rosenbrock module¶

The Rosenbrock analytic problem¶

Classes:

`RosenMF`([dimension])	RosenMF, a multi-fidelity Rosenbrock `MDODiscipline`, returns the value:
`Rosenbrock`([n_x, l_b, u_b, scalar_var, ...])	Rosenbrock `OptimizationProblem` uses the Rosenbrock objective function

class gemseo.problems.analytical.rosenbrock.RosenMF(dimension=2)[source]¶

Bases: gemseo.core.discipline.MDODiscipline

RosenMF, a multi-fidelity Rosenbrock MDODiscipline, returns the value:

\[\mathrm{fidelity} * \mathrm{Rosenbrock}(x)\]

where both \(\mathrm{fidelity}\) and \(x\) are provided as input data.

input_grammar¶

The input grammar.

Type: AbstractGrammar

output_grammar¶

The output grammar.

Type: AbstractGrammar

grammar_type¶

The type of grammar to be used for inputs and outputs declaration.

Type: str

comp_dir¶

The path to the directory of the discipline module file if any.

Type: str

data_processor¶

A tool to pre- and post-process discipline data.

Type: DataProcessor

re_exec_policy¶

The policy to re-execute the same discipline.

Type: str

residual_variables¶

The output variables to be considered as residuals; they shall be equal to zero.

Type: List[str]

jac¶

The Jacobians of the outputs wrt inputs of the form {output: {input: matrix}}.

Type: Dict[str, Dict[str, ndarray]]

exec_for_lin¶

Whether the last execution was due to a linearization.

Type: bool

name¶

The name of the discipline.

Type: str

cache¶

The cache containing one or several executions of the discipline according to the cache policy.

Type: AbstractCache

local_data¶

The last input and output data.

Type: Dict[str, Any]

The constructor defines the default inputs of the MDODiscipline, namely the default design parameter values and the fidelity.

Parameters

dimension (int) –

problem dimension

By default it is set to 2.

Attributes:

`APPROX_MODES`
`AVAILABLE_MODES`
`COMPLEX_STEP`
`FINITE_DIFFERENCES`
`HDF5_CACHE`
`JSON_GRAMMAR_TYPE`
`MEMORY_FULL_CACHE`
`N_CPUS`
`RE_EXECUTE_DONE_POLICY`
`RE_EXECUTE_NEVER_POLICY`
`SIMPLE_CACHE`
`SIMPLE_GRAMMAR_TYPE`
`STATUS_DONE`
`STATUS_FAILED`
`STATUS_PENDING`
`STATUS_RUNNING`
`STATUS_VIRTUAL`
`cache_tol`	The cache input tolerance.
`default_inputs`	The default inputs.
`exec_time`	The cumulated execution time of the discipline.
`grammar_type`	The grammar type.
`linearization_mode`	The linearization mode among `LINEARIZE_MODE_LIST`.
`n_calls`	The number of times the discipline was executed.
`n_calls_linearize`	The number of times the discipline was linearized.
`status`	The status of the discipline.
`time_stamps`

Methods:

`activate_time_stamps`()	Activate the time stamps.
`add_differentiated_inputs`([inputs])	Add inputs against which to differentiate the outputs.
`add_differentiated_outputs`([outputs])	Add outputs to be differentiated.
`add_status_observer`(obs)	Add an observer for the status.
`auto_get_grammar_file`([is_input, name, comp_dir])	Use a naming convention to associate a grammar file to a discipline.
`check_input_data`(input_data[, raise_exception])	Check the input data validity.
`check_jacobian`([input_data, derr_approx, ...])	Check if the analytical Jacobian is correct with respect to a reference one.
`check_output_data`([raise_exception])	Check the output data validity.
`deactivate_time_stamps`()	Deactivate the time stamps.
`deserialize`(in_file)	Deserialize a discipline from a file.
`execute`([input_data])	Execute the discipline.
`get_all_inputs`()	Return the local input data as a list.
`get_all_outputs`()	Return the local output data as a list.
`get_attributes_to_serialize`()	Define the names of the attributes to be serialized.
`get_data_list_from_dict`(keys, data_dict)	Filter the dict from a list of keys or a single key.
`get_expected_dataflow`()	Return the expected data exchange sequence.
`get_expected_workflow`()	Return the expected execution sequence.
`get_input_data`()	Return the local input data as a dictionary.
`get_input_data_names`()	Return the names of the input variables.
`get_input_output_data_names`()	Return the names of the input and output variables.
`get_inputs_asarray`()	Return the local output data as a large NumPy array.
`get_inputs_by_name`(data_names)	Return the local data associated with input variables.
`get_local_data_by_name`(data_names)	Return the local data of the discipline associated with variables names.
`get_output_data`()	Return the local output data as a dictionary.
`get_output_data_names`()	Return the names of the output variables.
`get_outputs_asarray`()	Return the local input data as a large NumPy array.
`get_outputs_by_name`(data_names)	Return the local data associated with output variables.
`get_sub_disciplines`()	Return the sub-disciplines if any.
`is_all_inputs_existing`(data_names)	Test if several variables are discipline inputs.
`is_all_outputs_existing`(data_names)	Test if several variables are discipline outputs.
`is_input_existing`(data_name)	Test if a variable is a discipline input.
`is_output_existing`(data_name)	Test if a variable is a discipline output.
`is_scenario`()	Whether the discipline is a scenario.
`linearize`([input_data, force_all, force_no_exec])	Execute the linearized version of the code.
`notify_status_observers`()	Notify all status observers that the status has changed.
`remove_status_observer`(obs)	Remove an observer for the status.
`reset_statuses_for_run`()	Set all the statuses to `PENDING`.
`serialize`(out_file)	Serialize the discipline and store it in a file.
`set_cache_policy`([cache_type, ...])	Set the type of cache to use and the tolerance level.
`set_disciplines_statuses`(status)	Set the sub-disciplines statuses.
`set_jacobian_approximation`([...])	Set the Jacobian approximation method.
`set_optimal_fd_step`([outputs, inputs, ...])	Compute the optimal finite-difference step.
`store_local_data`(**kwargs)	Store discipline data in local data.

