# The GEMSEO concepts¶

GEMSEO-based optimization relies on three main concepts: the Design space, the Optimization problem and the Driver.

## Design space¶

class gemseo.algos.design_space.DesignSpace(hdf_file=None, name=None)[source]

Description of a design space.

It defines a set of variables from their names, sizes, types and bounds.

In addition, it provides the current values of these variables that can be used as the initial solution of an OptimizationProblem.

A DesignSpace has the same API as a dictionary, e.g. variable = design_space["x"], other_design_space["x"] = design_space["x"], del design_space["x"], for name, value in design_space["x"].items(), …

Parameters:
• hdf_file (str | Path | None) – The path to the file containing the description of an initial design space. If None, start with an empty design space.

• name (str | None) – The name to be given to the design space, None if the design space is unnamed.

add_variable(name, size=1, var_type=DesignVariableType.FLOAT, l_b=None, u_b=None, value=None)[source]

Add a variable to the design space.

Parameters:
• name (str) – The name of the variable.

• size (int) –

The size of the variable.

By default it is set to 1.

• var_type (VarType) –

Either the type of the variable or the types of its components.

By default it is set to FLOAT.

• l_b (float | ndarray | None) – The lower bound of the variable. If None, use $$-\infty$$.

• u_b (float | ndarray | None) – The upper bound of the variable. If None, use $$+\infty$$.

• value (float | ndarray | None) – The default value of the variable. If None, do not use a default value.

Raises:

ValueError – Either if the variable already exists or if the size is not a positive integer.

Return type:

None

array_to_dict(x_array)[source]

Convert a design array into a dictionary indexed by the variables names.

Parameters:

x_array (ndarray) – A design value expressed as a NumPy array.

Returns:

The design value expressed as a dictionary of NumPy arrays.

Return type:
check()[source]

Check the state of the design space.

Raises:

ValueError – If the design space is empty.

Return type:

None

check_membership(x_vect, variable_names=None)[source]

Check whether the variables satisfy the design space requirements.

Parameters:
• x_vect (Mapping[str, ndarray] | ndarray) – The values of the variables.

• variable_names (Sequence[str] | None) – The names of the variables. If None, use the names of the variables of the design space.

Raises:

ValueError – Either if the dimension of the values vector is wrong, if the values are not specified as an array or a dictionary, if the values are outside the bounds of the variables or if the component of an integer variable is not an integer.

Return type:

None

dict_to_array(design_values, variable_names=None)[source]

Convert a point as dictionary into an array.

Parameters:
• design_values (dict[str, numpy.ndarray]) – The design point to be converted.

• variable_names (Optional[Iterable[str]]) – The variables to be considered. If None, use the variables of the design space.

Returns:

The point as an array.

Return type:

ndarray

export_hdf(file_path, append=False)[source]

Export the design space to an HDF file.

Parameters:
• file_path (str | Path) – The path to the file to export the design space.

• append (bool) –

If True, appends the data in the file.

By default it is set to False.

Return type:

None

Export the design space to a text file.

Parameters:
Return type:

None

extend(other)[source]

Extend the design space with another design space.

Parameters:

other (DesignSpace) – The design space to be appended to the current one.

Return type:

None

filter(keep_variables, copy=False)[source]

Filter the design space to keep a subset of variables.

Parameters:
• keep_variables (str | Iterable[str]) – The names of the variables to be kept.

• copy (bool) –

If True, then a copy of the design space is filtered, otherwise the design space itself is filtered.

By default it is set to False.

Returns:

Either the filtered original design space or a copy.

Raises:

ValueError – If the variable is not in the design space.

Return type:

DesignSpace

filter_dim(variable, keep_dimensions)[source]

Filter the design space to keep a subset of dimensions for a variable.

Parameters:
• variable (str) – The name of the variable.

• keep_dimensions (Iterable[int]) – The dimensions of the variable to be kept, between $$0$$ and $$d-1$$ where $$d$$ is the number of dimensions of the variable.

Returns:

The filtered design space.

Raises:

ValueError – If a dimension is unknown.

Return type:

DesignSpace

get_active_bounds(x_vec=None, tol=1e-08)[source]

Determine which bound constraints of a design value are active.

Parameters:
• x_vec (ndarray | None) – The design value at which to check the bounds. If None, use the current design value.

• tol (float) –

The tolerance of comparison of a scalar with a bound.

