/usr/share/pyshared/deap/cma.py is in python-deap 0.7.1-1.
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#
# 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 <http://www.gnu.org/licenses/>.
# Special thanks to Nikolaus Hansen for providing major part of
# this code. The CMA-ES algorithm is provided in many other languages
# and advanced versions at http://www.lri.fr/~hansen/cmaesintro.html.
"""A module that provides support for the Covariance Matrix Adaptation
Evolution Strategy.
"""
import logging
from math import sqrt, log, exp
import numpy
import random # Only used to seed numpy.random
import sys # Used to get maxint
import copy
numpy.random.seed(random.randint(0, sys.maxint))
_logger = logging.getLogger("deap.cma")
def esCMA(toolbox, population, ngen, halloffame=None, statistics=None):
"""The CMA-ES algorithm as described in Hansen, N. (2006). *The CMA
Evolution Strategy: A Comparing Rewiew.*
The provided *population* should be a list of one or more individuals.
"""
_logger.info("Start of evolution")
for g in xrange(ngen):
_logger.info("Evolving generation %i", g)
# Evaluate the individuals
for ind in population:
ind.fitness.values = toolbox.evaluate(ind)
if halloffame is not None:
halloffame.update(population)
# Update the Strategy with the evaluated individuals
toolbox.update(population)
if statistics is not None:
statistics.update(population)
_logger.debug(statistics)
_logger.info("End of (successful) evolution")
class CMAStrategy(object):
"""
Additional configuration may be passed through the *params* argument as a
dictionary,
+----------------+---------------------------+----------------------------+
| Parameter | Default | Details |
+================+===========================+============================+
| ``lambda_`` | ``floor(4 + 3 * log(N))`` | Number of children to |
| | | produce at each generation,|
| | | ``N`` is the individual's |
| | | size. |
+----------------+---------------------------+----------------------------+
| ``mu`` | ``floor(lambda_ / 2)`` | The number of parents to |
| | | keep from the |
| | | lambda children. |
+----------------+---------------------------+----------------------------+
| ``weights`` | ``"superlinear"`` | Decrease speed, can be |
| | | ``"superlinear"``, |
| | | ``"linear"`` or |
| | | ``"equal"``. |
+----------------+---------------------------+----------------------------+
| ``cs`` | ``(mueff + 2) / | Cumulation constant for |
| | (N + mueff + 3)`` | step-size. |
+----------------+---------------------------+----------------------------+
| ``damps`` | ``1 + 2 * max(0, sqrt(( | Damping for step-size. |
| | mueff - 1) / (N + 1)) - 1)| |
| | + cs`` | |
+----------------+---------------------------+----------------------------+
| ``ccum`` | ``4 / (N + 4)`` | Cumulation constant for |
| | | covariance matrix. |
+----------------+---------------------------+----------------------------+
| ``ccov1`` | ``2 / ((N + 1.3)^2 + | Learning rate for rank-one |
| | mueff)`` | update. |
+----------------+---------------------------+----------------------------+
| ``ccovmu`` | ``2 * (mueff - 2 + 1 / | Learning rate for rank-mu |
| | mueff) / ((N + 2)^2 + | update. |
| | mueff)`` | |
+----------------+---------------------------+----------------------------+
"""
def __init__(self, centroid, sigma, **kargs):
self.params = kargs
# Create a centroid as a numpy array
self.centroid = numpy.array(centroid)
self.dim = len(self.centroid)
self.sigma = sigma
self.pc = numpy.zeros(self.dim)
self.ps = numpy.zeros(self.dim)
self.chiN = sqrt(self.dim) * (1 - 1. / (4. * self.dim) + \
1. / (21. * self.dim**2))
self.B = numpy.identity(self.dim)
self.C = numpy.identity(self.dim)
self.diagD = numpy.ones(self.dim)
self.BD = self.B * self.diagD
self.cond = 1
self.lambda_ = self.params.get("lambda_", int(4 + 3 * log(self.dim)))
self.update_count = 0
self.computeParams(self.params)
def generate(self, ind_init):
"""Generate a population from the current strategy using the
centroid individual as parent.
"""
arz = numpy.random.standard_normal((self.lambda_, self.dim))
arz = self.centroid + self.sigma * numpy.dot(arz, self.BD.T)
return [ind_init(arzi) for arzi in arz]
def update(self, population):
"""Update the current covariance matrix strategy.
"""
population.sort(key=lambda ind: ind.fitness, reverse=True)
old_centroid = self.centroid
self.centroid = numpy.dot(self.weights, population[0:self.mu])
c_diff = self.centroid - old_centroid
# Cumulation : update evolution path
self.ps = (1 - self.cs) * self.ps \
+ sqrt(self.cs * (2 - self.cs) * self.mueff) / self.sigma \
* numpy.dot(self.B, (1. / self.diagD) \
* numpy.dot(self.B.T, c_diff))
hsig = float((numpy.linalg.norm(self.ps) /
sqrt(1. - (1. - self.cs)**(2. * (self.update_count + 1.))) / self.chiN
< (1.4 + 2. / (self.dim + 1.))))
