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(name='')[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:

name (str) –

The name to be given to the design space. If empty, the design space is unnamed.

By default it is set to “”.

class DesignVariable(size=1, var_type=_DesignVariableType.FLOAT, l_b=None, u_b=None, value=None)[source]

A design variable.

Create new instance of DesignVariable(size, var_type, l_b, u_b, value)

Parameters:

size (int | None) –

By default it is set to 1.
var_type (NDArray[_DesignVariableType] | _DesignVariableType | None) –

By default it is set to “float”.
l_b (ndarray | None) –
u_b (ndarray | None) –
value (ndarray | None) –

l_b: ndarray | None: Alias for field number 2

size: int | None: Alias for field number 0

u_b: ndarray | None: Alias for field number 3

value: ndarray | None: Alias for field number 4

var_type: NDArray[_DesignVariableType] | _DesignVariableType | None: Alias for field number 1

DesignVariableType: alias of _DesignVariableType

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 (DesignVariableType | Sequence[DesignVariableType]) –
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:: dict[str, ndarray]

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 mapping of design values into a NumPy array.

Parameters:

design_values (Mapping[str, ndarray]) – The mapping of design values.
variable_names (Iterable[str] | None) – The design variables to be considered. If None, consider all the design variables.

Returns:

The design values as a NumPy array.

Return type:

ndarray

Notes

The data type of the returned NumPy array is the most general data type of the values of the mapping design_values corresponding to the keys iterable from variables_names.

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

classmethod from_csv(file_path, header=None)[source]

Create a design space from a CSV file.

Parameters:

file_path (str | Path) – The path to the CSV 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 defined in the file.

Raises:

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

Return type:

DesignSpace

classmethod from_file(file_path, hdf_node_path='', **options)[source]

Create a design space from a file.

Parameters:

file_path (str | Path) – The path to the file. If the extension starts with “hdf”, the file will be considered as an HDF file.
hdf_node_path (str) –
The path of the HDF node from which the database should be imported. If empty, the root node is considered.

By default it is set to “”.
**options (Any) – The keyword reading options.

Returns:

The design space defined in the file.

Return type:

DesignSpace

classmethod from_hdf(file_path, hdf_node_path='')[source]

Create a design space from an HDF file.

Parameters:

file_path (str | Path) – The path to the HDF file.
hdf_node_path (str) –
The path of the HDF node from which the database should be imported. If empty, the root node is considered.

By default it is set to “”.

Returns:

The design space defined in the file.

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.

Optimization problem¶

class gemseo.algos.opt_problem.OptimizationProblem(design_space, pb_type=ProblemType.LINEAR, input_database=None, differentiation_method=DifferentiationMethod.USER_GRAD, fd_step=1e-07, parallel_differentiation=False, use_standardized_objective=True, hdf_node_path='', **parallel_differentiation_options)[source]

An optimization problem.

Create an optimization problem from:

a DesignSpace specifying the design variables in terms of names, lower bounds, upper bounds and initial guesses,
the objective function as an MDOFunction, which can be a vector,

execute it from an algorithm provided by a DriverLibrary, 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 (ProblemType) –
The type of the optimization problem.

By default it is set to “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 (DifferentiationMethod) –
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

By default it is set to False.
parallel. –
use_standardized_objective (bool) –
Whether to use standardized objective for logging and post-processing.

By default it is set to True.
hdf_node_path (str) –
The path of the HDF node from which the database should be imported. If empty, the root node is considered.

By default it is set to “”.
**parallel_differentiation_options (int | bool) – The options to approximate the derivatives in parallel.

AggregationFunction: alias of EvaluationFunction

class ApproximationMode(value)

The approximation derivation modes.

CENTERED_DIFFERENCES = 'centered_differences': The centered differences method used to approximate the Jacobians by perturbing each variable with a small real number.

COMPLEX_STEP = 'complex_step': The complex step method used to approximate the Jacobians by perturbing each variable with a small complex number.

FINITE_DIFFERENCES = 'finite_differences': The finite differences method used to approximate the Jacobians by perturbing each variable with a small real number.

class DifferentiationMethod(value)

The differentiation methods.

CENTERED_DIFFERENCES = 'centered_differences'

COMPLEX_STEP = 'complex_step'

FINITE_DIFFERENCES = 'finite_differences'

NO_DERIVATIVE = 'no_derivative'

USER_GRAD = 'user'

class ProblemType(value)[source]

The type of problem.

add_callback(callback_func, each_new_iter=True, each_store=False)[source]

Add a callback for some events.

