.get("uniform_height")
self.min_width = sc.get("min_width")
self.max_width = sc.get("max_width")
uniform_width = sc.get("uniform_width")
self.lambda_ = sc.get("lambda_")
self.move_severity = sc.get("move_severity")
self.height_severity = sc.get("height_severity")
self.width_severity = sc.get("width_severity")
self.peaks_position = [[self.random.uniform(self.min_coord, self.max_coord) for _ in range(dim)] for _ in range(npeaks)]
if uniform_height != 0:
self.peaks_height = [uniform_height for _ in range(npeaks)]
else:
self.peaks_height = [self.random.uniform(self.min_height, self.max_height) for _ in range(npeaks)]
if uniform_width != 0:
self.peaks_width = [uniform_width for _ in range(npeaks)]
else:
self.peaks_width = [self.random.uniform(self.min_width, self.max_width) for _ in range(npeaks)]
self.last_change_vector = [[self.random.random() - 0.5 for _ in range(dim)] for _ in range(npeaks)]
self.period = sc.get("period")
# Used by the Offline Error calculation
self._optimum = None
self._error = None
self._offline_error = 0
# Also used for auto change
self.nevals = 0
def globalMaximum(self):
"""Returns the global maximum value and position."""
# The global maximum is at one peak's position
potential_max = list()
for func, pos, height, width in zip(self.peaks_function,
self.peaks_position,
self.peaks_height,
self.peaks_width):
potential_max.append((func(pos, pos, height, width), pos))
return max(potential_max)
def maximums(self):
"""Returns all visible maximums value and position sorted with the
global maximum first.
"""
# The maximums are at the peaks position but might be swallowed by
# other peaks
maximums = list()
for func, pos, height, width in zip(self.peaks_function,
self.peaks_position,
self.peaks_height,
self.peaks_width):
val = func(pos, pos, height, width)
if val >= self.__call__(pos, count=False)[0]:
maximums.append((val, pos))
return sorted(maximums, reverse=True)
def __call__(self, individual, count=True):
possible_values = []
for func, pos, height, width in zip(self.peaks_function,
self.peaks_position,
self.peaks_height,
self.peaks_width):
possible_values.append(func(individual, pos, height, width))
if self.basis_function:
possible_values.append(self.basis_function(individual))
fitness = max(possible_values)
if count:
# Compute the offline error
self.nevals += 1
if self._optimum is None:
self._optimum = self.globalMaximum()[0]
self._error = abs(fitness - self._optimum)
self._error = min(self._error, abs(fitness - self._optimum))
self._offline_error += self._error
# We exausted the number of evaluation, change peaks for the next one.
if self.period > 0 and self.nevals % self.period == 0:
self.changePeaks()
return fitness,
def offlineError(self):
return self._offline_error / self.nevals
def currentError(self):
return self._error
def changePeaks(self):
"""Order the peaks to change position, height, width and number."""