By default it is set to 1e-08.

Returns:

Whether the components of the lower and upper bound constraints are active, the first returned value representing the lower bounds and the second one the upper bounds, e.g.

({'x': array(are_x_lower_bounds_active),
'y': array(are_y_lower_bounds_active)},
{'x': array(are_x_upper_bounds_active),
'y': array(are_y_upper_bounds_active)}
)


where:

are_x_lower_bounds_active = [True, False]
are_x_upper_bounds_active = [False, False]
are_y_lower_bounds_active = [False]
are_y_upper_bounds_active = [True]


Return type:

tuple[dict[str, ndarray], dict[str, ndarray]]

get_current_value(variable_names=None, complex_to_real=False, as_dict=False, normalize=False)[source]

Return the current design value.

If the names of the variables are empty then an empty data is returned.

Parameters:
• variable_names (Sequence[str] | None) – The names of the design variables. If None, use all the design variables.

• complex_to_real (bool) –

Whether to cast complex numbers to real ones.

By default it is set to False.

• as_dict (bool) –

Whether to return the current design value as a dictionary of the form {variable_name: variable_value}.

By default it is set to False.

• normalize (bool) –

Whether to normalize the design values in $$[0,1]$$ with the bounds of the variables.

By default it is set to False.

Returns:

The current design value.

Raises:

ValueError – If names in variable_names are not in the design space.

Return type:

ndarray | dict[str, ndarray]

Warning

For performance purposes, get_current_value() does not return a copy of the current value. This means that modifying the returned object will make the DesignSpace inconsistent (the current design value stored as a NumPy array and the current design value stored as a dictionary of NumPy arrays will be different). To modify the returned object without impacting the DesignSpace, you shall copy this object and modify the copy.

To modify the current value, please use set_current_value() or set_current_variable().

get_indexed_var_name(variable_name)[source]

Create the names of the components of a variable.

If the size of the variable is equal to 1, this method returns the name of the variable. Otherwise, it concatenates the name of the variable, the separator DesignSpace.SEP and the index of the component.

Parameters:

variable_name (str) – The name of the variable.

Returns:

The names of the components of the variable.

Return type:

str | list[str]

get_indexed_variables_names()[source]

Create the names of the components of all the variables.

If the size of the variable is equal to 1, this method uses its name. Otherwise, it concatenates the name of the variable, the separator DesignSpace.SEP and the index of the component.

Returns:

The name of the components of all the variables.

Return type:

list[str]

get_lower_bound(name)[source]

Return the lower bound of a variable.

Parameters:

name (str) – The name of the variable.

Returns:

The lower bound of the variable (possibly infinite).

Return type:

ndarray

get_lower_bounds(variable_names=None)[source]

Generate an array of the variables’ lower bounds.

Parameters:

variable_names (Sequence[str] | None) – The names of the variables of which the lower bounds are required. If None, use the variables of the design space.

Returns:

The lower bounds of the variables.

Return type:

ndarray

get_pretty_table(fields=None, with_index=False)[source]

Build a tabular view of the design space.

Parameters:
• fields (Sequence[str] | None) – The name of the fields to be exported. If None, export all the fields.

• with_index (bool) –

Whether to show index of names for arrays. This is ignored for scalars.

By default it is set to False.

Returns:

A tabular view of the design space.

Return type:

PrettyTable

get_size(name)[source]

Get the size of a variable.

Parameters:

name (str) – The name of the variable.

Returns:

The size of the variable, None if it is not known.

Return type:

int | None

get_type(name)[source]

Return the type of a variable.

Parameters:

name (str) – The name of the variable.

Returns:

The type of the variable, None if it is not known.

Return type:

str | None

get_upper_bound(name)[source]

Return the upper bound of a variable.

Parameters:

name (str) – The name of the variable.

Returns:

The upper bound of the variable (possibly infinite).

Return type:

ndarray

get_upper_bounds(variable_names=None)[source]

Generate an array of the variables’ upper bounds.

Parameters:

variable_names (Sequence[str] | None) – The names of the variables of which the upper bounds are required. If None, use the variables of the design space.

Returns:

The upper bounds of the variables.

Return type:

ndarray

get_variables_indexes(variable_names)[source]

Return the indexes of a design array corresponding to the variables names.

Parameters:

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

Returns:

The indexes of a design array corresponding to the variables names.