APPROX_MODES = ['finite_differences', 'complex_step']¶

AVAILABLE_MODES = ('auto', 'direct', 'adjoint', 'reverse', 'finite_differences', 'complex_step')¶

COMPLEX_STEP = 'complex_step'¶

FINITE_DIFFERENCES = 'finite_differences'¶

HDF5_CACHE = 'HDF5Cache'¶

JSON_GRAMMAR_TYPE = 'JSONGrammar'¶

MEMORY_FULL_CACHE = 'MemoryFullCache'¶

N_CPUS = 2¶

RE_EXECUTE_DONE_POLICY = 'RE_EXEC_DONE'¶

RE_EXECUTE_NEVER_POLICY = 'RE_EXEC_NEVER'¶

SIMPLE_CACHE = 'SimpleCache'¶

SIMPLE_GRAMMAR_TYPE = 'SimpleGrammar'¶

STATUS_DONE = 'DONE'¶

STATUS_FAILED = 'FAILED'¶

STATUS_PENDING = 'PENDING'¶

STATUS_RUNNING = 'RUNNING'¶

STATUS_VIRTUAL = 'VIRTUAL'¶

classmethod activate_time_stamps()¶

Activate the time stamps.

For storing start and end times of execution and linearizations.

Return type: None

add_differentiated_inputs(inputs=None)¶

Add inputs against which to differentiate the outputs.

This method updates _differentiated_inputs with inputs.

Parameters

inputs (Optional[Iterable[str]]) –

The input variables against which to differentiate the outputs. If None, all the inputs of the discipline are used.

By default it is set to None.

Raises

ValueError – When the inputs wrt which differentiate the discipline are not inputs of the latter.

Return type

None

add_differentiated_outputs(outputs=None)¶

Add outputs to be differentiated.

This method updates _differentiated_outputs with outputs.

Parameters

outputs (Optional[Iterable[str]]) –

The output variables to be differentiated. If None, all the outputs of the discipline are used.

By default it is set to None.

Raises

ValueError – When the outputs to differentiate are not discipline outputs.

Return type

None

add_status_observer(obs)¶

Add an observer for the status.

Add an observer for the status to be notified when self changes of status.

Parameters: obs (Any) – The observer to add.
Return type: None

auto_get_grammar_file(is_input=True, name=None, comp_dir=None)¶

Use a naming convention to associate a grammar file to a discipline.

This method searches in a directory for either an input grammar file named name + "_input.json" or an output grammar file named``name + “_output.json”``.

Parameters

is_input (bool) –
If True, autodetect the input grammar file; otherwise, autodetect the output grammar file.

By default it is set to True.
name (Optional[str]) –
The name to be searched in the file names. If None, use the name name of the discipline.

By default it is set to None.
comp_dir (Optional[Union[str, pathlib.Path]]) –
The directory in which to search the grammar file. If None, use comp_dir.

By default it is set to None.

Returns

The grammar file path.

Return type

pathlib.Path

property cache_tol¶

The cache input tolerance.

This is the tolerance for equality of the inputs in the cache. If norm(stored_input_data-input_data) <= cache_tol * norm(stored_input_data), the cached data for stored_input_data is returned when calling self.execute(input_data).

check_input_data(input_data, raise_exception=True)¶

Check the input data validity.

Parameters

input_data (Dict[str, Any]) – The input data needed to execute the discipline according to the discipline input grammar.
raise_exception (bool) –

By default it is set to True.

