print(' fx = {}'.format(fx))
# Save to solution history
x_hist = args[0]
fx_hist = args[1]
x_hist.append(x)
fx_hist.append(fx)
bounds = [(0, 10) for i in range(10)]
x_hist = list()
fx_hist = list()
args = (x_hist, fx_hist)
res = minimize(fun, bounds, args=args, callback=callback, workers=1)
# Print optimization result
print(res)
if __name__ == "__main__":
# Plot solution history
fig, ax = plt.subplots(2, 1, sharex=True)
ax[0].plot(x_hist)
ax[0].set_title('x')
ax[1].plot(fx_hist)
ax[1].set_title('f(x) = np.sum(x ** 2) + random.random()')
ax[1].set_xlabel('Generation')
plt.show()
def con_minimize(
fun, bounds, constr=(), x0=None, args=(), callback=None, options={}, workers=None
):
"""Constrained minimization of `fun` using Genetic Algorithm.
This function is a wrapper over modestga.minimize().
The constraints are defined as a tuple of functions
(`fcon1(x, *args)`, `fcon2(x, *args)`, `...`).
The algorithm searches for a solution minimizing
`fun(x, *args)` and satisfying the conditions
(`fcon1(x, *args) >= 0`, `fcon2(x, *args) >= 0`, `...`).
`callback` arguments: `x`, `fx`, `ng`, `*args`.
`fx` is the function value at the generation `ng`.
Returns an optimization result object with the following attributes:
- x - numpy 1D array, optimized parameters,
- message - str, exit message,
- ng - int, number of generations,
- fx - float, final function value.
:param fun: function to be minimized
:param bounds: tuple, parameter bounds
:param constr: tuple, functions defining constraints
:param x0: numpy 1D array, initial parameters
:param args: tuple, positional arguments to be passed to `fun` and to `fcon`
:param callback: function, called after every generation
:param options: dict, GA options
:param workers: int, number of processes to use (will use all CPUs if None)
:return: OptRes, optimization result
"""
# Wrap cost function with constraints
def fun_soft_con(x, *augmented_args):
# Unpack constraints and arguments
fcore = augmented_args[0] # Function to be minimized
fcons = augmented_args[1] # Constraints
user_args = augmented_args[2:] # Arguments
# Evaluate core function
ycore = fcore(x, *user_args)
# Initialize penalty
penalty = 0.0
# Update penalty
# (the more negative fcon() is, the higher penalty)
for f in fcons:
ycon = np.max([f(x, *user_args) * -1.0, 0.0])
pscale = ycore / (ycon + 1e-6)
penalty += ycon * pscale
return ycore + penalty
# Run minimization
augmented_args = (fun, constr, *args)
res = modestga.minimize(
fun=fun_soft_con,
bounds=bounds,
x0=x0,
args=augmented_args,
callback=callback,
options=options,
workers=workers,
)
# Extend result with contraint violation info
res.constr = [fcon(res.x, *args) for fcon in constr]
return res
def estimate(self):
# Objective function
self.logger.debug("Instantiating ObjectiveFun")
objective_fun = ObjectiveFun(self.fmu_path, self.inp, self.known,
self.est, self.ideal, self.ftype)
self.logger.debug(f"ObjectiveFun: {objective_fun}")
# Initial guess
x0 = [MODESTGA.scale(x.value, x.lo, x.hi) for x in self.est]
self.logger.debug("modestga x0 = {}".format(x0))
# Save initial guess in summary
row = pd.DataFrame(index=[0])
for x, c in zip(x0, MODESTGA.TMP_SUMMARY.columns):
row[c] = x
row[MODESTGA.ERR] = np.nan
row[MODESTGA.METHOD] = MODESTGA.NAME
MODESTGA.TMP_SUMMARY = MODESTGA.TMP_SUMMARY.append(row,
ignore_index=True)
# Parameter bounds
b = [(0.0, 1.0) for x in self.est]
self.logger.debug(f"bounds = {b}")
out = minimize(
objective_fun,
bounds=b,
x0=x0,
args=(),
callback=MODESTGA._callback,
options=self.options,
workers=self.workers,
)
self.logger.debug(f"out = {out}")
outx = [
MODESTGA.rescale(x, ep.lo, ep.hi)
for x, ep in zip(out.x.tolist(), self.est)
]
self.logger.debug("modestga x = {}".format(outx))
# Update summary
self.summary = MODESTGA.TMP_SUMMARY.copy()
self.summary.index += 1 # Adjust iteration counter
self.summary.index.name = MODESTGA.ITER # Rename index
# Update error
self.summary[MODESTGA.ERR] = list(
map(objective_fun,
self.summary[[x.name for x in self.est]].values))
for ep in self.est:
name = ep.name
# list(map(...)) - for Python 2/3 compatibility
self.summary[name] = list(
map(lambda x: MODESTGA.rescale(x, ep.lo, ep.hi),
self.summary[name])) # Rescale
# Reset temp placeholder
MODESTGA.TMP_SUMMARY = pd.DataFrame(columns=self.summary_cols)