Return type:

ndarray

has_current_value()[source]

Check if each variable has a current value.

Returns:

Whether the current design value is defined for all variables.

Return type:

bool

has_integer_variables()[source]

Check if the design space has at least one integer variable.

Returns:

Whether the design space has at least one integer variable.

Return type:

bool

import_hdf(file_path)[source]

Import a design space from an HDF file.

Parameters:

file_path (str | Path) – The path to the file containing the description of a design space.

Return type:

None

initialize_missing_current_values()[source]

Initialize the current values of the design variables when missing.

Use:

• the center of the design space when the lower and upper bounds are finite,

• the lower bounds when the upper bounds are infinite,

• the upper bounds when the lower bounds are infinite,

• zero when the lower and upper bounds are infinite.

Return type:

None

This method is based on the chain rule:

$\frac{df(x)}{dx} = \frac{df(x)}{dx_u}\frac{dx_u}{dx} = \frac{df(x)}{dx_u}\frac{1}{u_b-l_b}$

where $$x_u = \frac{x-l_b}{u_b-l_b}$$ is the normalized input vector, $$x$$ is the unnormalized input vector and $$l_b$$ and $$u_b$$ are the lower and upper bounds of $$x$$.

$\frac{df(x)}{dx_u} = (u_b-l_b)\frac{df(x)}{dx}$

where $$\frac{df(x)}{dx}$$ is the unnormalized one.

Parameters:

g_vect (ndarray) – The gradient to be normalized.

Returns:

Return type:

ndarray

normalize_vect(x_vect, minus_lb=True, out=None)[source]

Normalize a vector of the design space.

If minus_lb is True:

$x_u = \frac{x-l_b}{u_b-l_b}$

where $$l_b$$ and $$u_b$$ are the lower and upper bounds of $$x$$.

Otherwise:

$x_u = \frac{x}{u_b-l_b}$

Unbounded variables are not normalized.

Parameters:
• x_vect (ndarray) – The values of the design variables.

• minus_lb (bool) –

If True, remove the lower bounds at normalization.

By default it is set to True.

• out (ndarray | None) – The array to store the normalized vector. If None, create a new array.

Returns:

The normalized vector.

Return type:

ndarray

project_into_bounds(x_c, normalized=False)[source]

Project a vector onto the bounds, using a simple coordinate wise approach.

Parameters:
• normalized (bool) –

If True, then the vector is assumed to be normalized.

By default it is set to False.

• x_c (ndarray) – The vector to be projected onto the bounds.

Returns:

The projected vector.

Return type:

ndarray

Create a design space from a text file.

Parameters:
• input_file (str | Path) – The path to the file.

• header (Iterable[str] | None) – The names of the fields saved in the file. If None, read them in the file.

Returns:

The design space read from the file.

Raises:

ValueError – If the file does not contain the minimal variables in its header.

Return type:

DesignSpace

remove_variable(name)[source]

Remove a variable from the design space.

Parameters:

name (str) – The name of the variable to be removed.

Return type:

None

rename_variable(current_name, new_name)[source]

Rename a variable.

Parameters:
• current_name (str) – The name of the variable to rename.

• new_name (str) – The new name of the variable.

Return type:

None

round_vect(x_vect, copy=True)[source]

Round the vector where variables are of integer type.

Parameters:
• x_vect (ndarray) – The values to be rounded.

• copy (bool) –

Whether to round a copy of x_vect.

By default it is set to True.

Returns:

The rounded values.

Return type:

ndarray

set_current_value(value)[source]

Set the current design value.

Parameters:

value (ndarray | Mapping[str, ndarray] | OptimizationResult) – The value of the current design.

Raises:
Return type:

None

set_current_variable(name, current_value)[source]

Set the current value of a single variable.

Parameters:
• name (str) – The name of the variable.

• current_value (ndarray) – The current value of the variable.

Return type:

None

set_lower_bound(name, lower_bound)[source]

Set the lower bound of a variable.

Parameters:
• name (str) – The name of the variable.

• lower_bound (ndarray | None) – The value of the lower bound.

Raises:

ValueError – If the variable does not exist.

Return type:

None

set_upper_bound(name, upper_bound)[source]

Set the upper bound of a variable.

Parameters:
• name (str) – The name of the variable.

• upper_bound (ndarray | None) – The value of the upper bound.

Raises:

ValueError – If the variable does not exist.

Return type:

None

to_complex()[source]

Cast the current value to complex.

