def fmin_cma(objective_function, x0, xL, xU, sigma0=0.01, maxfun=1000):
""" Minimize objective function in hypercube using CMA-ES.
This function optimizes an objective function in a search space bounded by
a hypercube. One corner of the hypercube is given by xL and the opposite by
xU. The initial mean of the search distribution is given by x0. The search
space is scaled internally to the unit hypercube to accommodate CMA-ES.
Parameters
----------
objective_function : callable
The objective function to be minimized. Must return a scalar value
x0 : array-like
Initial mean of the search distribution
xL: array-like
Lower, left corner of the bounding hypercube
xU: array-like
Upper, right corner of the bounding hypercube
sigma0: float, default=0.01
Initial variance of search distribution of CMA-ES
maxfun: int, default=1000
Maximum number of evaluations of the objective function after which the
optimization is stopped.
Returns
----------
x_opt : array-like
The minimum of objective function identified by CMA-ES
"""
try:
from bolero.optimizer import fmin
except ImportError:
raise Exception("'cmaes' optimizer requires the package bolero.")
x0 = np.asarray(x0)
xL = np.asarray(xL)
xU = np.asarray(xU)
# Scale parameters such that search space is a unit-hypercube
x0 = (x0 - xL) / (xU - xL)
x0[~np.isfinite(x0)] = 0 # Deal with situations where xU == xL
bounds = np.array([np.zeros_like(x0), np.ones_like(x0)]).T
# Rescale in objective function
def scaled_objective_function(x):
return objective_function(x * (xU - xL) + xL)
# Minimize objective function using CMA-ES. Restart if no valid solution is
# found
res = (None, np.inf)
while not np.isfinite(res[1]):
res = fmin(scaled_objective_function, x0=x0, variance=sigma0,
bounds=bounds, maxfun=maxfun)
x_opt = res[0]
# Return rescaled solution
return x_opt * (xU - xL) + xL
def test_cmaes_maximize_eval_initial_x_best():
def x0_best(x):
if np.all(x == 0.0):
return 0.0
else:
return -1.0
_, f = fmin(x0_best, cma_type="standard", x0=np.zeros(2), random_state=0,
maxfun=300, maximize=True, eval_initial_x=True)
assert_equal(f, 0.0)
def fmin_cma(objective_function, x0, xL, xU, sigma0=0.01, maxfun=1000):
""" Minimize objective function in hypercube using CMA-ES.
This function optimizes an objective function in a search space bounded by
a hypercube. One corner of the hypercube is given by xL and the opposite by
xU. The initial mean of the search distribution is given by x0. The search
space is scaled internally to the unit hypercube to accommodate CMA-ES.
Parameters
----------
objective_function : callable
The objective function to be minimized. Must return a scalar value
x0 : array-like
Initial mean of the search distribution
xL: array-like
Lower, left corner of the bounding hypercube
xU: array-like
Upper, right corner of the bounding hypercube
sigma0: float, default=0.01
Initial variance of search distribution of CMA-ES
maxfun: int, default=1000
Maximum number of evaluations of the objective function after which the
optimization is stopped.
Returns
----------
x_opt : array-like
The minimum of objective function identified by CMA-ES
"""
try:
from bolero.optimizer import fmin
except ImportError:
raise Exception("'cmaes' optimizer requires the package bolero.")
x0 = np.asarray(x0)
xL = np.asarray(xL)
xU = np.asarray(xU)
# Scale parameters such that search space is a unit-hypercube
x0 = (x0 - xL) / (xU - xL)
x0[~np.isfinite(x0)] = 0 # Deal with situations where xU == xL
bounds = np.array([np.zeros_like(x0), np.ones_like(x0)]).T
# Rescale in objective function
def scaled_objective_function(x):
return objective_function(x * (xU - xL) + xL)
# Minimize objective function using CMA-ES. Restart if no valid solution is
# found
res = (None, np.inf)
while not np.isfinite(res[1]):
res = fmin(scaled_objective_function,
x0=x0,
variance=sigma0,
bounds=bounds,
maxfun=maxfun)
x_opt = res[0]
# Return rescaled solution
return x_opt * (xU - xL) + xL
def test_cmaes_maximize_eval_initial_x():
_, f = fmin(lambda x: -np.linalg.norm(x), cma_type="standard",
x0=np.ones(2), random_state=0, maxfun=300, maximize=True,
eval_initial_x=True)
assert_greater(f, -1e-5)
def test_cmaes_maximize():
_, f = fmin(lambda x: -np.linalg.norm(x), cma_type="standard",
x0=np.zeros(2), random_state=0, maxfun=300, maximize=True)
assert_greater(f, -1e-5)
def test_cmaes_minimize():
_, f = fmin(lambda x: np.linalg.norm(x), cma_type="standard",
x0=np.zeros(2), random_state=0, maxfun=300)
assert_less(f, 1e-5)
def test_bipop_cmaes():
_, f = fmin(lambda x: np.linalg.norm(x), cma_type="bipop",
x0=np.zeros(2), random_state=0, maxfun=300)
assert_less(f, 1e-5)
def test_cmaes_minimize_many_params():
_, f = fmin(lambda x: np.linalg.norm(x), cma_type="standard",
x0=np.zeros(30), random_state=0, maxfun=500)
assert_less(f, 1.0)