# Return DataFrame with estimates
par_vec = outx
par_df = pd.DataFrame(columns=[x.name for x in self.est], index=[0])
for col, x in zip(par_df.columns, par_vec):
par_df[col] = x
return par_df
def task(self, **kwargs):
"""
Args:
kwargs (dict, optional):
keyword arguments:
bounds (2D array_like of float):
array of min/max pairs for optimization constraints etc
method (str):
optimization method
y (1D array_like of float):
target of inverse problem (only if 'self' is of type
Inverse), shape: (nOut)
Returns:
(2-tuple of 1D array of float):
model input at optimum and corresponding model output,
shape: (nInp) and shape: (nOut)
Note:
- requires initial point(s) self.x for getting input number: nInp
- if inverse problem solution then self.y is required as target
"""
Base.task(self, **kwargs)
bounds = kwargs.get('bounds', None)
method = self.kwargsGet(kwargs, ('method', 'methods'), None)
if method is not None:
self.method = method
self.write('+++ method: ', self.method)
# sets target for Inverse
if type(self).__name__ in ('Inverse'):
y = kwargs.get('y', None)
self.y = np.atleast_1d(y) if y is not None else self.y
assert self.model is not None
xIni = self.x.copy()
self._history = []
for x0 in xIni:
self._trialHistory = []
if self.method.startswith('bas'):
res = scipy.optimize.basinhopping(func=self.objective,
x0=x0,
niter=100,
T=1.0,
stepsize=0.5,
minimizer_kwargs=None,
take_step=None,
accept_test=None,
callback=None,
interval=50,
disp=False,
niter_success=None)
x = np.atleast_1d(res.x)
y = np.atleast_1d(res.fun)
success = 'success' in res.message[0]
elif self.method.startswith('dif'):
if bounds is None:
bounds = [(-10, 10)] * len(x0)
res = scipy.optimize.differential_evolution(
func=self.objective,
bounds=bounds,
strategy='best1bin',
maxiter=None,
popsize=15,
tol=0.01,
mutation=(0.5, 1),
recombination=0.7,
seed=None,
disp=False,
polish=True,
init='latinhypercube')
x, y = res.x, res.fun
success = res.success
elif self.method == 'ga':
validKeys = ['tol', 'options', 'bounds']
kw = {k: kwargs[k] for k in validKeys if k in kwargs}
res = mg.minimize(
fun=self.objective,
x0=x0,
# method=self.method, # TODO .
**kw)
x, y = np.atleast_1d(res.x), np.atleast_1d(res.fx)
success = True # TODO .
else:
res = scipy.optimize.minimize(
fun=self.objective,
x0=x0,
method=self.method,
)
x = np.atleast_1d(res.x)
kw = self.kwargsDel(kwargs, 'x')
y = self.model.predict(x=res.x, **kw)[0]
success = res.success
self._history.append(self._trialHistory)
if not success:
self.write('+++ error message: ', res.message)
x = [None] * x.size
y = [None] * y.size
nTrial = len(self._history[0])
if nTrial > 1:
self.write('+++ Optima of all trials:')
for iTrial, history in enumerate(self._history):
self.write(' [' + str(iTrial) + '] x: ', history[-1][0],
'\n y: ', history[-1][1],
'\n objective: ', history[-1][2])
# self._history[iTrial][iLast=-1][jObj=2] -> list of best obj.
finalObjectives = [hist[-1][2] for hist in self._history]
if self.__class__.__name__ == 'Inverse':
absFinalObj = np.abs(finalObjectives)
iTrialBest = finalObjectives.index(min(absFinalObj))
else:
iTrialBest = finalObjectives.index(min(finalObjectives))
else:
iTrialBest = 0
# y: self._history[iTrialBest][iLast=-1][jY=1]
historyBest = self._history[iTrialBest]
finalBest = historyBest[-1]
self.x, self.y = finalBest[0], finalBest[1]
objectiveBest = finalBest[2]
self.write('+++ Best trial:\n [' + str(iTrialBest) + '] x: ',
self.x, '\n y: ', self.y, '\n objective: ',
objectiveBest)
return self.x, self.y
def minimizeLeastSquares(self, method, c0, **kwargs):
"""
Minimizes least squares: sum(self.f(self.X)-self.Y)^2)/X.size
for SINGLE initial fit param set
Updates self.ready and self.weights according to success of optimizer
Args:
method (str):
optimizing method for minimizing objective function
[recommendation: 'BFGS' or 'L-BFGS-B' if ill-conditioned
'Nelder-Mead' or 'Powell' if noisy data]
c0 (1D array_like of float):
initial guess of fit parameter set
kwargs (dict, optional):
keyword arguments:
bounds (2-tuple of float or 2-tuple of 1D array_like of float):
list of pairs (xMin, xMax) limiting x
... specific optimizer options
Returns:
(dict {str: float or int or str}):
results, see Model.train()
"""
results = self.initResults('method', method)
self.weights = None # required by Model.predict()