Return type:

None

transform_vect(vector, out=None)[source]

Map a point of the design space to a vector with components in $$[0,1]$$.

Parameters:
• vector (ndarray) – A point of the design space.

• out (ndarray | None) – The array to store the transformed vector. If None, create a new array.

Returns:

A vector with components in $$[0,1]$$.

Return type:

ndarray

This method is based on the chain rule:

$\frac{df(x)}{dx} = \frac{df(x)}{dx_u}\frac{dx_u}{dx} = \frac{df(x)}{dx_u}\frac{1}{u_b-l_b}$

where $$x_u = \frac{x-l_b}{u_b-l_b}$$ is the normalized input vector, $$x$$ is the unnormalized input vector, $$\frac{df(x)}{dx_u}$$ is the unnormalized gradient $$\frac{df(x)}{dx}$$ is the normalized one, and $$l_b$$ and $$u_b$$ are the lower and upper bounds of $$x$$.

Parameters:

g_vect (ndarray) – The gradient to be unnormalized.

Returns:

Return type:

ndarray

unnormalize_vect(x_vect, minus_lb=True, no_check=False, out=None)[source]

Unnormalize a normalized vector of the design space.

If minus_lb is True:

$x = x_u(u_b-l_b) + l_b$

where $$x_u$$ is the normalized input vector, $$x$$ is the unnormalized input vector and $$l_b$$ and $$u_b$$ are the lower and upper bounds of $$x$$.

Otherwise:

$x = x_u(u_b-l_b)$
Parameters:
• x_vect (ndarray) – The values of the design variables.

• minus_lb (bool) –

Whether to remove the lower bounds at normalization.

By default it is set to True.

• no_check (bool) –

Whether to check if the components are in $$[0,1]$$.

By default it is set to False.

• out (ndarray | None) – The array to store the unnormalized vector. If None, create a new array.

Returns:

The unnormalized vector.

Return type:

ndarray

untransform_vect(vector, no_check=False, out=None)[source]

Map a vector with components in $$[0,1]$$ to the design space.

Parameters:
• vector (ndarray) – A vector with components in $$[0,1]$$.

• no_check (bool) –

Whether to check if the components are in $$[0,1]$$.

By default it is set to False.

• out (ndarray | None) – The array to store the untransformed vector. If None, create a new array.

Returns:

A point of the variables space.

Return type:

ndarray

dimension: int

The total dimension of the space, corresponding to the sum of the sizes of the variables.

name: str | None

The name of the space.

normalize: dict[str, ndarray]

The normalization policies of the variables components indexed by the variables names; if True, the component can be normalized.

variables_names: list[str]

The names of the variables.

variables_sizes: dict[str, int]

The sizes of the variables.

variables_types: dict[str, ndarray]

The types of the variables components, which can be any DesignSpace.DesignVariableType.

## Optimization problem¶

class gemseo.algos.opt_problem.OptimizationProblem(design_space, pb_type='non-linear', input_database=None, differentiation_method='user', fd_step=1e-07, parallel_differentiation=False, use_standardized_objective=True, **parallel_differentiation_options)[source]

An optimization problem.

Create an optimization problem from:

execute it from an algorithm provided by a DriverLib, and store some execution data in a Database.

In particular, this Database stores the calls to all the functions so that no function is called twice with the same inputs.

An OptimizationProblem also has an automated scaling of function with respect to the bounds of the design variables so that the driving algorithms work with inputs scaled between 0 and 1.

Lastly, OptimizationProblem automates the generation of finite differences or complex step wrappers on functions, when analytical gradient is not available.

Parameters:
• design_space (DesignSpace) – The design space on which the functions are evaluated.

• pb_type (str) –

The type of the optimization problem among OptimizationProblem.AVAILABLE_PB_TYPES.

By default it is set to “non-linear”.

• input_database (str | Path | Database | None) – A database to initialize that of the optimization problem. If None, the optimization problem starts from an empty database.

• differentiation_method (str) –

The default differentiation method to be applied to the functions of the optimization problem.

By default it is set to “user”.

• fd_step (float) –

The step to be used by the step-based differentiation methods.

By default it is set to 1e-07.

• parallel_differentiation (bool) –

Whether to approximate the derivatives in parallel.

By default it is set to False.

• use_standardized_objective (bool) –

Whether to use standardized objective for logging and post-processing.

