def __init__(self,
goal='minimize',
batches=1,
boosted=True,
parallel=True,
sampling_strategies=2):
"""
A Bayesian optimization algorithm based on Bayesian Kernel Density estimation.
Args:
goal (str): The optimization goal, either 'minimize' or 'maximize'. Default is 'minimize'.
batches (int): number of parameter batches to return at each 'ask'
iteration.
boosted (bool): whether to use a lower fidelity approximation in
regions of low density during kernel density estimation. Setting
this to True reduces the run time of the planner.
parallel (bool): whether to run the code in parallel.
sampling_strategies (int): number of sampling strategies to use.
Each sampling strategy uses a different balance between
exploration and exploitation.
"""
AbstractPlanner.__init__(**locals())
self._observations = []
self._counter = 0
def __init__(self, goal='minimize', rng=None):
AbstractPlanner.__init__(**locals())
self.seed = 100691
self.rng = np.random.RandomState()
self.has_optimizer = False
self.is_converged = False
self.budget = 10**8
self.SUBMITTED_PARAMS = []
self.RECEIVED_VALUES = []
self._params = np.array([[]])
self._values = np.array([[]])
def __init__(self,
goal='minimize',
pop_size=10,
cx_prob=0.5,
mut_prob=0.2,
verbose=False,
mate_args={'function': tools.cxTwoPoint},
mutate_args={
'function': tools.mutGaussian,
'mu': 0,
'sigma': 0.2,
'indpb': 0.2
},
select_args={
'function': tools.selTournament,
'tournsize': 3
}):
"""Evolutionary Algorithm implemented using the DEAP library.
We initialize the population using a uniform probability across the parameter space. We then evaluate
one individual of the population at a time. After all individuals have been evaluated, we generate a set of
offsprings via selection, cross-over and mutation, using the functions chosen in `select_args`, `mate_args`
and `mutate_args`. Only novel offsprings, having a set of parameters different from those of the parent
population, are chosen to be evaluated, and are then proposed sequentially. Once all these offsprings have
been evaluated, a new set is generated following the same procedure.
Args:
goal (str): The optimization goal, either 'minimize' or 'maximize'. Default is 'minimize'.
pop_size (int): Size of the population. Default is 10.
cx_prob (float): Probability with which two individuals are crossed. Default is 0.5.
mut_prob (float): Probability for mutating an individual. Default is 0.2.
verbose (bool): Whether to print out information. Default is True.
mate_args (dict): Dictionary containing the details of the crossover function to be used. This should
contain all arguments that you want to provided to Toolbox.register("mate"). For all crossover
operations available see https://deap.readthedocs.io/en/master/api/tools.html.
mutate_args (dict): Dictionary containing the details of the mutation function to be used. This should
contain all arguments that you want to provided to Toolbox.register("mutate"). For all mutation
operations available see https://deap.readthedocs.io/en/master/api/tools.html.
select_args (dict): Dictionary containing the details of the selection function to be used. This should
contain all arguments that you want to provided to Toolbox.register("select"). For all selection
operations available see https://deap.readthedocs.io/en/master/api/tools.html.
"""
AbstractPlanner.__init__(**locals())
# define fitness function = minimize
creator.create(
"FitnessMin", base.Fitness,
weights=(-1.0, )) # -1 for minimisation, +1 for maximisation
creator.create("Individual", list, fitness=creator.FitnessMin)
# get Deap toolbox
self.toolbox = base.Toolbox()
def __init__(self, goal='minimize', show_progressbar=False):
"""
Tree of Parzen Estimators (TPE) as implemented in HyperOpt.
Args:
goal (str): The optimization goal, either 'minimize' or 'maximize'. Default is 'minimize'.
show_progressbar (bool): If True, show a progressbar.
"""
AbstractPlanner.__init__(**locals())
self._trials = Trials(
) # these is a Hyperopt object that stores the search history
self._hp_space = None # these are the params in the Hyperopt format
def __init__(self,
goal='minimize',
init_guess=None,
init_guess_method='random',
init_guess_seed=None):
'''
Args:
init_guess (array, optional): initial guess for the optimization
init_guess_method (str): method to construct initial guesses if init_guess is not provided.
Choose from: random
init_guess_seed (str): random seed for init_guess_method
'''
AbstractPlanner.__init__(**locals())
self.has_optimizer = False
self.is_converged = False
self.budget = 10**8
def __init__(self,
goal='minimize',
stddev=0.5,
init_guess=None,
init_guess_method='random',
init_guess_seed=None):
"""
Covariance Matrix Adaptation Evolution Strategy (CMA-ES) planner.
