SciPy generators

xopt.generators.sequential.neldermead.NelderMeadGenerator

NelderMeadGenerator(**kwargs)

Bases: SequentialGenerator

Nelder-Mead algorithm from SciPy in Xopt's Generator form. Converted to use a state machine to resume in exactly the last state.

Attributes:

Name	Type	Description
name	str	The name of the generator.
initial_point	Optional[Dict[str, float]]	Initial point for the optimization.
initial_simplex	Optional[Dict[str, Union[List[float], ndarray]]]	Initial simplex for the optimization.
adaptive	bool	Change hyperparameters based on dimensionality.
current_state	SimplexState	Current state of the simplex.
future_state	Optional[SimplexState]	Future state of the simplex.
x	Optional[ndarray]	Current x value.
y	Optional[float]	Current y value.

Methods:

Name	Description
add_data	Add new data to the generator.
generate	Generate a specified number of candidate samples.
_call_algorithm	Call the Nelder-Mead algorithm.
simplex	Returns the simplex in the current state.

Source code in xopt/generators/sequential/neldermead.py

def __init__(self, **kwargs):
    super().__init__(**kwargs)

    self._saved_options = self.model_dump(
        exclude={"current_state", "future_state"}
    ).copy()  # Used to keep track of changed options

    if self.initial_simplex:
        self._initial_simplex = np.array(
            [self.initial_simplex[k] for k in self.vocs.variable_names]
        ).T
    else:
        self._initial_simplex = None

Attributes

xopt.generators.sequential.neldermead.NelderMeadGenerator.simplex property

simplex

Returns the simplex in the current state.

Returns:

Type	Description
Dict[str, ndarray]	The simplex in the current state.

xopt.generators.sequential.neldermead.NelderMeadGenerator.x0 property

x0

Raw internal initial point for convenience. If initial_point is set, it will be used. Otherwise, if data is set, the last point will be used.

Returns:

Type	Description
ndarray	The initial point as a NumPy array.

xopt.generators.sequential.rcds.RCDSGenerator

RCDSGenerator(**kwargs)

Bases: SequentialGenerator

RCDS algorithm.

Reference: An algorithm for online optimization of accelerators Huang, X., Corbett, J., Safranek, J. and Wu, J. doi: 10.1016/j.nima.2013.05.046

This algorithm must be stepped serially.

Attributes:

Name	Type	Description
name	str	Name of the generator.
x0	Optional[list]	Initial solution vector.
init_mat	Optional[ndarray]	Initial direction matrix.
noise	PositiveFloat	Estimated noise level.
step	PositiveFloat	Step size for the optimization.
_ub	ndarray	Upper bounds of the variables.
_lb	ndarray	Lower bounds of the variables.
_powell	PowellMainStateMachine	Instance of the PowellMainStateMachine.
_sign	int	Sign of the objective function (1 for MINIMIZE, -1 for MAXIMIZE).

Source code in xopt/generator.py

def __init__(self, **kwargs):
    """
    Initialize the generator.

    """
    super().__init__(**kwargs)
    logger.info(f"Initialized generator {self.name}")

xopt.generators.sequential.extremumseeking.ExtremumSeekingGenerator

ExtremumSeekingGenerator(**kwargs)

Bases: SequentialGenerator

Extremum seeking algorithm.

Reference: Extremum Seeking-Based Control System for Particle Accelerator Beam Loss Minimization A. Scheinker, E. -C. Huang and C. Taylor doi: 10.1109/TCST.2021.3136133

This algorithm must be stepped serially.

Attributes:

Name	Type	Description
name	str	The name of the generator.
k	PositiveFloat	Feedback gain.
oscillation_size	PositiveFloat	Oscillation size.
decay_rate	PositiveFloat	Decay rate.
_nES	int	Number of extremum seeking parameters.
_wES	ndarray	Frequencies for extremum seeking.
_dtES	float	Time step for extremum seeking.
_aES	ndarray	Amplitudes for extremum seeking.
_p_ave	ndarray	Average of parameter bounds.
_p_diff	ndarray	Difference of parameter bounds.
_amplitude	float	Amplitude of oscillation.
_i	int	Evaluation counter.
_last_input	ndarray	Last input values.
_last_outcome	float	Last outcome value.

Methods:

Name	Description
add_data	Add new data to the generator.
p_normalize	Normalize parameters.
p_un_normalize	Un-normalize parameters.
generate	Generate a specified number of candidate samples.

Source code in xopt/generators/sequential/extremumseeking.py

def __init__(self, **kwargs):
    super().__init__(**kwargs)

    self._nES = len(self.vocs.variables)
    self._wES = np.linspace(1.0, 1.75, int(np.ceil(self._nES / 2)))
    self._dtES = 2 * np.pi / (10 * np.max(self._wES))
    self._aES = np.zeros(self._nES)
    for n in np.arange(self._nES):
        jw = int(np.floor(n / 2))
        self._aES[n] = self._wES[jw] * (self.oscillation_size) ** 2
    bound_low, bound_up = self.vocs.bounds
    self._p_ave = (bound_up + bound_low) / 2
    self._p_diff = bound_up - bound_low

Functions

xopt.generators.sequential.extremumseeking.ExtremumSeekingGenerator.p_normalize

p_normalize(p)

Normalize parameters.

Parameters:

Name	Type	Description	Default
p	ndarray	The parameters to normalize.	required

Returns:

Type	Description
ndarray	The normalized parameters.

Source code in xopt/generators/sequential/extremumseeking.py

def p_normalize(self, p: np.ndarray) -> np.ndarray:
    """
    Normalize parameters.

    Parameters
    ----------
    p : np.ndarray
        The parameters to normalize.

    Returns
    -------
    np.ndarray
        The normalized parameters.
    """
    p_norm = 2.0 * (p - self._p_ave) / self._p_diff
    return p_norm

xopt.generators.sequential.extremumseeking.ExtremumSeekingGenerator.p_un_normalize

p_un_normalize(p)

Un-normalize parameters.

Parameters:

Name	Type	Description	Default
p	ndarray	The parameters to un-normalize.	required

Returns:

Type	Description
ndarray	The un-normalized parameters.

Source code in xopt/generators/sequential/extremumseeking.py

def p_un_normalize(self, p: np.ndarray) -> np.ndarray:
    """
    Un-normalize parameters.

    Parameters
    ----------
    p : np.ndarray
        The parameters to un-normalize.

    Returns
    -------
    np.ndarray
        The un-normalized parameters.
    """
    p_un_norm = p * self._p_diff / 2.0 + self._p_ave
    return p_un_norm