By default it is set to True.

• **parallel_differentiation_options (int | bool) – The options to approximate the derivatives in parallel.

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 (float | None) – The value for which the constraint is active. If None, this value is 0.

• cstr_type (str | None) – The type of the constraint. Either equality or inequality.

• positive (bool) –

If True, then the inequality constraint is positive.

By default it is set to False.

Raises:
Return type:

None

Add an equality constraint to the optimization problem.

Parameters:
• cstr_func (MDOFunction) – The constraint.

• value (float | None) – The value for which the constraint is active. If None, this value is 0.

Return type:

None

Add an inequality constraint to the optimization problem.

Parameters:
• cstr_func (MDOFunction) – The constraint.

• value (float | None) – The value for which the constraint is active. If None, this value is 0.

• 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.

When the OptimizationProblem is executed, the observables are called following this sequence:

Parameters:
• obs_func (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)[source]

Aggregates a constraint to generate a reduced dimension constraint.

Parameters:
• constr_id (int) – The index of the constraint in constraints.

• method (str | Callable[[Callable], Callable]) –

The aggregation method, e.g. "max", "KS" or "IKS".

By default it is set to “max”.

• groups (tuple[ndarray] | None) – The groups for which to produce an output. If None, a single output constraint is produced.

• **options (Any) – The options of the aggregation method.

Raises:

ValueError – When the given is index is greater or equal than the number of constraints or when the method is aggregation unknown.

change_objective_sign()[source]

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()[source]

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)[source]

Check that a function is an instance of MDOFunction.

Parameters:

input_function (Any) – The function to be tested.

Raises:

TypeError – If the function is not a MDOFunction.

Return type:

None

clear_listeners()[source]

Clear all the listeners.

Return type:

None

evaluate_functions(x_vect=None, eval_jac=False, eval_obj=True, eval_observables=False, normalize=True, no_db_no_norm=False, constraints_names=None, observables_names=None, jacobians_names=None)[source]

Compute the functions of interest, and possibly their derivatives.

These functions of interest are the constraints, and possibly the objective.

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 (ndarray) – The input vector at which the functions must be evaluated; if None, the initial point x_0 is used.

• eval_jac (bool) –

Whether to compute the Jacobian matrices of the functions of interest. If True and jacobians_names is None then compute the Jacobian matrices (or gradients) of the functions that are selected for evaluation (with eval_obj, constraints_names, eval_observables andobservables_names). If False and jacobians_names is None then no Jacobian matrix is evaluated. If jacobians_names is not None then the value of eval_jac is ignored.

By default it is set to False.

• eval_obj (bool) –

Whether to consider the objective function as a function of interest.

By default it is set to True.

• eval_observables (bool) –

Whether to evaluate the observables. If True and observables_names is None then all the observables are evaluated. If False and observables_names is None then no observable is evaluated. If observables_names is not None then the value of eval_observables is ignored.

By default it is set to False.

• normalize (bool) –

Whether to consider the input vector x_vect 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.

• constraints_names (Iterable[str] | None) – The names of the constraints to evaluate. If None then all the constraints are evaluated.

• observables_names (Iterable[str] | None) – The names of the observables to evaluate. If None and eval_observables is True then all the observables are evaluated. If None and eval_observables is False then no observable is evaluated.

• jacobians_names (Iterable[str] | None) – The names of the functions whose Jacobian matrices (or gradients) to compute. If None and eval_jac is True then compute the Jacobian matrices (or gradients) of the functions that are selected for evaluation (with eval_obj, constraints_names, eval_observables andobservables_names). If None and eval_jac is False then no Jacobian matrix is computed.

Returns:

The output values of the functions of interest, as well as their Jacobian matrices if eval_jac is True.

Raises:

ValueError – If a name in jacobians_names is not the name of a function of the problem.

Return type:

tuple[dict[str, float | ndarray], dict[str, ndarray]]

execute_observables_callback(last_x)[source]

The callback function to be passed to the database.

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

Parameters:

last_x (ndarray) – The design variables values from the last evaluation.

Return type:

None

export_hdf(file_path, append=False)[source]

Export the optimization problem to an HDF file.

Parameters:
• file_path (str | Path) – The path of 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, input_values=None)[source]

Export the database of the optimization problem to a Dataset.