Args:
goal (str): The optimization goal, either 'minimize' or 'maximize'. Default is 'minimize'.
stddev (float): Initial standard deviation.
init_guess (array, optional): initial guess for the optimization
init_guess_method (str): method to construct initial guesses if init_guess is not provided.
Choose from: random
init_guess_seed (str): random seed for init_guess_method
"""
AbstractPlanner.__init__(**locals())
self.has_optimizer = False
self.is_converged = False
def __init__(self,
goal='minimize',
max_iters=10**8,
options={
'c1': 0.5,
'c2': 0.3,
'w': 0.9
},
particles=10):
"""
Particle swarm optimizer.
Args:
goal (str): The optimization goal, either 'minimize' or 'maximize'. Default is 'minimize'.
max_iters (int): The maximum number of iterations for the swarm to search.
options (dict): ???
particles (int): The number of particles in the swarm.
"""
AbstractPlanner.__init__(**locals())
self.has_optimizer = False
self.is_converged = False
def __init__(self,
goal='minimize',
batch_size=1,
exact_eval=True,
model_type='GP_MCMC',
acquisition_type='EI_MCMC'):
"""
Gaussian Process optimization as implemented in GPyOpt.
Args:
goal (str): The optimization goal, either 'minimize' or 'maximize'. Default is 'minimize'.
batch_size (int): size of the batch in which the objective is evaluated.
exact_eval (bool): whether the outputs are exact.
model_type (str): type of model to use as surrogate. 'GP': standard Gaussian process. 'GP_MCMC': Gaussian
process with prior in the hyper-parameters. 'sparseGP': sparse Gaussian process. 'warperdGP': warped
Gaussian process. 'InputWarpedGP': input warped Gaussian process. 'RF': random forest (scikit-learn).
acquisition_type (str): type of acquisition function to use. 'EI': expected improvement. 'EI_MCMC': integrated
expected improvement (requires GP_MCMC model). 'MPI': maximum probability of improvement. 'MPI_MCMC':
maximum probability of improvement (requires GP_MCMC model). 'LCB': GP-Lower confidence bound. 'LCB_MCMC':
integrated GP-Lower confidence bound (requires GP_MCMC model).
"""
AbstractPlanner.__init__(**locals())
def __init__(self, goal='minimize', 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, seed=None,
init_guess=None, init_guess_method='random', init_guess_seed=None):
"""
Find the global minimum of a function using the basin-hopping algorithm
Parameters
----------
goal (str): The optimization goal, either 'minimize' or 'maximize'. Default is 'minimize'.
func : callable ``f(x, *args)``
Function to be optimized. ``args`` can be passed as an optional item
in the dict ``minimizer_kwargs``
x0 : ndarray
Initial guess.
niter : integer, optional
The number of basin hopping iterations
T : float, optional
The "temperature" parameter for the accept or reject criterion. Higher
"temperatures" mean that larger jumps in function value will be
accepted. For best results ``T`` should be comparable to the
separation
(in function value) between local minima.
stepsize : float, optional
initial step size for use in the random displacement.
minimizer_kwargs : dict, optional
Extra keyword arguments to be passed to the minimizer
``scipy.optimize.minimize()`` Some important options could be:
method : str
The minimization method (e.g. ``"L-BFGS-B"``)
args : tuple
Extra arguments passed to the objective function (``func``) and
its derivatives (Jacobian, Hessian).
take_step : callable ``take_step(x)``, optional
Replace the default step taking routine with this routine. The default
step taking routine is a random displacement of the coordinates, but
other step taking algorithms may be better for some systems.
``take_step`` can optionally have the attribute ``take_step.stepsize``.
If this attribute exists, then ``basinhopping`` will adjust
``take_step.stepsize`` in order to try to optimize the global minimum
search.
accept_test : callable, ``accept_test(f_new=f_new, x_new=x_new, f_old=fold, x_old=x_old)``, optional
Define a test which will be used to judge whether or not to accept the
step. This will be used in addition to the Metropolis test based on
"temperature" ``T``. The acceptable return values are True,
False, or ``"force accept"``. If any of the tests return False
then the step is rejected. If the latter, then this will override any
other tests in order to accept the step. This can be used, for example,
to forcefully escape from a local minimum that ``basinhopping`` is
trapped in.
callback : callable, ``callback(x, f, accept)``, optional
A callback function which will be called for all minima found. ``x``
and ``f`` are the coordinates and function value of the trial minimum,
and ``accept`` is whether or not that minimum was accepted. This can be
used, for example, to save the lowest N minima found. Also,
``callback`` can be used to specify a user defined stop criterion by
optionally returning True to stop the ``basinhopping`` routine.
interval : integer, optional
interval for how often to update the ``stepsize``
disp : bool, optional
Set to True to print status messages
niter_success : integer, optional
Stop the run if the global minimum candidate remains the same for this
number of iterations.
seed : int or `np.random.RandomState`, optional
If `seed` is not specified the `np.RandomState` singleton is used.