Return type

None

check_jacobian(input_data=None, derr_approx='finite_differences', step=1e-07, threshold=1e-08, linearization_mode='auto', inputs=None, outputs=None, parallel=False, n_processes=2, use_threading=False, wait_time_between_fork=0, auto_set_step=False, plot_result=False, file_path='jacobian_errors.pdf', show=False, figsize_x=10, figsize_y=10, reference_jacobian_path=None, save_reference_jacobian=False, indices=None)¶

Check if the analytical Jacobian is correct with respect to a reference one.

If reference_jacobian_path is not None and save_reference_jacobian is True, compute the reference Jacobian with the approximation method and save it in reference_jacobian_path.

If reference_jacobian_path is not None and save_reference_jacobian is False, do not compute the reference Jacobian but read it from reference_jacobian_path.

If reference_jacobian_path is None, compute the reference Jacobian without saving it.

Parameters

input_data –
The input data needed to execute the discipline according to the discipline input grammar. If None, use the default_inputs.

By default it is set to None.
derr_approx –
The approximation method, either “complex_step” or “finite_differences”.

By default it is set to finite_differences.
threshold –
The acceptance threshold for the Jacobian error.

By default it is set to 1e-08.
linearization_mode –
the mode of linearization: direct, adjoint or automated switch depending on dimensions of inputs and outputs (Default value = ‘auto’)

By default it is set to auto.
inputs –
The names of the inputs wrt which to differentiate the outputs.

By default it is set to None.
outputs –
The names of the outputs to be differentiated.

By default it is set to None.
step –
The differentiation step.

By default it is set to 1e-07.
parallel –
Whether to differentiate the discipline in parallel.

By default it is set to False.
n_processes –
The maximum number of processors on which to run.

By default it is set to 2.
use_threading –
Whether to use threads instead of processes to parallelize the execution; multiprocessing will copy (serialize) all the disciplines, while threading will share all the memory This is important to note if you want to execute the same discipline multiple times, you shall use multiprocessing.

By default it is set to False.
wait_time_between_fork –
The time waited between two forks of the process / thread.

By default it is set to 0.
auto_set_step –
Whether to compute the optimal step for a forward first order finite differences gradient approximation.

By default it is set to False.
plot_result –
Whether to plot the result of the validation (computed vs approximated Jacobians).

By default it is set to False.
file_path –
The path to the output file if plot_result is True.

By default it is set to jacobian_errors.pdf.
show –
Whether to open the figure.

By default it is set to False.
figsize_x –
The x-size of the figure in inches.

By default it is set to 10.
figsize_y –
The y-size of the figure in inches.

By default it is set to 10.
reference_jacobian_path –
The path of the reference Jacobian file.

By default it is set to None.
save_reference_jacobian –
Whether to save the reference Jacobian.

By default it is set to False.
indices –
The indices of the inputs and outputs for the different sub-Jacobian matrices, formatted as {variable_name: variable_components} where variable_components can be either an integer, e.g. 2 a sequence of integers, e.g. [0, 3], a slice, e.g. slice(0,3), the ellipsis symbol (…) or None, which is the same as ellipsis. If a variable name is missing, consider all its components. If None, consider all the components of all the inputs and outputs.

By default it is set to None.

Returns

Whether the analytical Jacobian is correct with respect to the reference one.

check_output_data(raise_exception=True)¶

Check the output data validity.

Parameters

raise_exception (bool) –

Whether to raise an exception when the data is invalid.

By default it is set to True.

Return type

None

classmethod deactivate_time_stamps()¶

Deactivate the time stamps.

For storing start and end times of execution and linearizations.

Return type: None

property default_inputs¶

The default inputs.

Raises: TypeError – When the default inputs are not passed as a dictionary.

static deserialize(in_file)¶

Deserialize a discipline from a file.

Parameters: in_file (Union[str, pathlib.Path]) – The path to the file containing the discipline.
Returns: The discipline instance.
Return type: gemseo.core.discipline.MDODiscipline

property exec_time¶: The cumulated execution time of the discipline.

Note

This property is multiprocessing safe.

execute(input_data=None)¶

Execute the discipline.

This method executes the discipline:

Adds the default inputs to the input_data if some inputs are not defined in input_data but exist in _default_inputs.
Checks whether the last execution of the discipline was called with identical inputs, ie. cached in cache; if so, directly returns self.cache.get_output_cache(inputs).
Caches the inputs.
Checks the input data against input_grammar.
If data_processor is not None, runs the preprocessor.
Updates the status to RUNNING.
Calls the _run() method, that shall be defined.
If data_processor is not None, runs the postprocessor.
Checks the output data.
Caches the outputs.
Updates the status to DONE or FAILED.
Updates summed execution time.

Parameters

input_data (Optional[Dict[str, Any]]) –

The input data needed to execute the discipline according to the discipline input grammar. If None, use the default_inputs.

By default it is set to None.

Returns

The discipline local data after execution.

Return type

Dict[str, Any]

get_all_inputs()¶

Return the local input data as a list.

The order is given by get_input_data_names().