The variables can be classified into groups: Dataset.DESIGN_GROUP or Dataset.INPUT_GROUP for the design variables and Dataset.FUNCTION_GROUP or Dataset.OUTPUT_GROUP for the functions (objective, constraints and observables).

Parameters:
Returns:

A dataset built from the database of the optimization problem.

Return type:

Dataset

get_active_ineq_constraints(x_vect, tol=1e-06)[source]

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

Parameters:
• x_vect (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:
get_all_functions()[source]

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()[source]

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()[source]

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:
get_constraints_names()[source]

Retrieve the names of the constraints.

Returns:

The names of the constraints.

Return type:

list[str]

get_constraints_number()[source]

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)[source]

Return the data for specific names of variables.

Parameters:
• names (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:

ndarray | dict[str, ndarray]

get_design_variable_names()[source]

Retrieve the names of the design variables.

Returns:

The names of the design variables.

Return type:

list[str]

get_dimension()[source]

Retrieve the total number of design variables.

Returns:

The dimension of the design space.

Return type:

int

get_eq_constraints()[source]

Retrieve all the equality constraints.

Returns:

The equality constraints.

Return type:
get_eq_constraints_number()[source]

Retrieve the number of equality constraints.

Returns:

The number of equality constraints.

Return type:

int

get_eq_cstr_total_dim()[source]

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()[source]

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[ndarray], list[dict[str, float | list[int]]]]

get_function_dimension(name)[source]

Return the dimension of a function of the problem (e.g. a constraint).

Parameters:

name (str) – The name of the function.

Returns:

The dimension of the function.

Raises:
• ValueError – If the function name is unknown to the problem.

• RuntimeError – If the function dimension is not unavailable.

Return type:

int

get_function_names(names)[source]

Return the names of the functions stored in the database.

Parameters:

names (Iterable[str]) – The names of the outputs or constraints specified by the user.

Returns:

The names of the constraints stored in the database.

Return type:

list[str]

get_functions_dimensions(names=None)[source]

Return the dimensions of the outputs of the problem functions.

Parameters:

names (Iterable[str] | None) – The names of the functions. If None, then the objective and all the constraints are considered.

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()[source]

Retrieve all the inequality constraints.

Returns:

The inequality constraints.

Return type:
get_ineq_constraints_number()[source]

Retrieve the number of inequality constraints.

Returns:

The number of inequality constraints.

Return type:

int

get_ineq_cstr_total_dim()[source]

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()[source]

Retrieve the non-processed constraints.

Returns:

The non-processed constraints.

Return type:
get_nonproc_objective()[source]

Retrieve the non-processed objective function.

Return type:

MDOFunction

get_number_of_unsatisfied_constraints(design_variables)[source]

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

Parameters:

design_variables (ndarray) – The design variables.

Returns:

The number of unsatisfied scalar constraints.

Return type:

int

get_objective_name(standardize=True)[source]

Retrieve the name of the objective function.

Parameters:

standardize (bool) –

Whether to use the name of the objective expressed as a cost, e.g. "-f" when the user seeks to maximize "f".

By default it is set to True.

Returns:

The name of the objective function.

Return type:

str

get_observable(name)[source]

Return an observable of the problem.

Parameters:

name (str) – The name of the observable.

Returns:

The pre-processed observable if the functions of the problem have already been pre-processed, otherwise the original one.

Return type:

MDOFunction

get_optimum()[source]

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:
get_scalar_constraints_names()[source]

Return the names of the scalar constraints.

Returns:

The names of the scalar constraints.

Return type:

list[str]

get_violation_criteria(x_vect)[source]

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 (ndarray) – The vector of the design variables values.

Returns:

The feasibility of the point and the violation measure.

Return type:
get_x0_normalized(cast_to_real=False)[source]

Return the current values of the design variables after normalization.

Parameters:

cast_to_real (bool) –

Whether to cast the return value to real.

By default it is set to False.

Returns:

The current values of the design variables normalized between 0 and 1 from their lower and upper bounds.

Return type:

ndarray

has_constraints()[source]

Check if the problem has equality or inequality constraints.

Returns:

True if the problem has equality or inequality constraints.

has_eq_constraints()[source]

Check if the problem has equality constraints.

Returns:

True if the problem has equality constraints.

Return type:

bool

has_ineq_constraints()[source]

Check if the problem has inequality constraints.

Returns:

True if the problem has inequality constraints.

Return type:

bool

has_nonlinear_constraints()[source]

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)[source]

Import an optimization history from an HDF file.