self.ready = True # required by Model.predict()
if method in self.scipyMinimizers:
if method.startswith('bas'):
nItMax = kwargs.get('nItMax', 100)
res = scipy.optimize.basinhopping(func=self.meanSquareErrror,
x0=c0,
niter=nItMax,
T=1.0,
stepsize=0.5,
minimizer_kwargs=None,
take_step=None,
accept_test=None,
callback=None,
interval=50,
disp=False,
niter_success=None)
if 'success' in res.message[0]:
results['weights'] = np.atleast_1d(res.x)
results['iterations'] = res.nit
results['evaluations'] = res.nfev
else:
self.write('\n??? ', method, ': ', res.message)
elif method.startswith('dif'):
nItMax = kwargs.get('nItMax', None)
res = scipy.optimize.differential_evolution(
func=self.meanSquareErrror,
bounds=[[-10, 10]] * c0.size,
strategy='best1bin',
maxiter=nItMax,
popsize=15,
tol=0.01,
mutation=(0.5, 1),
recombination=0.7,
seed=None,
disp=False,
polish=True,
init='latinhypercube')
if res.success:
results['weights'] = np.atleast_1d(res.x)
results['iterations'] = res.nit
results['evaluations'] = res.nfev
else:
self.write('\n??? ', method, ': ', res.message)
else:
validKeys = ['nItMax', 'adaptive', 'goal']
kw = {}
if any(k in kwargs for k in validKeys):
kw['options'] = {}
kw['options']['maxiter'] = kwargs.get('nItMax', None)
if method == 'Nelder-Mead':
kw['options']['xatol'] = kwargs.get('goal', 1e-4)
try:
res = scipy.optimize.minimize(fun=self.meanSquareErrror,
x0=c0,
method=method,
**kw)
if res.success:
results['weights'] = np.atleast_1d(res.x)
results['iterations'] = res.nit \
if method != 'COBYLA' else -1
results['evaluations'] = res.nfev
else:
self.write('\n??? ', method, ': ', res.message)
except scipy.optimize.OptimizeWarning:
results['weights'] = None
self.write('\n??? ', method, ': ', res.message)
elif method in self.scipyRootFinders:
nItMax = kwargs.get('nItMax', 0)
if method.startswith('lm'):
res = scipy.optimize.root(
fun=self.difference,
x0=c0,
args=(),
method='lm',
jac=None,
tol=None,
callback=None,
options={ # 'func': None,mesg:_root_leastsq() got multiple
# values for argument 'func'
'col_deriv': 0,
'xtol': 1.49012e-08,
'ftol': 1.49012e-8,
'gtol': 0.,
'maxiter': nItMax,
'eps': 0.0,
'factor': 100,
'diag': None
})
if res.success:
results['weights'] = np.atleast_1d(res.x)
results['iterations'] = -1
results['evaluations'] = res.nfev
else:
self.write('\n??? ', method, ': ', res.message)
else:
print("\n??? method:'" + str(method) + "' not implemented")
elif method in self.scipyEquationMinimizers:
if method.startswith('leastsq'):
x, cov_x, infodict, mesg, ier = scipy.optimize.leastsq(
self.difference, c0, full_output=True)
if ier in [1, 2, 3, 4]:
results['weights'] = np.atleast_1d(x)
results['iterations'] = -1
results['evaluations'] = infodict['nfev']
else:
self.write('\n??? ', method, ': ', mesg)
elif method == 'least_squares':
res = scipy.optimize.least_squares(self.difference, c0)
if res.success:
results['weights'] = np.atleast_1d(res.x)
results['iterations'] = -1
results['evaluations'] = res.nfev
else:
self.write('\n??? ', method, ': ', res.message)
elif method in self.geneticMinimizers:
if 'modestga' in sys.modules and method == 'ga':
assert method != 'ga' or 'modestga' in sys.modules
validKeys = ['tol', 'options', 'bounds']
# see scipy's minimize
kw = {k: kwargs[k] for k in validKeys if k in kwargs}
res = mg.minimize(
fun=self.meanSquareErrror,
x0=c0,
# TODO method=method,
**kw)
if True: # TODO res.success:
results['weights'] = np.atleast_1d(res.x)
results['iterations'] = -1 # res.nit
results['evaluations'] = res.ng # TODO res.nfev =? ng
else:
self.write('\n??? ', method, ': ', res.message)
else:
assert 0, '??? LightGray, invalid method: ' + str(method)
self.weights = results['weights']
self.ready = self.weights is not None
return results
fx_hist = args[1]
x_hist.append(x)
fx_hist.append(fx)
bounds = [(-5.12, 5.12) for i in range(N)]
x_hist = list()
fx_hist = list()
args = (x_hist, fx_hist)
options = {
'generations': 500,
}
res = minimize(fun, bounds, args=args, callback=callback, options=options)
# Print optimization result
print(res)
if __name__ == "__main__":
# Plot solution history
fig, ax = plt.subplots(2, 1, sharex=True)
ax[0].plot(x_hist, alpha=0.1, color='k')
ax[0].set_title('x')
ax[1].plot(fx_hist, color='k')
ax[1].set_title('f(x) = RASTRIGIN FUNC.')
ax[1].set_xlabel('Generation')
plt.show()