Returns: The local input data.
Return type: List[Any]

get_all_outputs()¶

Return the local output data as a list.

The order is given by get_output_data_names().

Returns: The local output data.
Return type: List[Any]

get_attributes_to_serialize()¶

Define the names of the attributes to be serialized.

Shall be overloaded by disciplines

Returns: The names of the attributes to be serialized.

static get_data_list_from_dict(keys, data_dict)¶

Filter the dict from a list of keys or a single key.

If keys is a string, then the method return the value associated to the key. If keys is a list of strings, then the method returns a generator of value corresponding to the keys which can be iterated.

Parameters

keys (Union[str, Iterable]) – One or several names.
data_dict (Dict[str, Any]) – The mapping from which to get the data.

Returns

Either a data or a generator of data.

Return type

Union[Any, Generator[Any]]

get_expected_dataflow()¶

Return the expected data exchange sequence.

This method is used for the XDSM representation.

The default expected data exchange sequence is an empty list.

See also

https://en.wikipedia.org/wiki/Numerical_differentiation and “Numerical Algorithms and Digital Representation”, Knut Morken , Chapter 11, “Numerical Differenciation”

Parameters

inputs –
The inputs wrt which the outputs are linearized. If None, use the _differentiated_inputs.

By default it is set to None.
outputs –
The outputs to be linearized. If None, use the _differentiated_outputs.

By default it is set to None.
force_all –
Whether to consider all the inputs and outputs of the discipline;

By default it is set to False.
print_errors –
Whether to display the estimated errors.

By default it is set to False.
numerical_error –
The numerical error associated to the calculation of f. By default, this is the machine epsilon (appx 1e-16), but can be higher when the calculation of f requires a numerical resolution.

By default it is set to 2.220446049250313e-16.

Returns

The estimated errors of truncation and cancellation error.

Raises

ValueError – When the Jacobian approximation method has not been set.

property status¶: The status of the discipline.

store_local_data(**kwargs)¶

Store discipline data in local data.

Parameters

kwargs – The data to be stored in local_data.
**kwargs (Any) –

Return type

None

time_stamps = None¶

class gemseo.problems.analytical.rosenbrock.Rosenbrock(n_x=2, l_b=- 2.0, u_b=2.0, scalar_var=False, initial_guess=None)[source]¶

Bases: gemseo.algos.opt_problem.OptimizationProblem

Rosenbrock OptimizationProblem uses the Rosenbrock objective function

\[f(x) = \sum_{i=2}^{n_x} 100(x_{i} - x_{i-1}^2)^2 + (1 - x_{i-1})^2\]

with the default DesignSpace \([-0.2,0.2]^{n_x}\).

The constructor initializes the Rosenbrock OptimizationProblem by defining the DesignSpace and the objective function.

Parameters

n_x (int) –
problem dimension

By default it is set to 2.
l_b (float) –
lower bound (common value to all variables)

By default it is set to -2.0.
u_b (float) –
upper bound (common value to all variables)

By default it is set to 2.0.
scalar_var (bool) –
if True the design space will contain only scalar variables (as many as the problem dimension); if False the design space will contain a single multidimensional variable (whose size equals the problem dimension)

By default it is set to False.
initial_guess (numpy array) –
initial guess for optimal solution

By default it is set to None.

Attributes:

`AVAILABLE_PB_TYPES`
`COMPLEX_STEP`
`CONSTRAINTS_GROUP`
`DESIGN_SPACE_ATTRS`
`DESIGN_SPACE_GROUP`
`DESIGN_VAR_NAMES`
`DESIGN_VAR_SIZE`
`DIFFERENTIATION_METHODS`
`FINITE_DIFFERENCES`
`FUNCTIONS_ATTRS`
`GGOBI_FORMAT`
`HDF5_FORMAT`
`LINEAR_PB`
`NON_LINEAR_PB`
`NO_DERIVATIVES`
`OBJECTIVE_GROUP`
`OPTIM_DESCRIPTION`
`OPT_DESCR_GROUP`
`SOLUTION_GROUP`
`USER_GRAD`
`differentiation_method`	The differentiation method.
`dimension`	The dimension of the design space.
`is_mono_objective`	Whether the optimization problem is mono-objective.
`objective`	The objective function.
`parallel_differentiation`	Whether to approximate the derivatives in parallel.
`parallel_differentiation_options`	The options to approximate the derivatives in parallel.

