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CMAES.py
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CMAES.py
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#!/usr/bin/env python3
from collections import deque
import math
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
class CMAES:
def __init__(self, xmean0, sigma0, lam=None):
"""
Parameters
----------
xmean0 : 1d array-like
initial mean vector
sigma0 : 1d array-like
initial diagonal decoding
lam : int, optional (default = None)
population size
beta_eig : float, optional (default = None)
coefficient to control the frequency of matrix decomposition
"""
self.N = len(xmean0)
self.chiN = np.sqrt(self.N) * (1. - 1. / (4. * self.N) + 1. / (21. * self.N **2))
# parameters for recombination and step-size adaptation
self.lam = lam if lam else 4 + int(3 * math.log(self.N))
assert self.lam > 2
w = math.log((self.lam + 1) / 2.0) - np.log(np.arange(1, self.lam+1))
w[w > 0] /= np.sum(w[w > 0])
w[w < 0] = 0.
self.w = w
self.mu = self.lam // 2
self.mueff = 1. / np.sum(self.w**2)
self.cm = 1.
self.cs = (self.mueff + 2.) / (self.N + self.mueff + 5.)
self.ds = 1. + self.cs + 2.*max(0., math.sqrt((self.mueff - 1.) / (self.N + 1.)) - 1.)
# parameters for covariance matrix adaptation
self.cone = 2. / ((self.N + 1.3)**2 + self.mueff)
self.cmu = min(1. - self.cone,
2.*(self.mueff - 2. + 1./self.mueff) / ((self.N + 2.)**2 + self.mueff))
self.cc = (4. + self.mueff/self.N) / (self.N + 4. + 2.*self.mueff / self.N)
# others
self.neval = 0
self.niter = 0
# dynamic parameters
self.xmean = np.array(xmean0, copy=True)
self.sigma = np.array(sigma0, copy=True)
self.D = np.ones(self.N)
self.cov = np.diag(self.D ** 2)
self._decompose()
self.ps = np.zeros(self.N)
self.ps_factor = 0.0
self.pc = np.zeros(self.N)
self.pc_factor = 0.0
# storage for checker and logger
self.arx = np.zeros((self.lam, self.N)) * np.nan
self.arf = np.zeros(self.lam) * np.nan
# decomposition performed after given #f-calls
# For more detail, see
# Y. Akimoto and N. Hansen., "Diagonal Acceleration for Covariance Matrix Adaptation Evolution Strategies"
self.eigen_frequency = int(self.lam / (10 * self.N * (self.cone + self.cmu)))
self.eigneval = 0
def transform(self, z):
y = np.dot(z, self.sqrtC)
return y * (self.D * self.sigma)
def transform_inverse(self, y):
z = y / (self.D * self.sigma)
return np.dot(z, self.invsqrtC)
def sample_candidate(self):
arz = np.random.randn(self.lam, self.N)
ary = np.dot(arz, self.sqrtC.T)
arx = self.xmean + self.sigma * ary
return arx
def _decompose(self):
"""Decompose the covariance matrix and update relevant parameters"""
DD, self.B = np.linalg.eigh(self.cov)
self.D = np.sqrt(DD)
if not (self.D.max() < self.D.min() * 1e7):
raise RuntimeError('Condition number > 1e7 or nan appears.')