If `seed` is an int, a new `np.random.RandomState` instance is used,
seeded with seed.
If `seed` is already a `np.random.RandomState instance`, then that
`np.random.RandomState` instance is used.
Specify `seed` for repeatable minimizations. The random numbers
generated with this seed only affect the default Metropolis
`accept_test` and the default `take_step`. If you supply your own
`take_step` and `accept_test`, and these functions use random
number generation, then those functions are responsible for the state
of their random number generator.
init_guess (array, optional): initial guess for the optimization
init_guess_method (str): method to construct initial guesses if init_guess is not provided.
Choose from: random
init_guess_seed (str): random seed for init_guess_method
Returns
-------
res : OptimizeResult
The optimization result represented as a ``OptimizeResult`` object. Important
attributes are: ``x`` the solution array, ``fun`` the value of the
function at the solution, and ``message`` which describes the cause of
the termination. The ``OptimzeResult`` object returned by the selected
minimizer at the lowest minimum is also contained within this object
and can be accessed through the ``lowest_optimization_result`` attribute.
See `OptimizeResult` for a description of other attributes.
See Also
--------
minimize :
The local minimization function called once for each basinhopping step.
``minimizer_kwargs`` is passed to this routine.
Notes
-----
Basin-hopping is a stochastic algorithm which attempts to find the global
minimum of a smooth scalar function of one or more variables [1]_ [2]_ [3]_
[4]_. The algorithm in its current form was described by David Wales and
Jonathan Doye [2]_ http://www-wales.ch.cam.ac.uk/.
The algorithm is iterative with each cycle composed of the following
features
1) random perturbation of the coordinates
2) local minimization
3) accept or reject the new coordinates based on the minimized function
value
The acceptance test used here is the Metropolis criterion of standard Monte
Carlo algorithms, although there are many other possibilities [3]_.
This global minimization method has been shown to be extremely efficient
for a wide variety of problems in physics and chemistry. It is
particularly useful when the function has many minima separated by large
barriers. See the Cambridge Cluster Database
http://www-wales.ch.cam.ac.uk/CCD.html for databases of molecular systems
that have been optimized primarily using basin-hopping. This database
includes minimization problems exceeding 300 degrees of freedom.
See the free software program GMIN (http://www-wales.ch.cam.ac.uk/GMIN) for
a Fortran implementation of basin-hopping. This implementation has many
different variations of the procedure described above, including more
advanced step taking algorithms and alternate acceptance criterion.
For stochastic global optimization there is no way to determine if the true
global minimum has actually been found. Instead, as a consistency check,
the algorithm can be run from a number of different random starting points
to ensure the lowest minimum found in each example has converged to the
global minimum. For this reason ``basinhopping`` will by default simply
run for the number of iterations ``niter`` and return the lowest minimum
found. It is left to the user to ensure that this is in fact the global
minimum.
Choosing ``stepsize``: This is a crucial parameter in ``basinhopping`` and
depends on the problem being solved. Ideally it should be comparable to
the typical separation between local minima of the function being
optimized. ``basinhopping`` will, by default, adjust ``stepsize`` to find
an optimal value, but this may take many iterations. You will get quicker
results if you set a sensible value for ``stepsize``.
Choosing ``T``: The parameter ``T`` is the temperature used in the
metropolis criterion. Basinhopping steps are accepted with probability
``1`` if ``func(xnew) < func(xold)``, or otherwise with probability::
exp( -(func(xnew) - func(xold)) / T )
So, for best results, ``T`` should to be comparable to the typical
difference in function values between local minima.
.. versionadded:: 0.12.0
References
----------
.. [1] Wales, David J. 2003, Energy Landscapes, Cambridge University Press,
Cambridge, UK.
.. [2] Wales, D J, and Doye J P K, Global Optimization by Basin-Hopping and
the Lowest Energy Structures of Lennard-Jones Clusters Containing up to
110 Atoms. Journal of Physical Chemistry A, 1997, 101, 5111.
.. [3] Li, Z. and Scheraga, H. A., Monte Carlo-minimization approach to the
multiple-minima problem in protein folding, Proc. Natl. Acad. Sci. USA,
1987, 84, 6611.
.. [4] Wales, D. J. and Scheraga, H. A., Global optimization of clusters,
crystals, and biomolecules, Science, 1999, 285, 1368.
Examples
--------
The following example is a one-dimensional minimization problem, with many
local minima superimposed on a parabola.