Methods:

`add_callback`(callback_func[, each_new_iter, ...])	Add a callback function after each store operation or new iteration.
`add_constraint`(cstr_func[, value, ...])	Add a constraint (equality and inequality) to the optimization problem.
`add_eq_constraint`(cstr_func[, value])	Add an equality constraint to the optimization problem.
`add_ineq_constraint`(cstr_func[, value, positive])	Add an inequality constraint to the optimization problem.
`add_observable`(obs_func[, new_iter])	Add a function to be observed.
`aggregate_constraint`(constr_id[, method, groups])	Aggregates a constraint to generate a reduced dimension constraint.
`change_objective_sign`()	Change the objective function sign in order to minimize its opposite.
`check`()	Check if the optimization problem is ready for run.
`check_format`(input_function)	Check that a function is an instance of `MDOFunction`.
`clear_listeners`()	Clear all the listeners.
`evaluate_functions`([x_vect, eval_jac, ...])	Compute the objective and the constraints.
`execute_observables_callback`(last_x)	The callback function to be passed to the database.
`export_hdf`(file_path[, append])	Export the optimization problem to an HDF file.
`export_to_dataset`([name, by_group, ...])	Export the database of the optimization problem to a `Dataset`.
`get_active_ineq_constraints`(x_vect[, tol])	For each constraint, indicate if its different components are active.
`get_all_functions`()	Retrieve all the functions of the optimization problem.
`get_all_functions_names`()	Retrieve the names of all the function of the optimization problem.
`get_best_infeasible_point`()	Retrieve the best infeasible point within a given tolerance.
`get_constraints_names`()	Retrieve the names of the constraints.
`get_constraints_number`()	Retrieve the number of constraints.
`get_data_by_names`(names[, as_dict, ...])	Return the data for specific names of variables.
`get_design_variable_names`()	Retrieve the names of the design variables.
`get_dimension`()	Retrieve the total number of design variables.
`get_eq_constraints`()	Retrieve all the equality constraints.
`get_eq_constraints_number`()	Retrieve the number of equality constraints.
`get_eq_cstr_total_dim`()	Retrieve the total dimension of the equality constraints.
`get_feasible_points`()	Retrieve the feasible points within a given tolerance.
`get_functions_dimensions`()	Return the dimensions of the outputs of the problem functions.
`get_ineq_constraints`()	Retrieve all the inequality constraints.
`get_ineq_constraints_number`()	Retrieve the number of inequality constraints.
`get_ineq_cstr_total_dim`()	Retrieve the total dimension of the inequality constraints.
`get_nonproc_constraints`()	Retrieve the non-processed constraints.
`get_nonproc_objective`()	Retrieve the non-processed objective function.
`get_number_of_unsatisfied_constraints`(...)	Return the number of scalar constraints not satisfied by design variables.
`get_objective_name`()	Retrieve the name of the objective function.
`get_observable`(name)	Retrieve an observable from its name.
`get_optimum`()	Return the optimum solution within a given feasibility tolerances.
`get_scalar_constraints_names`()	Return the names of the scalar constraints.
`get_solution`()	Return the theoretical optimal value.
`get_violation_criteria`(x_vect)	Compute a violation measure associated to an iteration.
`get_x0_normalized`()	Return the current values of the design variables after normalization.
`has_constraints`()	Check if the problem has equality or inequality constraints.
`has_eq_constraints`()	Check if the problem has equality constraints.
`has_ineq_constraints`()	Check if the problem has inequality constraints.
`has_nonlinear_constraints`()	Check if the problem has non-linear constraints.
`import_hdf`(file_path[, x_tolerance])	Import an optimization history from an HDF file.
`is_max_iter_reached`()	Check if the maximum amount of iterations has been reached.
`is_point_feasible`(out_val[, constraints])	Check if a point is feasible.
`preprocess_functions`([normalize, ...])	Pre-process all the functions and eventually the gradient.
`repr_constraint`(func, ctype[, value, positive])	Express a constraint as a string expression.

AVAILABLE_PB_TYPES = ['linear', 'non-linear']¶

COMPLEX_STEP = 'complex_step'¶

CONSTRAINTS_GROUP = 'constraints'¶

DESIGN_SPACE_ATTRS = ['u_bounds', 'l_bounds', 'x_0', 'x_names', 'dimension']¶

DESIGN_SPACE_GROUP = 'design_space'¶

DESIGN_VAR_NAMES = 'x_names'¶

DESIGN_VAR_SIZE = 'x_size'¶

DIFFERENTIATION_METHODS = ['user', 'complex_step', 'finite_differences', 'no_derivatives']¶

FINITE_DIFFERENCES = 'finite_differences'¶

FUNCTIONS_ATTRS = ['objective', 'constraints']¶

GGOBI_FORMAT = 'ggobi'¶

HDF5_FORMAT = 'hdf5'¶

LINEAR_PB = 'linear'¶

NON_LINEAR_PB = 'non-linear'¶

NO_DERIVATIVES = 'no_derivatives'¶

OBJECTIVE_GROUP = 'objective'¶

OPTIM_DESCRIPTION = ['minimize_objective', 'fd_step', 'differentiation_method', 'pb_type', 'ineq_tolerance', 'eq_tolerance']¶

OPT_DESCR_GROUP = 'opt_description'¶

SOLUTION_GROUP = 'solution'¶

USER_GRAD = 'user'¶

add_callback(callback_func, each_new_iter=True, each_store=False)¶

Add a callback function after each store operation or new iteration.

