gemseo / formulations

# bilevel module¶

A Bi-level formulation.

class gemseo.formulations.bilevel.BiLevel(disciplines, objective_name, design_space, maximize_objective=False, main_mda_name='MDAChain', inner_mda_name='MDAJacobi', parallel_scenarios=False, multithread_scenarios=True, apply_cstr_tosub_scenarios=True, apply_cstr_to_system=True, reset_x0_before_opt=False, grammar_type='JSONGrammar', **main_mda_options)[source]

A bi-level formulation.

This formulation draws an optimization architecture that involves multiple optimization problems to be solved to obtain the solution of the MDO problem.

Here, at each iteration on the global design variables, the bi-level MDO formulation implementation performs:

1. a first MDA to compute the coupling variables,

2. several disciplinary optimizations on the local design variables in parallel,

3. a second MDA to update the coupling variables.

Parameters
• disciplines (Sequence[gemseo.core.discipline.MDODiscipline]) – The disciplines.

• objective_name (str) – The name of the objective function. If a sequence is passed, a vector objective function is created.

• design_space (gemseo.algos.design_space.DesignSpace) – The design space.

• maximize_objective (bool) –

If True, the objective function is maximized.

By default it is set to False.

• main_mda_name (str) –

The name of the class used for the main MDA, typically the MDAChain, but one can force to use MDAGaussSeidel for instance.

By default it is set to MDAChain.

• inner_mda_name (str) –

The name of the class used for the inner-MDA of the main MDA, if any; typically when the main MDA is an MDAChain.

By default it is set to MDAJacobi.

• parallel_scenarios (bool) –

Whether to run the sub-scenarios in parallel.

By default it is set to False.

• multithread_scenarios (bool) –

If True and parallel_scenarios=True, the sub-scenarios are run in parallel using multi-threading; if False and parallel_scenarios=True, multi-processing is used.

By default it is set to True.

• apply_cstr_tosub_scenarios (bool) –

Whether the add_constraint() method adds the constraint to the optimization problem of the sub-scenario capable of computing the constraint.

By default it is set to True.

• apply_cstr_to_system (bool) –

Whether the add_constraint() method adds the constraint to the optimization problem of the system scenario.

By default it is set to True.

• reset_x0_before_opt (bool) –

Whether to restart the sub optimizations from the initial guesses, otherwise warm start them.

By default it is set to False.

• grammar_type (str) –

The type of the input and output grammars, either MDODiscipline.JSON_GRAMMAR_TYPE or MDODiscipline.SIMPLE_GRAMMAR_TYPE.

By default it is set to JSONGrammar.

• **main_mda_options (Any) – The options of the main MDA, which may include those of the inner-MDA.

add_constraint(output_name, constraint_type='eq', constraint_name=None, value=None, positive=False, levels=None)[source]

Add a constraint to the formulation.

Parameters
• output_name (str) – The name of the output to be used as a constraint. For instance, if g_1 is given and constraint_type=”eq”, g_1=0 will be added as a constraint to the optimizer.

• constraint_type (str) –

The type of constraint, either “eq” for equality constraint or “ineq” for inequality constraint.

By default it is set to eq.

• constraint_name (str | None) –

The name of the constraint to be stored, If None, the name is generated from the output name.

By default it is set to None.

• value (float | None) –

The value of activation of the constraint. If None, the value is equal to 0.

By default it is set to None.

• positive (bool) –

If True, the inequality constraint is positive.

By default it is set to False.

• levels (list[str] | None) –

The levels at which the constraint is to be added (sublist of Bilevel.LEVELS). By default the policy set at the initialization of the formulation is enforced.

By default it is set to None.

Raises

ValueError – When the constraint levels are not a sublist of BiLevel.LEVELS.

Return type

None

Add an observable to the optimization problem.

The repartition strategy of the observable is defined in the formulation class.

Parameters
• output_names (str | Sequence[str]) – The name(s) of the output(s) to observe.

• observable_name (str | None) –

The name of the observable.

By default it is set to None.

• discipline (MDODiscipline | None) –

The discipline computing the observed outputs. If None, the discipline is detected from inner disciplines.

By default it is set to None.

Return type

None

classmethod get_default_sub_options_values(**options)[source]

Return the options value of the selected MDA.

Parameters

**options (str) – The options of the BiLevel formulation.

Returns

The MDA options values.

Raises

ValueError – When the MDA name is not provided.

Return type

Mapping[str, str | int | float | bool | None] | None

get_expected_dataflow()[source]

Get the expected data exchange sequence.