>>> from scipy.optimize import basinhopping
>>> func = lambda x: np.cos(14.5 * x - 0.3) + (x + 0.2) * x
>>> x0=[1.]
Basinhopping, internally, uses a local minimization algorithm. We will use
the parameter ``minimizer_kwargs`` to tell basinhopping which algorithm to
use and how to set up that minimizer. This parameter will be passed to
``scipy.optimize.minimize()``.
>>> minimizer_kwargs = {"method": "BFGS"}
>>> ret = basinhopping(func, x0, minimizer_kwargs=minimizer_kwargs,
... niter=200)
>>> print("global minimum: x = %.4f, f(x0) = %.4f" % (ret.x, ret.fun))
global minimum: x = -0.1951, f(x0) = -1.0009
Next consider a two-dimensional minimization problem. Also, this time we
will use gradient information to significantly speed up the search.
>>> def func2d(x):
... f = np.cos(14.5 * x[0] - 0.3) + (x[1] + 0.2) * x[1] + (x[0] +
... 0.2) * x[0]
... df = np.zeros(2)
... df[0] = -14.5 * np.sin(14.5 * x[0] - 0.3) + 2. * x[0] + 0.2
... df[1] = 2. * x[1] + 0.2
... return f, df
We'll also use a different local minimization algorithm. Also we must tell
the minimizer that our function returns both energy and gradient (jacobian)
>>> minimizer_kwargs = {"method":"L-BFGS-B", "jac":True}
>>> x0 = [1.0, 1.0]
>>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs,
... niter=200)
>>> print("global minimum: x = [%.4f, %.4f], f(x0) = %.4f" % (ret.x[0],
... ret.x[1],
... ret.fun))
global minimum: x = [-0.1951, -0.1000], f(x0) = -1.0109
Here is an example using a custom step taking routine. Imagine you want
the first coordinate to take larger steps then the rest of the coordinates.
This can be implemented like so:
>>> class MyTakeStep(object):
... def __init__(self, stepsize=0.5):
... self.stepsize = stepsize
... def __call__(self, x):
... s = self.stepsize
... x[0] += np.random.uniform(-2.*s, 2.*s)
... x[1:] += np.random.uniform(-s, s, x[1:].shape)
... return x
Since ``MyTakeStep.stepsize`` exists basinhopping will adjust the magnitude
of ``stepsize`` to optimize the search. We'll use the same 2-D function as
before
>>> mytakestep = MyTakeStep()
>>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs,
... niter=200, take_step=mytakestep)
>>> print("global minimum: x = [%.4f, %.4f], f(x0) = %.4f" % (ret.x[0],
... ret.x[1],
... ret.fun))
global minimum: x = [-0.1951, -0.1000], f(x0) = -1.0109
Now let's do an example using a custom callback function which prints the
value of every minimum found
>>> def print_fun(x, f, accepted):
... print("at minimum %.4f accepted %d" % (f, int(accepted)))
We'll run it for only 10 basinhopping steps this time.
>>> np.random.seed(1)
>>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs,
... niter=10, callback=print_fun)
at minimum 0.4159 accepted 1
at minimum -0.9073 accepted 1
at minimum -0.1021 accepted 1
at minimum -0.1021 accepted 1
at minimum 0.9102 accepted 1
at minimum 0.9102 accepted 1
at minimum 2.2945 accepted 0
at minimum -0.1021 accepted 1
at minimum -1.0109 accepted 1
at minimum -1.0109 accepted 1
The minimum at -1.0109 is actually the global minimum, found already on the
8th iteration.
Now let's implement bounds on the problem using a custom ``accept_test``:
>>> class MyBounds(object):
... def __init__(self, xmax=[1.1,1.1], xmin=[-1.1,-1.1] ):
... self.xmax = np.array(xmax)
... self.xmin = np.array(xmin)
... def __call__(self, **kwargs):
... x = kwargs["x_new"]
... tmax = bool(np.all(x <= self.xmax))
... tmin = bool(np.all(x >= self.xmin))
... return tmax and tmin
>>> mybounds = MyBounds()
>>> ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs,
... niter=10, accept_test=mybounds)
"""
kwargs = locals().copy()
self.goal = kwargs['goal']
for attr in ['self', 'goal', 'init_guess', 'init_guess_method', 'init_guess_seed']:
del kwargs[attr]
self.kwargs = kwargs
self.has_minimizer = False
self.is_converged = False
AbstractPlanner.__init__(**locals())
def __init__(self, *args, **kwargs):
AbstractPlanner.__init__(self, *args, **kwargs)
self.has_minimizer = False
self.is_converged = False