gemseo / problems / analytical

# 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]

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 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 the time stamps. deserialize(in_file) Deserialize a discipline from a file. execute([input_data]) Execute the discipline. Return the local input data as a list. Return the local output data as a list. 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. Return the expected data exchange sequence. Return the expected execution sequence. Return the local input data as a dictionary. Return the names of the input variables. Return the names of the input and output variables. 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. Return the local output data as a dictionary. Return the names of the output variables. Return the local input data as a large NumPy array. get_outputs_by_name(data_names) Return the local data associated with output variables. 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. Whether the discipline is a scenario. linearize([input_data, force_all, force_no_exec]) Execute the linearized version of the code. Notify all status observers that the status has changed. Remove an observer for the status. 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 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

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 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 namedname + “_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.

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.

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.

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.

MDOFormulation.get_expected_dataflow

Returns

The data exchange arcs.

Return type

List[Tuple[gemseo.core.discipline.MDODiscipline, gemseo.core.discipline.MDODiscipline, List[str]]]

get_expected_workflow()

Return the expected execution sequence.

This method is used for the XDSM representation.

The default expected execution sequence is the execution of the discipline itself.

MDOFormulation.get_expected_workflow

Returns

The expected execution sequence.

Return type

SerialExecSequence

get_input_data()

Return the local input data as a dictionary.

Returns

The local input data.

Return type

Dict[str, Any]

get_input_data_names()

Return the names of the input variables.

Returns

The names of the input variables.

Return type

List[str]

get_input_output_data_names()

Return the names of the input and output variables.

Returns

The name of the input and output variables.

Return type

List[str]

get_inputs_asarray()

Return the local output data as a large NumPy array.

The order is the one of get_all_outputs().

Returns

The local output data.

Return type

numpy.ndarray

get_inputs_by_name(data_names)

Return the local data associated with input variables.

Parameters

data_names (Iterable[str]) – The names of the input variables.

Returns

The local data for the given input variables.

Raises

ValueError – When a variable is not an input of the discipline.

Return type

List[Any]

get_local_data_by_name(data_names)

Return the local data of the discipline associated with variables names.

Parameters

data_names (Iterable[str]) – The names of the variables.

Returns

The local data associated with the variables names.

Raises

ValueError – When a name is not not a discipline input name.

Return type

Generator[Any]

get_output_data()

Return the local output data as a dictionary.

Returns

The local output data.

Return type

Dict[str, Any]

get_output_data_names()

Return the names of the output variables.

Returns

The names of the output variables.

Return type

List[str]

get_outputs_asarray()

Return the local input data as a large NumPy array.

The order is the one of get_all_inputs().

Returns

The local input data.

Return type

numpy.ndarray

get_outputs_by_name(data_names)

Return the local data associated with output variables.

Parameters

data_names (Iterable[str]) – The names of the output variables.

Returns

The local data for the given output variables.

Raises

ValueError – When a variable is not an output of the discipline.

Return type

List[Any]

get_sub_disciplines()

Return the sub-disciplines if any.

Returns

The sub-disciplines.

Return type
property grammar_type

The grammar type.

is_all_inputs_existing(data_names)

Test if several variables are discipline inputs.

Parameters

data_names (Iterable[str]) – The names of the variables.

Returns

Whether all the variables are discipline inputs.

Return type

bool

is_all_outputs_existing(data_names)

Test if several variables are discipline outputs.

Parameters

data_names (Iterable[str]) – The names of the variables.

Returns

Whether all the variables are discipline outputs.

Return type

bool

is_input_existing(data_name)

Test if a variable is a discipline input.

Parameters

data_name (str) – The name of the variable.

Returns

Whether the variable is a discipline input.

Return type

bool

is_output_existing(data_name)

Test if a variable is a discipline output.

Parameters

data_name (str) – The name of the variable.

Returns

Whether the variable is a discipline output.

Return type

bool

static is_scenario()

Whether the discipline is a scenario.

Return type

bool

property linearization_mode

The linearization mode among LINEARIZE_MODE_LIST.

