# MDO formulations¶

Warning

Some capabilities may require the installation of GEMSEO with all its features and some others may depend on plugins.

Note

All the features of the wrapped libraries may not be exposed through GEMSEO.

## BiLevel¶

Module: `gemseo.formulations.bilevel`

- Required parameters
**design_space**:*DesignSpace*The design space.

**disciplines**:*list[MDODiscipline]*The disciplines.

**objective_name**:*str*The name(s) of the discipline output(s) used as objective. If multiple names are passed, the objective will be a vector.

- Optional parameters
**apply_cstr_to_system**:*bool, optional*Whether the

`add_constraint()`

method adds the constraint to the optimization problem of the system scenario.By default it is set to True.

**apply_cstr_tosub_scenarios**:*bool, optional*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.

**differentiated_input_names_substitute**:*Iterable[str], optional*The names of the discipline inputs against which to differentiate the discipline outputs used as objective, constraints and observables. If empty, consider the inputs of these functions. More precisely, for each function, an

`MDOFunction`

is built from the`disciplines`

, which depend on input variables \(x_1,\ldots,x_d,x_{d+1}\), and over an input space spanned by the input variables \(x_1,\ldots,x_d\) and depending on both the MDO formulation and the`design_space`

. Then, the methods`MDOFunction.evaluate()`

and`MDOFunction.jac()`

are called at a given point of the input space and return the output value and the Jacobian matrix, i.e. the matrix concatenating the partial derivatives with respect to the inputs \(x_1,\ldots,x_d\) at this point of the input space. This argument can be used to compute the matrix concatenating the partial derivatives at the same point of the input space but with respect to custom inputs, e.g. \(x_{d-1}\) and \(x_{d+1}\). Mathematically speaking, this matrix returned by`MDOFunction.jac()`

is no longer a Jacobian.By default it is set to ().

**grammar_type**:*MDODiscipline.GrammarType, optional*The type of the input and output grammars.

By default it is set to JSONGrammar.

**inner_mda_name**:*str, optional*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.

**main_mda_name**:*str, optional*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.

**maximize_objective**:*bool, optional*Whether to maximize the objective.

By default it is set to False.

**multithread_scenarios**:*bool, optional*If

`True`

and parallel_scenarios=True, the sub-scenarios are run in parallel using multi-threading; if False and parallel_scenarios=True, multiprocessing is used.By default it is set to True.

**parallel_scenarios**:*bool, optional*Whether to run the sub-scenarios in parallel.

By default it is set to False.

**reset_x0_before_opt**:*bool, optional*Whether to restart the sub optimizations from the initial guesses, otherwise warm start them.

By default it is set to False.

**sub_scenarios_log_level**:*int | None, optional*The level of the root logger during the sub-scenarios executions. If

`None`

, do not change the level of the root logger.By default it is set to None.

****main_mda_options**:*Any*The options of the main MDA, which may include those of the inner-MDA.

## DisciplinaryOpt¶

Module: `gemseo.formulations.disciplinary_opt`

- Required parameters
**design_space**:*DesignSpace*The design space.

**disciplines**:*list[MDODiscipline]*The disciplines.

**objective_name**:*str*The name(s) of the discipline output(s) used as objective. If multiple names are passed, the objective will be a vector.

- Optional parameters
**differentiated_input_names_substitute**:*Iterable[str], optional*The names of the discipline inputs against which to differentiate the discipline outputs used as objective, constraints and observables. If empty, consider the inputs of these functions. More precisely, for each function, an

`MDOFunction`

is built from the`disciplines`

, which depend on input variables \(x_1,\ldots,x_d,x_{d+1}\), and over an input space spanned by the input variables \(x_1,\ldots,x_d\) and depending on both the MDO formulation and the`design_space`

. Then, the methods`MDOFunction.evaluate()`

and`MDOFunction.jac()`

are called at a given point of the input space and return the output value and the Jacobian matrix, i.e. the matrix concatenating the partial derivatives with respect to the inputs \(x_1,\ldots,x_d\) at this point of the input space. This argument can be used to compute the matrix concatenating the partial derivatives at the same point of the input space but with respect to custom inputs, e.g. \(x_{d-1}\) and \(x_{d+1}\). Mathematically speaking, this matrix returned by`MDOFunction.jac()`

is no longer a Jacobian.By default it is set to ().