The callback functions are attached to the database, which means they are triggered when new values are stored within the database of the optimization problem.

Parameters:

callback_func (Callable[[ndarray], Any]) – A function to be called after some events, whose argument is a design vector.
each_new_iter (bool) –
Whether to evaluate the callback functions after evaluating all functions of the optimization problem for a given point and storing their values in the database.

By default it is set to True.
each_store (bool) –
Whether to evaluate the callback functions after storing any new value in the database.

By default it is set to False.

Return type:

None

add_constraint(cstr_func, value=None, cstr_type=None, positive=False)[source]

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 (MDOFunction.ConstraintType | None) – The type of the constraint.
positive (bool) –
If True, then the inequality constraint is positive.

By default it is set to False.

Raises:

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

Return type:

None

add_eq_constraint(cstr_func, value=None)[source]

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_ineq_constraint(cstr_func, value=None, positive=False)[source]

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_observable(obs_func, new_iter=True)[source]

Add a function to be observed.

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

The optimization algorithm calls the objective function with a normalized x_vect.

The OptimizationProblem.preprocess_functions() wraps the function as a NormDBFunction, which unnormalizes the x_vect before evaluation.

The unnormalized x_vect and the result of the evaluation are stored in the OptimizationProblem.database.

The previous step triggers the OptimizationProblem.new_iter_listeners, which calls the observables with the unnormalized x_vect.

The observables themselves are wrapped as a NormDBFunction by OptimizationProblem.preprocess_functions(), but in this case the input is always expected as unnormalized to avoid an additional normalizing-unnormalizing step.

Finally, the output is stored in the OptimizationProblem.database.

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(constraint_index, method=EvaluationFunction.MAX, groups=None, **options)[source]

Aggregate a constraint to generate a reduced dimension constraint.

Parameters:

constraint_index (int) – The index of the constraint in constraints.
method (Callable[[NDArray[float]], float] | AggregationFunction) –
The aggregation method, e.g. "max", "lower_bound_KS", "upper_bound_KS"``or ``"IKS".

By default it is set to “MAX”.
groups (Iterable[Sequence[int]] | None) – The groups of components of the constraint to aggregate to produce one aggregation constraint per group of components; if None, a single aggregation constraint is produced.
**options (Any) – The options of the aggregation method.

Raises:

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

Return type:

None

apply_exterior_penalty(objective_scale=1.0, scale_inequality=1.0, scale_equality=1.0)[source]

Reformulate the optimization problem using exterior penalty.

Given the optimization problem with equality and inequality constraints:

\[ \begin{align}\begin{aligned}min_x f(x)\\s.t.\\g(x)\leq 0\\h(x)=0\\l_b\leq x\leq u_b\end{aligned}\end{align} \]

The exterior penalty approach consists in building a penalized objective function that takes into account constraints violations:

\[ \begin{align}\begin{aligned}min_x \tilde{f}(x) = \frac{f(x)}{o_s} + s[\sum{H(g(x))g(x)^2}+\sum{h(x)^2}]\\s.t.\\l_b\leq x\leq u_b\end{aligned}\end{align} \]

Where \(H(x)\) is the Heaviside function, \(o_s\) is the objective_scale parameter and \(s\) is the scale parameter. The solution of the new problem approximate the one of the original problem. Increasing the values of objective_scale and scale, the solutions are closer but the optimization problem requires more and more iterations to be solved.

Parameters:

scale_equality (float | ndarray) –
The equality constraint scaling constant.

By default it is set to 1.0.
objective_scale (float) –
The objective scaling constant.

By default it is set to 1.0.
scale_inequality (float | ndarray) –
The inequality constraint scaling constant.

By default it is set to 1.0.

Return type:

None

change_objective_sign()[source]

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

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

Return type:: None

check()[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 an 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=True, normalize=True, no_db_no_norm=False, constraint_names=None, observable_names=None, jacobian_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 jacobian_names is None then compute the Jacobian matrices (or gradients) of the functions that are selected for evaluation (with eval_obj, constraint_names, eval_observables and``observable_names``). If False and jacobian_names is None then no Jacobian matrix is evaluated. If jacobian_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 observable_names is None then all the observables are evaluated. If False and observable_names is None then no observable is evaluated. If observable_names is not None then the value of eval_observables is ignored.

By default it is set to True.
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.
constraint_names (Iterable[str] | None) – The names of the constraints to evaluate. If None then all the constraints are evaluated.
observable_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.
jacobian_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, constraint_names, eval_observables and``observable_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 jacobian_names is not the name of a function of the problem.