Parameters:
• file_path (str | Path) – 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:

OptimizationProblem

is_max_iter_reached()[source]

Check if the maximum amount of iterations has been reached.

Returns:

Whether the maximum amount of iterations has been reached.

Return type:

bool

is_point_feasible(out_val, constraints=None)[source]

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, ndarray]) – The values of the objective function, and eventually constraints.

• constraints (Iterable[MDOFunction] | None) – The constraints whose values are to be tested. If None, then take all constraints of the problem.

Returns:

The feasibility of the point.

Return type:

bool

preprocess_functions(is_function_input_normalized=True, use_database=True, round_ints=True, eval_obs_jac=False)[source]

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:
• is_function_input_normalized (bool) –

Whether to consider the function input as normalized and unnormalize it before the evaluation takes place.

By default it is set to True.

• use_database (bool) –

Whether to wrap the functions in the database.

By default it is set to True.

• round_ints (bool) –

Whether to round the integer variables.

By default it is set to True.

• eval_obs_jac (bool) –

Whether to evaluate the Jacobian of the observables.

By default it is set to False.

Return type:

None

static repr_constraint(func, ctype, value=None, positive=False)[source]

Express a constraint as a string expression.

Parameters:
• func (MDOFunction) – The constraint function.

• ctype (str) – The type of the constraint. Either equality or inequality.

• value (float | None) – The value for which the constraint is active. If None, this value is 0.

• 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

reset(database=True, current_iter=True, design_space=True, function_calls=True, preprocessing=True)[source]

Partially or fully reset the optimization problem.

Parameters:
• database (bool) –

Whether to clear the database.

By default it is set to True.

• current_iter (bool) –

Whether to reset the current iteration OptimizationProblem.current_iter.

By default it is set to True.

• design_space (bool) –

Whether to reset the current point of the OptimizationProblem.design_space to its initial value (possibly none).

By default it is set to True.

• function_calls (bool) –

Whether to reset the number of calls of the functions.

By default it is set to True.

• preprocessing (bool) –

Whether to turn the pre-processing of functions to False.

By default it is set to True.

Return type:

None

activate_bound_check: ClassVar[bool] = True

Whether to check if a point is in the design space before calling functions.

constraint_names: dict[str, list[str]]

The standardized constraint names bound to the original ones.

constraints: list[gemseo.core.mdofunctions.mdo_function.MDOFunction]

The constraints.

current_iter: int

The current iteration.

database: Database

The database to store the optimization problem data.

design_space: DesignSpace

The design space on which the optimization problem is solved.

property differentiation_method: str

The differentiation method.

property dimension: int

The dimension of the design space.

eq_tolerance: float

The tolerance for the equality constraints.

fd_step: float

The finite differences step.

ineq_tolerance: float

The tolerance for the inequality constraints.

property is_mono_objective: bool

Whether the optimization problem is mono-objective.

max_iter: int

The maximum iteration.

minimize_objective: bool

Whether to maximize the objective.

new_iter_observables: list[gemseo.core.mdofunctions.mdo_function.MDOFunction]

The observables to be called at each new iterate.

nonproc_constraints: list[gemseo.core.mdofunctions.mdo_function.MDOFunction]

The non-processed constraints.

nonproc_new_iter_observables: list[gemseo.core.mdofunctions.mdo_function.MDOFunction]

The non-processed observables to be called at each new iterate.

nonproc_objective: MDOFunction

The non-processed objective function.

nonproc_observables: list[gemseo.core.mdofunctions.mdo_function.MDOFunction]

The non-processed observables.

property objective: MDOFunction

The objective function.

observables: list[gemseo.core.mdofunctions.mdo_function.MDOFunction]

The observables.

property parallel_differentiation: bool

Whether to approximate the derivatives in parallel.

property parallel_differentiation_options: dict[str, int | bool]

The options to approximate the derivatives in parallel.

pb_type: str

The type of optimization problem.

preprocess_options: dict

The options to pre-process the functions.

solution: OptimizationResult

The solution of the optimization problem.

stop_if_nan: bool

Whether the optimization stops when a function returns NaN.

use_standardized_objective: bool

Whether to use standardized objective for logging and post-processing.

The standardized objective corresponds to the original one expressed as a cost function to minimize. A DriverLib works with this standardized objective and the Database stores its values. However, for convenience, it may be more relevant to log the expression and the values of the original objective.