This method is used for the XDSM representation and can be overloaded by subclasses.

Returns

The expected sequence of data exchange where the i-th item is described by the starting discipline, the ending discipline and the coupling variables.

Return type
get_expected_workflow()[source]

Get the expected sequence of execution of the disciplines.

This method is used for the XDSM representation and can be overloaded by subclasses.

For instance:

• [A, B] denotes the execution of A, then the execution of B

• (A, B) denotes the concurrent execution of A and B

• [A, (B, C), D] denotes the execution of A, then the concurrent execution of B and C, then the execution of D.

Returns

A sequence of elements which are either an ExecutionSequence or a tuple of ExecutionSequence for concurrent execution.

Return type
get_optim_variables_names()

Get the optimization unknown names to be provided to the optimizer.

This is different from the design variable names provided by the user, since it depends on the formulation, and can include target values for coupling for instance in IDF.

Returns

The optimization variable names.

Return type

list[str]

get_sub_disciplines()

Accessor to the sub-disciplines.

This method lists the sub scenarios’ disciplines.

Returns

The sub-disciplines.

Return type
classmethod get_sub_options_grammar(**options)[source]

Return the grammar of the selected MDA.

Parameters

**options (str) – The options of the BiLevel formulation.

Returns

The MDA grammar.

Raises

ValueError – When the MDA name is not provided.

Return type

gemseo.core.grammars.json_grammar.JSONGrammar

get_sub_scenarios()

List the disciplines that are actually scenarios.

Returns

The scenarios.

Return type
get_top_level_disc()[source]

Return the disciplines which inputs are required to run the scenario.

A formulation seeks to evaluate objective function and constraints from inputs. It structures the optimization problem into multiple levels of disciplines. The disciplines directly depending on these inputs are called top level disciplines.

By default, this method returns all disciplines. This method can be overloaded by subclasses.

Returns

The top level disciplines.

Return type

Mask a vector from a subset of names, with respect to a set of names.

This method eventually swaps the order of the values if the order of the data names is inconsistent between these sets.

Parameters
• masking_data_names (Iterable[str]) – The names of the kept data.

• x_vect – The vector to mask.

• all_data_names (Iterable[str] | None) –

The set of all names. If None, use the design variables stored in the design space.

By default it is set to None.

Returns

The masked version of the input vector.

Raises
• IndexError – when the sizes of variables are inconsistent.

• ValueError – when the names of variables are inconsistent.

Return type

ndarray

get_x_names_of_disc(discipline)

Get the design variables names of a given discipline.

Parameters

discipline (gemseo.core.discipline.MDODiscipline) – The discipline.

Returns

The names of the design variables.

Return type

list[str]

Mask a vector from a subset of names, with respect to a set of names.

This method eventually swaps the order of the values if the order of the data names is inconsistent between these sets.

Parameters
• masking_data_names (Iterable[str]) – The names of the kept data.

• x_vect (ndarray) – The vector to mask.

• all_data_names (Iterable[str] | None) –

The set of all names. If None, use the design variables stored in the design space.

By default it is set to None.

Returns

The masked version of the input vector.

Raises

IndexError – when the sizes of variables are inconsistent.

Return type

ndarray

Unmask a vector from a subset of names, with respect to a set of names.

This method eventually swaps the order of the values if the order of the data names is inconsistent between these sets.

Parameters
• masking_data_names (Iterable[str]) – The names of the kept data.

• x_masked (ndarray) – The boolean vector to unmask.

• all_data_names (Iterable[str] | None) –

The set of all names. If None, use the design variables stored in the design space.

By default it is set to None.

• x_full (ndarray) –

The default values for the full vector. If None, use the zero vector.

By default it is set to None.

Returns

The vector related to the input mask.

Raises

IndexError – when the sizes of variables are inconsistent.

Return type

ndarray

LEVELS = ('system', 'sub-scenarios')
NAME: ClassVar[str] = 'MDOFormulation'

The name of the MDO formulation.

SUBSCENARIOS_LEVEL = 'sub-scenarios'
SYSTEM_LEVEL = 'system'
property design_space: gemseo.algos.design_space.DesignSpace

The design space on which the formulation is applied.

disciplines: Sequence[MDODiscipline]

The disciplines of the MDO process.

property mda1: gemseo.core.discipline.MDODiscipline

The MDA1 instance.

property mda2: gemseo.core.discipline.MDODiscipline

The MDA2 instance.

opt_problem: OptimizationProblem

The optimization problem generated by the formulation from the disciplines.