Raises

ValueError – When the linearization mode is unknown.

linearize(input_data=None, force_all=False, force_no_exec=False)

Execute the linearized version of the code.

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

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

By default it is set to None.

• force_all (bool) –

If False, _differentiated_inputs and differentiated_output are used to filter the differentiated variables. otherwise, all outputs are differentiated wrt all inputs.

By default it is set to False.

• force_no_exec (bool) –

If True, the discipline is not re executed, cache is loaded anyway.

By default it is set to False.

Returns

The Jacobian of the discipline.

Return type

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

property n_calls

The number of times the discipline was executed.

Note

This property is multiprocessing safe.

property n_calls_linearize

The number of times the discipline was linearized.

Note

This property is multiprocessing safe.

notify_status_observers()

Notify all status observers that the status has changed.

Return type

None

remove_status_observer(obs)

Remove an observer for the status.

Parameters

obs (Any) – The observer to remove.

Return type

None

reset_statuses_for_run()

Set all the statuses to PENDING.

Raises

ValueError – When the discipline cannot be run because of its status.

Return type

None

serialize(out_file)

Serialize the discipline and store it in a file.

Parameters

out_file (Union[str, pathlib.Path]) – The path to the file to store the discipline.

Return type

None

set_cache_policy(cache_type='SimpleCache', cache_tolerance=0.0, cache_hdf_file=None, cache_hdf_node_name=None, is_memory_shared=True)

Set the type of cache to use and the tolerance level.

This method defines when the output data have to be cached according to the distance between the corresponding input data and the input data already cached for which output data are also cached.

The cache can be either a SimpleCache recording the last execution or a cache storing all executions, e.g. MemoryFullCache and HDF5Cache. Caching data can be either in-memory, e.g. SimpleCache and MemoryFullCache, or on the disk, e.g. HDF5Cache.

The attribute CacheFactory.caches provides the available caches types.

Parameters
• cache_type (str) –

The type of cache.

By default it is set to SimpleCache.

• cache_tolerance (float) –

The maximum relative norm of the difference between two input arrays to consider that two input arrays are equal.

By default it is set to 0.0.

• cache_hdf_file (Optional[Union[str, pathlib.Path]]) –

The path to the HDF file to store the data; this argument is mandatory when the HDF5Cache policy is used.

By default it is set to None.

• cache_hdf_node_name (Optional[str]) –

The name of the HDF file node to store the discipline data. If None, name is used.

By default it is set to None.

• is_memory_shared (bool) –

Whether to store the data with a shared memory dictionary, which makes the cache compatible with multiprocessing.

By default it is set to True.

Return type

None

set_disciplines_statuses(status)

Set the sub-disciplines statuses.

To be implemented in subclasses.

Parameters

status (str) – The status.

Return type

None

Set the Jacobian approximation method.

Sets the linearization mode to approx_method, sets the parameters of the approximation for further use when calling linearize().

Parameters
• jac_approx_type (str) –

The approximation method, either “complex_step” or “finite_differences”.

By default it is set to finite_differences.

• jax_approx_step (float) –

The differentiation step.

By default it is set to 1e-07.

• jac_approx_n_processes (int) –

The maximum number of processors on which to run.

By default it is set to 1.

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.

• jac_approx_wait_time (float) –

The time waited between two forks of the process / thread.

By default it is set to 0.

Return type

None

set_optimal_fd_step(outputs=None, inputs=None, force_all=False, print_errors=False, numerical_error=2.220446049250313e-16)

Compute the optimal finite-difference step.

Compute the optimal step for a forward first order finite differences gradient approximation. Requires a first evaluation of the perturbed functions values. The optimal step is reached when the truncation error (cut in the Taylor development), and the numerical cancellation errors (roundoff when doing f(x+step)-f(x))

are approximately equal.

Warning

This calls the discipline execution twice per input variables.

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]

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:

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'

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 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 an equality constraint to the optimization problem.

Parameters
Return type

None

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 a function to be observed.

Parameters
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()

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 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.

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
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
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
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
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

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