Return type:

EvaluationType

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

classmethod from_hdf(file_path, x_tolerance=0.0, hdf_node_path='')[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.
hdf_node_path (str) –
The path of the HDF node from which the database should be imported. If empty, the root node is considered.

By default it is set to “”.

Returns:

The read optimization problem.

Return type:

OptimizationProblem

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:

dict[MDOFunction, ndarray]

get_all_function_name()[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_all_functions(original=False)[source]

Retrieve all the functions of the optimization problem.

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

Parameters:

original (bool) –

Whether to return the original functions or the preprocessed ones.

By default it is set to False.

Returns:

All the functions of the optimization problem.

Return type:

list[MDOFunction]

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:: tuple[ndarray | None, ndarray | None, bool, dict[str, ndarray]]

get_constraint_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:: list[MDOFunction]

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:: list[MDOFunction]

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_last_point()[source]

Return the last design point.

Returns:

The last point result, defined by:

the value of the objective function,
the value of the design variables,
the indicator of feasibility of the last point,
the value of the constraints,
the value of the gradients of the constraints.

Raises:

ValueError – When the optimization database is empty.

Return type:

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

get_nonproc_constraints()[source]

Retrieve the non-processed constraints.

Returns:: The non-processed constraints.
Return type:: list[MDOFunction]

get_nonproc_objective()[source]

Retrieve the non-processed objective function.

Return type:: MDOFunction

get_number_of_unsatisfied_constraints(design_variables, values=mappingproxy({}))[source]

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

Parameters:

design_variables (ndarray) – The design variables.
values (Mapping[str, float | ndarray]) –
The values of the constraints. N.B. the missing values will be read from the database or computed.

By default it is set to {}.

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.

Raises:

ValueError – When the optimization database is empty.

Return type:

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

get_reformulated_problem_with_slack_variables()[source]

Add slack variables and replace inequality constraints with equality ones.

Given the original optimization problem,

\[ \begin{align}\begin{aligned}min_x f(x)\\s.t.\\g(x)\leq 0\\h(x)=0\\l_b\leq x\leq u_b\end{aligned}\end{align} \]

Slack variables are introduced for all inequality constraints that are non-positive. An equality constraint for each slack variable is then defined.

\[ \begin{align}\begin{aligned}min_{x,s} F(x,s) = f(x)\\s.t.\\H(x,s) = h(x)=0\\G(x,s) = g(x)-s=0\\l_b\leq x\leq u_b\\s\leq 0\end{aligned}\end{align} \]

Returns:: An optimization problem without inequality constraints.
Return type:: OptimizationProblem

get_scalar_constraint_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]

Check if a design point is feasible and measure its constraint violation.

The constraint violation measure at a design point \(x\) is

\[\lVert\max(g(x)-\varepsilon_{\text{ineq}},0)\rVert_2^2 +\lVert|\max(|h(x)|-\varepsilon_{\text{eq}},0)\rVert_2^2\]

where \(\|.\|_2\) is the Euclidean norm, \(g(x)\) is the inequality constraint vector, \(h(x)\) is the equality constraint vector, \(\varepsilon_{\text{ineq}}\) is the tolerance for the inequality constraints and \(\varepsilon_{\text{eq}}\) is the tolerance for the equality constraints.

If the design point is feasible, the constraint violation measure is 0.

Parameters:: x_vect (ndarray) – The design point \(x\).
Returns:: Whether the design point is feasible, and its constraint violation measure.
Return type:: tuple[bool, float]

get_x0_normalized(cast_to_real=False, as_dict=False)[source]

Return the initial values of the design variables after normalization.

Parameters:

cast_to_real (bool) –
Whether to return the real part of the initial values.

By default it is set to False.
as_dict (bool) –
Whether to return the values as a dictionary of the form {variable_name: variable_value}.

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 | dict[str, ndarray]

has_constraints()[source]

Check if the problem has equality or inequality constraints.

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

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

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.

Notes

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, support_sparse_jacobian=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.
support_sparse_jacobian (bool) –
Whether the driver support sparse Jacobian.

By default it is set to False.

Return type:

None

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

Express a constraint as a string expression.

Parameters:

func (MDOFunction) – The constraint function.
cstr_type (MDOFunction.ConstraintType) – The type of 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.

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

to_dataset(name='', categorize=True, opt_naming=True, export_gradients=False, input_values=())[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:

name (str) –
The name to be given to the dataset. If empty, use the name of the OptimizationProblem.database.

By default it is set to “”.
categorize (bool) –
Whether to distinguish between the different groups of variables. Otherwise, group all the variables in Dataset.PARAMETER_GROUP`.