self.sqrtC = np.dot(self.B * self.D, self.B.T)
self.invsqrtC = np.dot(self.B / self.D, self.B.T)
self.eigneval = self.neval
def update(self, idx, arx):
# shortcut
sary = (arx[idx] - self.xmean) / self.sigma
sarx = arx[idx]
# recombination
dy = np.dot(self.w, sary)
self.xmean += self.sigma * dy
# step-size adaptation
self.ps_factor = (1. - self.cs)**2 * self.ps_factor + self.cs * (2. - self.cs)
self.ps *= (1. - self.cs)
self.ps += math.sqrt(self.cs * (2. - self.cs) * self.mueff) * np.dot(dy, self.invsqrtC)
normsquared = np.sum(self.ps * self.ps)
hsig = (normsquared <
((1.4 + 2.0 / (self.N + 1.)) * self.chiN * math.sqrt(self.ps_factor))**2)
self.sigma *= math.exp((math.sqrt(normsquared) / self.chiN
- math.sqrt(self.ps_factor)) * self.cs / self.ds)
# covariance matrix adaptation
# Rank-mu
rank_mu = np.dot(sary.T * self.w, sary) - self.cov
# Rank-one
self.pc = (1. - self.cc) * self.pc
self.pc += hsig * math.sqrt(self.cc * (2. - self.cc) * self.mueff) * dy
self.pc_factor = (1. - self.cc)**2 * self.pc_factor + hsig * self.cc * (2. - self.cc)
rank_one = np.outer(self.pc, self.pc) - self.pc_factor * self.cov
# Update
self.cov += self.cmu * rank_mu + self.cone * rank_one
# update the square root of the covariance matrix
if (self.neval - self.eigneval) > self.eigen_frequency:
self._decompose()
def onestep(self, func):
"""
Parameter
---------
func : callable
parameter : 2d array-like with candidate solutions (x) as elements
return : 1d array-like with f(x) as elements
"""
# sampling
arx = self.sample_candidate() # (lam, dim)-array
# evaluation
arf = func(arx)
self.neval += len(arf)
# sort
idx = np.argsort(arf)
# update
self.update(idx, arx)
# finalize
self.arx = arx
self.arf = arf
self.niter += 1
@property
def coordinate_std(self):
return self.sigma * np.sqrt(np.diag(self.cov))
class Checker(object):
"""Termination Checker for BBOB
Termination condition implemented in [Hansen 2009] (BI-POP-CMA-ES on BBOB 2019)
is implemented here.
"""
def __init__(self, cma):
assert isinstance(cma, CMAES)
assert hasattr(cma, 'sigma')
self._cma = cma
self._init_std = self._cma.sigma
self._N = self._cma.N
self._lam = self._cma.lam
self._hist_fbest = deque(maxlen=10 + int(np.ceil(30 * self._N / self._lam)))
self._hist_feq_flag = deque(maxlen=self._N)
self._hist_fmin = deque()
self._hist_fmed = deque()
def __call__(self):
return self.bbob_check()
def check_maxiter(self):
return self._cma.niter > 100 + 50 * (self._N + 3) ** 2 / np.sqrt(self._lam)
def check_tolhistfun(self):
self._hist_fbest.append(np.min(self._cma.arf))
return (self._cma.niter >= 10 + int(np.ceil(30 * self._N / self._lam)) and
np.max(self._hist_fbest) - np.min(self._hist_fbest) < 1e-12)
def check_equalfunvals(self):
k = int(math.ceil(0.1 + self._lam / 4))
sarf = np.sort(self._cma.arf)
self._hist_feq_flag.append(sarf[0] == sarf[k])
return 3 * sum(self._hist_feq_flag) > self._N
def check_tolx(self):
assert hasattr(self._cma, 'pc')
assert hasattr(self._cma, 'sigma')
return (np.all(np.abs(self._cma.pc) * (self._cma.sigma / self._init_std) < 1e-12) and
np.all(self._cma.coordinate_std / self._init_std) < 1e-12)
def check_tolupsigma(self):
assert hasattr(self._cma, 'sigma')
assert hasattr(self._cma, 'D')
return np.any((self._cma.sigma / self._init_std) > 1e20 * np.max(self._cma.D))
def check_stagnation(self):
self._hist_fmin.append(np.min(self._cma.arf))
self._hist_fmed.append(np.median(self._cma.arf))
_len = int(np.ceil(self._cma.niter / 5 + 120 + 30 * self._N / self._lam))