# Change the number of peaks
if self.minpeaks is not None and self.maxpeaks is not None:
npeaks = len(self.peaks_function)
u = self.random.random()
r = self.maxpeaks - self.minpeaks
if u < 0.5:
# Remove n peaks or less depending on the minimum number of peaks
u = self.random.random()
n = min(npeaks - self.minpeaks, int(round(r * u * self.number_severity)))
for i in range(n):
idx = self.random.randrange(len(self.peaks_function))
self.peaks_function.pop(idx)
self.peaks_position.pop(idx)
self.peaks_height.pop(idx)
self.peaks_width.pop(idx)
self.last_change_vector.pop(idx)
else:
# Add n peaks or less depending on the maximum number of peaks
u = self.random.random()
n = min(self.maxpeaks - npeaks, int(round(r * u * self.number_severity)))
for i in range(n):
self.peaks_function.append(self.random.choice(self.pfunc_pool))
self.peaks_position.append([self.random.uniform(self.min_coord, self.max_coord) for _ in range(self.dim)])
self.peaks_height.append(self.random.uniform(self.min_height, self.max_height))
self.peaks_width.append(self.random.uniform(self.min_width, self.max_width))
self.last_change_vector.append([self.random.random() - 0.5 for _ in range(self.dim)])
for i in range(len(self.peaks_function)):
# Change peak position
shift = [self.random.random() - 0.5 for _ in range(len(self.peaks_position[i]))]
shift_length = sum(s**2 for s in shift)
shift_length = self.move_severity / math.sqrt(shift_length) if shift_length > 0 else 0
shift = [shift_length * (1.0 - self.lambda_) * s \
+ self.lambda_ * c for s, c in zip(shift, self.last_change_vector[i])]
shift_length = sum(s**2 for s in shift)
shift_length = self.move_severity / math.sqrt(shift_length) if shift_length > 0 else 0
shift = [s*shift_length for s in shift]
new_position = []
final_shift = []
for pp, s in zip(self.peaks_position[i], shift):
new_coord = pp + s
if new_coord < self.min_coord:
new_position.append(2.0 * self.min_coord - pp - s)
final_shift.append(-1.0 * s)
elif new_coord > self.max_coord:
new_position.append(2.0 * self.max_coord - pp - s)
final_shift.append(-1.0 * s)
else:
new_position.append(new_coord)
final_shift.append(s)
self.peaks_position[i] = new_position
self.last_change_vector[i] = final_shift
# Change peak height
change = self.random.gauss(0, 1) * self.height_severity
new_value = change + self.peaks_height[i]
if new_value < self.min_height:
self.peaks_height[i] = 2.0 * self.min_height - self.peaks_height[i] - change
elif new_value > self.max_height:
self.peaks_height[i] = 2.0 * self.max_height - self.peaks_height[i] - change
else:
self.peaks_height[i] = new_value
# Change peak width
change = self.random.gauss(0, 1) * self.width_severity
new_value = change + self.peaks_width[i]
if new_value < self.min_width:
self.peaks_width[i] = 2.0 * self.min_width - self.peaks_width[i] - change
elif new_value > self.max_width:
self.peaks_width[i] = 2.0 * self.max_width - self.peaks_width[i] - change
else:
self.peaks_width[i] = new_value
self._optimum = None
SCENARIO_1 = {"pfunc" : function1,
"npeaks" : 5,
"bfunc": None,
"min_coord": 0.0,
"max_coord": 100.0,
"min_height": 30.0,
"max_height": 70.0,
"uniform_height": 50.0,
"min_width": 0.0001,
"max_width": 0.2,
"uniform_width": 0.1,
"lambda_": 0.0,
"move_severity": 1.0,
"height_severity": 7.0,
"width_severity": 0.01,
"period": 5000}
SCENARIO_2 = {"pfunc" : cone,
"npeaks" : 10,
"bfunc" : None,
"min_coord": 0.0,
"max_coord": 100.0,
"min_height": 30.0,
"max_height": 70.0,
"uniform_height": 50.0,
"min_width": 1.0,
"max_width": 12.0,
"uniform_width": 0,
"lambda_": 0.5,
"move_severity": 1.0,
"height_severity": 7.0,
"width_severity": 1.0,
"period": 5000}
SCENARIO_3 = {"pfunc" : cone,
"npeaks" : 50,
"bfunc" : lambda x: 10,
"min_coord": 0.0,
"max_coord": 100.0,
"min_height": 30.0,
"max_height": 70.0,
"uniform_height": 0,
"min_width": 1.0,
"max_width": 12.0,
"uniform_width": 0,
"lambda_": 0.5,
"move_severity": 1.0,
"height_severity": 1.0,
"width_severity": 0.5,
"period": 1000}
def diversity(population):
nind = len(population)
ndim = len(population[0])
d = [0.0] * ndim
for x in population:
d = [di + xi for di, xi in zip(d, x)]
d = [di / nind for di in d]
return math.sqrt(sum((di - xi)**2 for x in population for di, xi in zip(d, x)))
if __name__ == "__main__":
mpb = MovingPeaks(dim=2, npeaks=[1,1,10], number_severity=0.1)
print mpb.maximums()
mpb.changePeaks()
print mpb.maximums()