Parameters

callback_func (Callable) – A function to be called after some event.
each_new_iter (bool) –
If True, then callback at every iteration.

By default it is set to True.
each_store (bool) –
If True, then callback at every call to Database.store.

By default it is set to False.

Return type

None

add_constraint(cstr_func, value=None, cstr_type=None, positive=False)¶

Add a constraint (equality and inequality) to the optimization problem.

Parameters

cstr_func (MDOFunction) – The constraint.
value (Optional[value]) –
The value for which the constraint is active. If None, this value is 0.

By default it is set to None.
cstr_type (Optional[str]) –
The type of the constraint. Either equality or inequality.

By default it is set to None.
positive (bool) –
If True, then the inequality constraint is positive.

By default it is set to False.

Raises

TypeError – When the constraint of a linear optimization problem is not an MDOLinearFunction.
ValueError – When the type of the constraint is missing.

Return type

None

add_eq_constraint(cstr_func, value=None)¶

Add an equality constraint to the optimization problem.

Parameters

cstr_func (gemseo.core.mdofunctions.mdo_function.MDOFunction) – The constraint.
value (Optional[float]) –
The value for which the constraint is active. If None, this value is 0.

By default it is set to None.

Return type

None

add_ineq_constraint(cstr_func, value=None, positive=False)¶

Add an inequality constraint to the optimization problem.

Parameters

cstr_func (MDOFunction) – The constraint.
value (Optional[value]) –
The value for which the constraint is active. If None, this value is 0.

By default it is set to None.
positive (bool) –
If True, then the inequality constraint is positive.

By default it is set to False.

Return type

None

add_observable(obs_func, new_iter=True)¶

Add a function to be observed.

Parameters

obs_func (gemseo.core.mdofunctions.mdo_function.MDOFunction) – An observable to be observed.
new_iter (bool) –
If True, then the observable will be called at each new iterate.

By default it is set to True.

Return type

None

aggregate_constraint(constr_id, method='max', groups=None, **options)¶

Aggregates a constraint to generate a reduced dimension constraint.

Parameters

constr_id (int) – index of the constraint in self.constraints
method (str or callable, that takes a function and returns a function) –
aggregation method, among (‘max’,’KS’, ‘IKS’)

By default it is set to max.
groups (tuple of ndarray) –
if None, a single output constraint is produced otherwise, one output per group is produced.

By default it is set to None.

change_objective_sign()¶

Change the objective function sign in order to minimize its opposite.

The OptimizationProblem expresses any optimization problem as a minimization problem. Then, an objective function originally expressed as a performance function to maximize must be converted into a cost function to minimize, by means of this method.

Return type: None

check()¶

Check if the optimization problem is ready for run.

Raises: ValueError – If the objective function is missing.
Return type: None

static check_format(input_function)¶

Check that a function is an instance of MDOFunction.

Parameters: input_function – The function to be tested.
Raises: TypeError – If the function is not a MDOFunction.
Return type: None

clear_listeners()¶

Clear all the listeners.

Return type: None

property differentiation_method¶: The differentiation method.

property dimension¶: The dimension of the design space.

evaluate_functions(x_vect=None, eval_jac=False, eval_obj=True, normalize=True, no_db_no_norm=False)¶

Compute the objective and the constraints.

Some optimization libraries require the number of constraints as an input parameter which is unknown by the formulation or the scenario. Evaluation of initial point allows to get this mandatory information. This is also used for design of experiments to evaluate samples.

Parameters

x_vect (Optional[numpy.ndarray]) –
The input vector at which the functions must be evaluated; if None, x_0 is used.

By default it is set to None.
eval_jac (bool) –
If True, then the Jacobian is evaluated

By default it is set to False.
eval_obj (bool) –
If True, then the objective function is evaluated

By default it is set to True.
normalize (bool) –
If True, then input vector is considered normalized

By default it is set to True.
no_db_no_norm (bool) –
If True, then do not use the pre-processed functions, so we have no database, nor normalization.

By default it is set to False.

Returns

The functions values and/or the Jacobian values according to the passed arguments.

Raises

ValueError – If both no_db_no_norm and normalize are True.

Return type

Tuple[Dict[str, Union[float, numpy.ndarray]], Dict[str, numpy.ndarray]]

execute_observables_callback(last_x)¶

The callback function to be passed to the database.

Call all the observables with the last design variables values as argument.

Parameters: last_x (numpy.ndarray) – The design variables values from the last evaluation.
Return type: None

export_hdf(file_path, append=False)¶

Export the optimization problem to an HDF file.

Parameters

file_path (str) – The file to store the data.
append (bool) –
If True, then the data are appended to the file if not empty.

By default it is set to False.

Return type

None

export_to_dataset(name=None, by_group=True, categorize=True, opt_naming=True, export_gradients=False)¶

Export the database of the optimization problem to a Dataset.