self.update_count += 1
self.pc = (1 - self.cc) * self.pc + hsig \
* sqrt(self.cc * (2 - self.cc) * self.mueff) / self.sigma \
* c_diff
# Update covariance matrix
artmp = population[0:self.mu] - old_centroid
self.C = (1 - self.ccov1 - self.ccovmu + (1 - hsig) \
* self.ccov1 * self.cc * (2 - self.cc)) * self.C \
+ self.ccov1 * numpy.outer(self.pc, self.pc) \
+ self.ccovmu * numpy.dot((self.weights * artmp.T), artmp) \
/ self.sigma**2
self.sigma *= numpy.exp((numpy.linalg.norm(self.ps) / self.chiN - 1.) \
* self.cs / self.damps)
self.diagD, self.B = numpy.linalg.eigh(self.C)
indx = numpy.argsort(self.diagD)
self.cond = self.diagD[indx[-1]]/self.diagD[indx[0]]
self.diagD = self.diagD[indx]**0.5
self.B = self.B[:, indx]
self.BD = self.B * self.diagD
arz = numpy.random.standard_normal((self.lambda_, self.dim))
arz = self.centroid + self.sigma * numpy.dot(arz, self.BD.T)
for ind, arzi in zip(population, arz):
del ind[:]
ind.extend(arzi)
def computeParams(self, params):
"""Those parameters depends on lambda and need to computed again if it
changes during evolution.
"""
self.mu = params.get("mu", self.lambda_ / 2)
rweights = params.get("weights", "superlinear")
if rweights == "superlinear":
self.weights = log(self.mu + 0.5) - \
numpy.log(numpy.arange(1, self.mu + 1))
elif rweights == "linear":
self.weights = self.mu + 0.5 - numpy.arange(1, self.mu + 1)
elif rweights == "equal":
self.weights = numpy.ones(self.mu)
else:
pass # Print some warning ?
self.weights /= sum(self.weights)
self.mueff = 1. / sum(self.weights**2)
self.cc = params.get("ccum", 4. / (self.dim + 4.))
self.cs = params.get("cs", (self.mueff + 2.) /
(self.dim + self.mueff + 3.))
self.ccov1 = params.get("ccov1", 2. / ((self.dim + 1.3)**2 + \
self.mueff))
self.ccovmu = params.get("ccovmu", 2. * (self.mueff - 2. + \
1. / self.mueff) / \
((self.dim + 2.)**2 + self.mueff))
self.ccovmu = min(1 - self.ccov1, self.ccovmu)
self.damps = 1. + 2. * max(0, sqrt((self.mueff - 1.) / \
(self.dim + 1.)) - 1.) + self.cs
self.damps = params.get("damps", self.damps)
class CMA1pLStrategy(object):
def __init__(self, parent, sigma, **kargs):
self.parent = parent
self.sigma = sigma
self.dim = len(self.parent)
self.C = numpy.identity(self.dim)
self.A = numpy.identity(self.dim)
self.pc = numpy.zeros(self.dim)
self.computeParams(kargs)
self.psucc = self.ptarg
def computeParams(self, params):
# Selection :
self.lambda_ = params.get("lambda_", 1)
# Step size control :
self.d = params.get("d", 1.0 + self.dim/(2.0*self.lambda_))
self.ptarg = params.get("ptarg", 1.0/(5+sqrt(self.lambda_)/2.0))
self.cp = params.get("cp", self.ptarg*self.lambda_/(2+self.ptarg*self.lambda_))
# Covariance matrix adaptation
self.cc = params.get("cc", 2.0/(self.dim+2.0))
self.ccov = params.get("ccov", 2.0/(self.dim**2 + 6.0))
self.pthresh = params.get("pthresh", 0.44)
def generate(self, ind_init):
# self.y = numpy.dot(self.A, numpy.random.standard_normal(self.dim))
arz = numpy.random.standard_normal((self.lambda_, self.dim))
arz = self.parent + self.sigma * numpy.dot(arz, self.A.T)
return [ind_init(arzi) for arzi in arz]
def update(self, population):
population.sort(key=lambda ind: ind.fitness, reverse=True)
lambda_succ = sum(self.parent.fitness <= ind.fitness for ind in population)
p_succ = float(lambda_succ) / self.lambda_
self.psucc = (1-self.cp)*self.psucc + self.cp*p_succ
if self.parent.fitness <= population[0].fitness:
x_step = (population[0] - numpy.array(self.parent)) / self.sigma
self.parent = copy.deepcopy(population[0])
if self.psucc < self.pthresh:
self.pc = (1 - self.cc)*self.pc + sqrt(self.cc * (2 - self.cc)) * x_step
self.C = (1-self.ccov)*self.C + self.ccov * numpy.dot(self.pc, self.pc.T)
else:
self.pc = (1 - self.cc)*self.pc
self.C = (1-self.ccov)*self.C + self.ccov * (numpy.dot(self.pc, self.pc.T) + self.cc*(2-self.cc)*self.C)
self.sigma = self.sigma * exp(1.0/self.d * (self.psucc - self.ptarg)/(1.0-self.ptarg))
# We use Cholesky since for now we have no use of eigen decomposition
# Basically, Cholesky returns a matrix A as C = A*A.T
# Eigen decomposition returns two matrix B and D^2 as C = B*D^2*B.T = B*D*D*B.T
# So A == B*D
# To compute the new individual we need to multiply each vector z by A
# as y = centroid + sigma * A*z
# So the Cholesky is more straightforward as we don't need to compute
# the squareroot of D^2, and multiply B and D in order to get A, we directly get A.
# This can't be done (without cost) with the standard CMA-ES as the eigen decomposition is used
# to compute covariance matrix inverse in the step-size evolutionary path computation.
self.A = numpy.linalg.cholesky(self.C)
arz = numpy.random.standard_normal((self.lambda_, self.dim))
arz = self.parent + self.sigma * numpy.dot(arz, self.A.T)
for ind, arzi in zip(population, arz):
del ind[:]
ind.extend(arzi)
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