By default it is set to True.
opt_naming (bool) –
Whether to use Dataset.DESIGN_GROUP and Dataset.FUNCTION_GROUP as groups. Otherwise, use Dataset.INPUT_GROUP and Dataset.OUTPUT_GROUP.

By default it is set to True.
export_gradients (bool) –
Whether to export 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.
input_values (Iterable[ndarray]) –
The input values to be considered. If empty, consider all the input values of the database.

By default it is set to ().

Returns:

A dataset built from the database of the optimization problem.

Return type:

Dataset

to_hdf(file_path, append=False, hdf_node_path='')[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.
hdf_node_path (str) –
The path of the HDF node in which the database should be exported. If empty, the root node is considered.

By default it is set to “”.

Return type:

None

activate_bound_check: ClassVar[bool] = True: Whether to check if a point is in the design space before calling functions.

property constraint_names: dict[str, list[str]]: The standardized constraint names bound to the original ones.

constraints: list[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 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.

Raises:: ValueError – When the dimension of the objective cannot be determined.

max_iter: int: The maximum iteration.

property minimize_objective: bool: Whether to minimize the objective.

new_iter_observables: list[MDOFunction]: The observables to be called at each new iterate.

nonproc_constraints: list[MDOFunction]: The non-processed constraints.

nonproc_new_iter_observables: list[MDOFunction]: The non-processed observables to be called at each new iterate.

nonproc_objective: MDOFunction: The non-processed objective function.

nonproc_observables: list[MDOFunction]: The non-processed observables.

property objective: MDOFunction: The objective function.

observables: list[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: ProblemType: The type of optimization problem.

preprocess_options: dict: The options to pre-process the functions.

solution: OptimizationResult | None: The solution of the optimization problem if solved; otherwise None.

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 DriverLibrary 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.

Examples

Driver¶

class gemseo.algos.driver_library.DriverLibrary[source]

Abstract class for driver library 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.

class ApproximationMode(value)

The approximation derivation modes.

CENTERED_DIFFERENCES = 'centered_differences': The centered differences method used to approximate the Jacobians by perturbing each variable with a small real number.

COMPLEX_STEP = 'complex_step': The complex step method used to approximate the Jacobians by perturbing each variable with a small complex number.

FINITE_DIFFERENCES = 'finite_differences': The finite differences method used to approximate the Jacobians by perturbing each variable with a small real number.

class DifferentiationMethod(value)

The differentiation methods.

CENTERED_DIFFERENCES = 'centered_differences'

COMPLEX_STEP = 'complex_step'

FINITE_DIFFERENCES = 'finite_differences'

USER_GRAD = 'user'

clear_listeners()[source]

Remove the listeners from the database.

Return type:: None

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 (bool) –
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_adapted_algorithms(problem)

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]

Return the optimization result from the database.

Return type:: OptimizationResult

get_x0_and_bounds_vects(normalize_ds: bool, as_dict: Literal[False] = False) → tuple[ndarray, ndarray, ndarray][source]

get_x0_and_bounds_vects(normalize_ds: bool, as_dict: Literal[True] = False) → tuple[dict[str, ndarray], dict[str, ndarray], dict[str, ndarray]]

Return the initial design variable values and their lower and upper bounds.

Parameters:

normalize_ds – Whether to normalize the design variables.
as_dict – Whether to return dictionaries instead of NumPy arrays.

Returns:

The initial values of the design variables, their lower bounds, and their 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 of the progress bar status.

By default it is set to “”.

Raises:

ValueError – If max_iter is lower than 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

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)[source]

Iterate the progress bar, implement the stop criteria.

Parameters:: x_vect (ndarray) – The design variables values.
Raises:: MaxTimeReached – If the elapsed time is greater than the maximum execution time.
Return type:: None

requires_gradient(driver_name)[source]

Check if a driver requires the gradient.

Parameters:: driver_name (str) – The name of the driver.
Returns:: Whether the driver requires the gradient.
Return type:: bool

LIBRARY_NAME: ClassVar[str | None] = None: The name of the interfaced library.

OPTIONS_DIR: ClassVar[str | Path] = 'options': The name of the directory containing the files of the grammars of the options.

OPTIONS_MAP: ClassVar[dict[str, str]] = {}: The names of the options in GEMSEO mapping to those in the wrapped library.

USE_ONE_LINE_PROGRESS_BAR: ClassVar[bool] = False: Whether to use a one line progress bar.

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: OptimizationProblem: The optimization problem the driver library is bonded to.