## Driver¶

class gemseo.algos.driver_lib.DriverLib[source]

Abstract class for DOE & optimization libraries interfaces.

Lists available methods in the library for the proposed problem to be solved.

To integrate an optimization package, inherit from this class and put your file in gemseo.algos.doe or gemseo.algo.opt packages.

deactivate_progress_bar()[source]

Deactivate the progress bar.

Return type:

None

driver_has_option(option_name)

Check the existence of an option.

Parameters:

option_name (str) – The name of the option.

Returns:

Whether the option exists.

Return type:

bool

ensure_bounds(orig_func, normalize=True)[source]

Project the design vector onto the design space before execution.

Parameters:
• orig_func – The original function.

• normalize

Whether to use the normalized design space.

By default it is set to True.

Returns:

A function calling the original function with the input data projected onto the design space.

execute(problem, algo_name=None, eval_obs_jac=False, skip_int_check=False, **options)[source]

Execute the driver.

Parameters:
• problem (OptimizationProblem) – The problem to be solved.

• algo_name (str | None) – The name of the algorithm. If None, use the algo_name attribute which may have been set by the factory.

• eval_obs_jac (bool) –

Whether to evaluate the Jacobian of the observables.

By default it is set to False.

• skip_int_check (bool) –

Whether to skip the integer variable handling check of the selected algorithm.

By default it is set to False.

• **options (DriverLibOptionType) – The options for the algorithm.

Returns:

The optimization result.

Raises:

ValueError – If algo_name was not either set by the factory or given as an argument.

Return type:

OptimizationResult

Filter the algorithms capable of solving the problem.

Parameters:

problem (Any) – The problem to be solved.

Returns:

The names of the algorithms adapted to this problem.

Return type:

list[str]

finalize_iter_observer()[source]

Finalize the iteration observer.

Return type:

None

get_optimum_from_database(message=None, status=None)[source]

Retrieve the optimum from the database and build an optimization.

get_x0_and_bounds_vects(normalize_ds)[source]

Return x0 and bounds.

Parameters:

normalize_ds – Whether to normalize the input variables that are not integers, according to the normalization policy of the design space.

Returns:

The current value, the lower bounds and the upper bounds.

init_iter_observer(max_iter, message='...')[source]

Initialize the iteration observer.

It will handle the stopping criterion and the logging of the progress bar.

Parameters:
• max_iter (int) – The maximum number of iterations.

• message (str) –

The message to display at the beginning.

By default it is set to “…”.

Raises:

ValueError – If the max_iter is not greater than or equal to one.

Return type:

None

init_options_grammar(algo_name)

Initialize the options’ grammar.

Parameters:

algo_name (str) – The name of the algorithm.

Return type:

JSONGrammar

Returns True if the algorithm requires a gradient evaluation.

Parameters:

algo_name – The name of the algorithm.

classmethod is_algorithm_suited(algorithm_description, problem)

Check if an algorithm is suited to a problem according to its description.

Parameters:
• algorithm_description (AlgorithmDescription) – The description of the algorithm.

• problem (Any) – The problem to be solved.

Returns:

Whether the algorithm is suited to the problem.

Return type:

bool

new_iteration_callback(x_vect=None)[source]

Iterate the progress bar, implement the stop criteria.

Parameters:

x_vect (ndarray | None) – The design variables values. If None, use the values of the last iteration.

Raises:

MaxTimeReached – If the elapsed time is greater than the maximum execution time.

Return type:

None

LIBRARY_NAME: ClassVar[str | None] = None

The name of the interfaced library.

OPTIONS_DIR: Final[str] = 'options'

The name of the directory containing the files of the grammars of the options.

OPTIONS_MAP: dict[str, str] = {}

The names of the options in GEMSEO mapping to those in the wrapped library.

activate_progress_bar: ClassVar[bool] = True

Whether to activate the progress bar in the optimization log.

algo_name: str | None

The name of the algorithm used currently.

property algorithms: list[str]

The available algorithms.

descriptions: dict[str, AlgorithmDescription]

The description of the algorithms contained in the library.

internal_algo_name: str | None

The internal name of the algorithm used currently.

It typically corresponds to the name of the algorithm in the wrapped library if any.

opt_grammar: JSONGrammar | None

The grammar defining the options of the current algorithm.

problem: Any | None

The problem to be solved.