**grammar_type**:*MDODiscipline.GrammarType, optional*The type of the input and output grammars.

By default it is set to JSONGrammar.

**maximize_objective**:*bool, optional*Whether to maximize the objective.

By default it is set to False.

## IDF¶

Module: `gemseo.formulations.idf`

- Required parameters
**design_space**:*DesignSpace*The design space.

**disciplines**:*list[MDODiscipline]*The disciplines.

**objective_name**:*str*The name(s) of the discipline output(s) used as objective. If multiple names are passed, the objective will be a vector.

- Optional parameters
**differentiated_input_names_substitute**:*Iterable[str], optional*The names of the discipline inputs against which to differentiate the discipline outputs used as objective, constraints and observables. If empty, consider the inputs of these functions. More precisely, for each function, an

`MDOFunction`

is built from the`disciplines`

, which depend on input variables \(x_1,\ldots,x_d,x_{d+1}\), and over an input space spanned by the input variables \(x_1,\ldots,x_d\) and depending on both the MDO formulation and the`design_space`

. Then, the methods`MDOFunction.evaluate()`

and`MDOFunction.jac()`

are called at a given point of the input space and return the output value and the Jacobian matrix, i.e. the matrix concatenating the partial derivatives with respect to the inputs \(x_1,\ldots,x_d\) at this point of the input space. This argument can be used to compute the matrix concatenating the partial derivatives at the same point of the input space but with respect to custom inputs, e.g. \(x_{d-1}\) and \(x_{d+1}\). Mathematically speaking, this matrix returned by`MDOFunction.jac()`

is no longer a Jacobian.By default it is set to ().

**grammar_type**:*MDODiscipline.GrammarType, optional*The type of the input and output grammars.

By default it is set to JSONGrammar.

**maximize_objective**:*bool, optional*Whether to maximize the objective.

By default it is set to False.

**n_processes**:*int, optional*The maximum simultaneous number of threads, if

`use_threading`

is True, or processes otherwise, used to parallelize the execution.By default it is set to 1.

**normalize_constraints**:*bool, optional*If

`True`

, the outputs of the coupling consistency constraints are scaled.By default it is set to True.

**start_at_equilibrium**:*bool, optional*If

`True`

, an MDA is used to initialize the coupling variables.By default it is set to False.

**use_threading**:*bool, optional*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 True.

****mda_options_for_start_at_equilibrium**:*Any*The options for the MDA when

`start_at_equilibrium=True`

. See detailed options in`MDAChain`

.

## MDF¶

Module: `gemseo.formulations.mdf`

- Required parameters
**design_space**:*DesignSpace*The design space.

**disciplines**:*list[MDODiscipline]*The disciplines.

**objective_name**:*str*

- Optional parameters
**differentiated_input_names_substitute**:*Iterable[str], optional*`MDOFunction`

is built from the`disciplines`

, which depend on input variables \(x_1,\ldots,x_d,x_{d+1}\), and over an input space spanned by the input variables \(x_1,\ldots,x_d\) and depending on both the MDO formulation and the`design_space`

. Then, the methods`MDOFunction.evaluate()`

and`MDOFunction.jac()`

are called at a given point of the input space and return the output value and the Jacobian matrix, i.e. the matrix concatenating the partial derivatives with respect to the inputs \(x_1,\ldots,x_d\) at this point of the input space. This argument can be used to compute the matrix concatenating the partial derivatives at the same point of the input space but with respect to custom inputs, e.g. \(x_{d-1}\) and \(x_{d+1}\). Mathematically speaking, this matrix returned by`MDOFunction.jac()`

is no longer a Jacobian.By default it is set to ().

**grammar_type**:*MDODiscipline.GrammarType, optional*The type of the input and output grammars.

By default it is set to JSONGrammar.

**inner_mda_name**:*str, optional*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.

**main_mda_name**:*str, optional*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.

**maximize_objective**:*bool, optional*Whether to maximize the objective.

By default it is set to False.

****main_mda_options**:*Any*The options of the main MDA, which may include those of the inner-MDA.