if len(self._hist_fmin) > _len:
self._hist_fmin.popleft()
self._hist_fmed.popleft()
fmin_med = np.median(np.asarray(self._hist_fmin)[-20:])
fmed_med = np.median(np.asarray(self._hist_fmed)[:20])
return self._cma.niter >= _len and fmin_med >= fmed_med
def check_conditioncov(self):
assert hasattr(self._cma, 'D')
return np.max(self._cma.D) / np.min(self._cma.D) > 1e7
def check_noeffectaxis(self):
assert hasattr(self._cma, 'sigma')
assert hasattr(self._cma, 'D')
assert hasattr(self._cma, 'B')
t = self._cma.niter % self._N
test = 0.1 * self._cma.sigma * self._cma.D[t] * self._cma.B[:, t]
return np.all(self._cma.xmean == self._cma.xmean + test)
def check_noeffectcoor(self):
return np.all(self._cma.xmean == self._cma.xmean + 0.2 * self._cma.coordinate_std)
def check_flat(self):
return np.max(self._cma.arf) == np.min(self._cma.arf)
def bbob_check(self):
if self.check_maxiter():
return True, 'bbob_maxiter'
if self.check_tolhistfun():
return True, 'bbob_tolhistfun'
if self.check_equalfunvals():
return True, 'bbob_equalfunvals'
if self.check_tolx():
return True, 'bbob_tolx'
if self.check_tolupsigma():
return True, 'bbob_tolupsigma'
if self.check_stagnation():
return True, 'bbob_stagnation'
if self.check_conditioncov():
return True, 'bbob_conditioncov'
if self.check_noeffectaxis():
return True, 'bbob_noeffectaxis'
if self.check_noeffectcoor():
return True, 'bbob_noeffectcoor'
if self.check_flat():
return True, 'bbob_flat'
return False, ''
class Logger:
"""Logger for CMAES"""
def __init__(self, cma, prefix='log', variable_list=['xmean', 'D', 'sigma']):
"""
Parameters
----------
cma : CMAES instance
prefix : string
prefix for the log file path
variable_list : list of string
list of names of attributes of `cma` to be monitored
"""
self._cma = cma
self.prefix = prefix
self.variable_list = variable_list
self.logger = dict()
self.fmin_logger = self.prefix + '_fmin.dat'
with open(self.fmin_logger, 'w') as f:
f.write('#' + type(self).__name__ + "\n")
for key in self.variable_list:
self.logger[key] = self.prefix + '_' + key + '.dat'
with open(self.logger[key], 'w') as f:
f.write('#' + type(self).__name__ + "\n")
def __call__(self, condition=''):
self.log(condition)
def log(self, condition=''):
with open(self.fmin_logger, 'a') as f:
f.write("{} {} {}\n".format(self._cma.niter, self._cma.neval, np.min(self._cma.arf)))
if condition:
f.write('# End with condition = ' + condition)
for key, log in self.logger.items():
key_split = key.split('.')
key = key_split.pop(0)
var = getattr(self._cma, key)
for i in key_split:
var = getattr(var, i)
if isinstance(var, np.ndarray) and len(var.shape) > 1:
var = var.flatten()
varlist = np.hstack((self._cma.niter, self._cma.neval, var))
with open(log, 'a') as f:
f.write(' '.join(map(repr, varlist)) + "\n")
def my_formatter(self, x, pos):
"""Float Number Format for Axes"""
float_str = "{0:2.1e}".format(x)
if "e" in float_str:
base, exponent = float_str.split("e")
return r"{0}e{1}".format(base, int(exponent))
else:
return r"" + float_str + ""
def plot(self,
xaxis=0,
ncols=None,
figsize=None,
cmap_='Spectral'):
"""Plot the result
Parameters
----------
xaxis : int, optional (default = 0)
0. vs iterations
1. vs function evaluations
ncols : int, optional (default = None)
number of columns
figsize : tuple, optional (default = None)
figure size
cmap_ : string, optional (default = 'spectral')
cmap
Returns
-------
fig : figure object.