The variables can be classified into groups, separating the design variables and functions (objective function and constraints). This classification can use either an optimization naming, with Database.DESIGN_GROUP and Database.FUNCTION_GROUP or an input-output naming, with Database.INPUT_GROUP and Database.OUTPUT_GROUP

Parameters

name (Optional[str]) –
A name to be given to the dataset. If None, use the name of the database.

By default it is set to None.
by_group (bool) –
If True, then store the data by group. Otherwise, store them by variables.

By default it is set to True.
categorize (bool) –
If True, then distinguish between the different groups of variables.

By default it is set to True.
opt_naming (bool) –
If True, then use an optimization naming.

By default it is set to True.
export_gradients (bool) –
If True, then export also the gradients of the functions (objective function, constraints and observables) if the latter are available in the database of the optimization problem.

By default it is set to False.

Returns

A dataset built from the database of the optimization problem.

Return type

gemseo.core.dataset.Dataset

get_active_ineq_constraints(x_vect, tol=1e-06)¶

For each constraint, indicate if its different components are active.

Parameters

x_vect (numpy.ndarray) – The vector of design variables.
tol (float) –
The tolerance for deciding whether a constraint is active.

By default it is set to 1e-06.

Returns

For each constraint, a boolean indicator of activation of its different components.

Return type

Dict[str, numpy.ndarray]

get_all_functions()¶

Retrieve all the functions of the optimization problem.

These functions are the constraints, the objective function and the observables.

Returns: All the functions of the optimization problem.
Return type: List[gemseo.core.mdofunctions.mdo_function.MDOFunction]

get_all_functions_names()¶

Retrieve the names of all the function of the optimization problem.

These functions are the constraints, the objective function and the observables.

Returns: The names of all the functions of the optimization problem.
Return type: List[str]

get_best_infeasible_point()¶

Retrieve the best infeasible point within a given tolerance.

Returns: The best infeasible point expressed as the design variables values, the objective function value, the feasibility of the point and the functions values.
Return type: Tuple[Optional[numpy.ndarray], Optional[numpy.ndarray], bool, Dict[str, numpy.ndarray]]

get_constraints_names()¶

Retrieve the names of the constraints.

Returns: The names of the constraints.
Return type: List[str]

get_constraints_number()¶

Retrieve the number of constraints.

Returns: The number of constraints.
Return type: int

get_data_by_names(names, as_dict=True, filter_non_feasible=False)¶

Return the data for specific names of variables.

Parameters

names (Union[str, Iterable[str]]) – The names of the variables.
as_dict (bool) –
If True, return values as dictionary.

By default it is set to True.
filter_non_feasible (bool) –
If True, remove the non-feasible points from the data.

By default it is set to False.

Returns

The data related to the variables.

Return type

Union[numpy.ndarray, Dict[str, numpy.ndarray]]

get_design_variable_names()¶

Retrieve the names of the design variables.

Returns: The names of the design variables.
Return type: List[str]

get_dimension()¶

Retrieve the total number of design variables.

Returns: The dimension of the design space.
Return type: int

get_eq_constraints()¶

Retrieve all the equality constraints.

Returns: The equality constraints.
Return type: List[gemseo.core.mdofunctions.mdo_function.MDOFunction]

get_eq_constraints_number()¶

Retrieve the number of equality constraints.

Returns: The number of equality constraints.
Return type: int

get_eq_cstr_total_dim()¶

Retrieve the total dimension of the equality constraints.

This dimension is the sum of all the outputs dimensions of all the equality constraints.

Returns: The total dimension of the equality constraints.
Return type: int

get_feasible_points()¶

Retrieve the feasible points within a given tolerance.

This tolerance is defined by OptimizationProblem.eq_tolerance for equality constraints and OptimizationProblem.ineq_tolerance for inequality ones.

Returns: The values of the design variables and objective function for the feasible points.
Return type: Tuple[List[numpy.ndarray], List[Dict[str, Union[float, List[int]]]]]

get_functions_dimensions()¶

Return the dimensions of the outputs of the problem functions.

Returns: The dimensions of the outputs of the problem functions. The dictionary keys are the functions names and the values are the functions dimensions.
Return type: Dict[str, int]

get_ineq_constraints()¶

Retrieve all the inequality constraints.

Returns: The inequality constraints.
Return type: List[gemseo.core.mdofunctions.mdo_function.MDOFunction]

get_ineq_constraints_number()¶

Retrieve the number of inequality constraints.

Returns: The number of inequality constraints.
Return type: int

get_ineq_cstr_total_dim()¶

Retrieve the total dimension of the inequality constraints.

This dimension is the sum of all the outputs dimensions of all the inequality constraints.

Returns: The total dimension of the inequality constraints.
Return type: int

get_nonproc_constraints()¶

Retrieve the non-processed constraints.