figure object
axdict : dictionary of axes
the keys are the names of variables given in `variable_list`
"""
mpl.rc('lines', linewidth=2, markersize=8)
mpl.rc('font', size=12)
mpl.rc('grid', color='0.75', linestyle=':')
mpl.rc('ps', useafm=True) # Force to use
mpl.rc('pdf', use14corefonts=True) # only Type 1 fonts
mpl.rc('text', usetex=True) # for a paper submision
prefix = self.prefix
variable_list = self.variable_list
# Default settings
nfigs = 1 + len(variable_list)
if ncols is None:
ncols = int(np.ceil(np.sqrt(nfigs)))
nrows = int(np.ceil(nfigs / ncols))
if figsize is None:
figsize = (4 * ncols, 3 * nrows)
axdict = dict()
# Figure
fig = plt.figure(figsize=figsize)
# The first figure
x = np.loadtxt(prefix + '_fmin.dat')
x = x[~np.isnan(x[:, xaxis]), :] # remove columns where xaxis is nan
# Axis
ax = plt.subplot(nrows, ncols, 1)
ax.set_title('fmin')
ax.grid(True)
ax.grid(which='major', linewidth=0.50)
ax.grid(which='minor', linewidth=0.25)
plt.plot(x[:, xaxis], x[:, 2:])
ax.xaxis.set_major_formatter(mpl.ticker.FuncFormatter(self.my_formatter))
ax.yaxis.set_major_formatter(mpl.ticker.FuncFormatter(self.my_formatter))
axdict['fmin'] = ax
# The other figures
idx = 1
for key in variable_list:
idx += 1
x = np.loadtxt(prefix + '_' + key + '.dat')
x = x[~np.isnan(
x[:, xaxis]), :] # remove columns where xaxis is nan
ax = plt.subplot(nrows, ncols, idx)
ax.set_title(r'\detokenize{' + key + '}')
ax.grid(True)
ax.grid(which='major', linewidth=0.50)
ax.grid(which='minor', linewidth=0.25)
cmap = plt.get_cmap(cmap_)
cNorm = mpl.colors.Normalize(vmin=0, vmax=x.shape[1] - 2)
scalarMap = mpl.cm.ScalarMappable(norm=cNorm, cmap=cmap)
for i in range(x.shape[1] - 2):
plt.plot(
x[:, xaxis], x[:, 2 + i], color=scalarMap.to_rgba(i))
ax.xaxis.set_major_formatter(
mpl.ticker.FuncFormatter(self.my_formatter))
ax.yaxis.set_major_formatter(
mpl.ticker.FuncFormatter(self.my_formatter))
axdict[key] = ax
plt.tight_layout() # NOTE: not sure if it works fine
return fig, axdict
def main():
def sphere(x):
return 0.5 * np.sum(x ** 2, axis=-1)
# Main loop
N = 20
cma = CMAES(xmean0=np.random.randn(N), sigma0=np.ones(N))
checker = Checker(cma)
logger = Logger(cma)
issatisfied = False
fbestsofar = np.inf
while not issatisfied:
cma.onestep(func=sphere)
fbest = np.min(cma.arf)
fbestsofar = min(fbest, fbestsofar)
if fbest < 1e-8:
issatisfied, condition = True, 'ftarget'
else:
issatisfied, condition = checker()
if cma.niter % 10 == 0:
print(cma.niter, cma.neval, fbest, fbestsofar)
logger()
print(cma.niter, cma.neval, fbest, fbestsofar)
print("Terminated with condition: " + condition)
logger(condition)
# Produce a figure
fig, axdict = logger.plot()
for key in axdict:
if key not in ('xmean'):
axdict[key].set_yscale('log')
plt.savefig(logger.prefix + '.pdf', tight_layout=True)
if __name__ == '__main__':
main()