Returns: The non-processed constraints.
Return type: List[gemseo.core.mdofunctions.mdo_function.MDOFunction]

get_nonproc_objective()¶

Retrieve the non-processed objective function.

Return type: gemseo.core.mdofunctions.mdo_function.MDOFunction

get_number_of_unsatisfied_constraints(design_variables)¶

Return the number of scalar constraints not satisfied by design variables.

Parameters: design_variables (numpy.ndarray) – The design variables.
Returns: The number of unsatisfied scalar constraints.
Return type: int

get_objective_name()¶

Retrieve the name of the objective function.

Returns: The name of the objective function.
Return type: str

get_observable(name)¶

Retrieve an observable from its name.

Parameters: name (str) – The name of the observable.
Returns: The observable.
Raises: ValueError – If the observable cannot be found.
Return type: gemseo.core.mdofunctions.mdo_function.MDOFunction

get_optimum()¶

Return the optimum solution within a given feasibility tolerances.

Returns

The optimum result, defined by:

the value of the objective function,
the value of the design variables,
the indicator of feasibility of the optimal solution,
the value of the constraints,
the value of the gradients of the constraints.

Return type

Tuple[numpy.ndarray, numpy.ndarray, bool, Dict[str, numpy.ndarray], Dict[str, numpy.ndarray]]

get_scalar_constraints_names()¶

Return the names of the scalar constraints.

Returns: The names of the scalar constraints.
Return type: List[str]

get_solution()[source]¶

Return the theoretical optimal value.

Returns: design variables values of optimized values, function value at optimum
Return type: numpy array

get_violation_criteria(x_vect)¶

Compute a violation measure associated to an iteration.

For each constraint, when it is violated, add the absolute distance to zero, in L2 norm.

If 0, all constraints are satisfied

Parameters: x_vect (numpy.ndarray) – The vector of the design variables values.
Returns: The feasibility of the point and the violation measure.
Return type: Tuple[bool, float]

get_x0_normalized()¶

Return the current values of the design variables after normalization.

Returns: The current values of the design variables normalized between 0 and 1 from their lower and upper bounds.
Return type: numpy.ndarray

has_constraints()¶

Check if the problem has equality or inequality constraints.

Returns: True if the problem has equality or inequality constraints.

has_eq_constraints()¶

Check if the problem has equality constraints.

Returns: True if the problem has equality constraints.
Return type: bool

has_ineq_constraints()¶

Check if the problem has inequality constraints.

Returns: True if the problem has inequality constraints.
Return type: bool

has_nonlinear_constraints()¶

Check if the problem has non-linear constraints.

Returns: True if the problem has equality or inequality constraints.
Return type: bool

classmethod import_hdf(file_path, x_tolerance=0.0)¶

Import an optimization history from an HDF file.

Parameters

file_path (str) – The file containing the optimization history.
x_tolerance (float) –
The tolerance on the design variables when reading the file.

By default it is set to 0.0.

Returns

The read optimization problem.

Return type

gemseo.algos.opt_problem.OptimizationProblem

is_max_iter_reached()¶

Check if the maximum amount of iterations has been reached.

Returns: Whether the maximum amount of iterations has been reached.
Return type: bool

property is_mono_objective¶: Whether the optimization problem is mono-objective.

is_point_feasible(out_val, constraints=None)¶

Check if a point is feasible.

Note

If the value of a constraint is absent from this point, then this constraint will be considered satisfied.

Parameters

out_val (Dict[str, numpy.ndarray]) – The values of the objective function, and eventually constraints.
constraints (Optional[Iterable[gemseo.core.mdofunctions.mdo_function.MDOFunction]]) –
The constraints whose values are to be tested. If None, then take all constraints of the problem.

By default it is set to None.

Returns

The feasibility of the point.

Return type

bool

property objective¶: The objective function.

property parallel_differentiation¶: Whether to approximate the derivatives in parallel.

property parallel_differentiation_options¶: The options to approximate the derivatives in parallel.

preprocess_functions(normalize=True, use_database=True, round_ints=True)¶

Pre-process all the functions and eventually the gradient.

Required to wrap the objective function and constraints with the database and eventually the gradients by complex step or finite differences.

Parameters

normalize (bool) –
Whether to unnormalize the input vector of the function before evaluate it.

By default it is set to True.
use_database (bool) –
If True, then the functions are wrapped in the database.

By default it is set to True.
round_ints (bool) –
If True, then round the integer variables.

By default it is set to True.

Return type

None

static repr_constraint(func, ctype, value=None, positive=False)¶

Express a constraint as a string expression.

Parameters

func (gemseo.core.mdofunctions.mdo_function.MDOFunction) – The constraint function.
ctype (str) – The type of the constraint. Either equality or inequality.
value (Optional[float]) –
The value for which the constraint is active. If None, this value is 0.

By default it is set to None.
positive (bool) –
If True, then the inequality constraint is positive.

By default it is set to False.

Returns

A string representation of the constraint.

Return type

str