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
- 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.
- 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:
- 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:
- 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 fromvariables_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:
- Returns:
Either the filtered original design space or a copy.
- Raises:
ValueError – If the variable is not in the design space.
- Return type:
- filter_dim(variable, keep_dimensions)[source]
Filter the design space to keep a subset of dimensions for a variable.
- Parameters:
- Returns:
The filtered design space.
- Raises:
ValueError – If a dimension is unknown.
- Return type:
- classmethod from_csv(file_path, header=None)[source]
Create a design space from a CSV file.
- Parameters:
- Returns:
The design space defined in the file.
- Raises:
ValueError – If the file does not contain the minimal variables in its header.
- Return type:
- classmethod from_file(file_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.
**options (Any) – The keyword reading options.
- Returns:
The design space defined in the file.
- Return type:
- classmethod from_hdf(file_path)[source]
Create a design space from an HDF file.
- Parameters:
file_path (str | Path) – The path to the HDF file.
- Returns:
The design space defined in the file.
- Return type:
- 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:
- 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:
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 theDesignSpace
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 theDesignSpace
, you shall copy this object and modify the copy.See also
To modify the current value, please use
set_current_value()
orset_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.
- get_indexed_variable_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.
- 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 | None
- get_lower_bounds(variable_names: Sequence[str] | None = None, as_dict: Literal[False] = False) ndarray [source]
- get_lower_bounds(variable_names: Sequence[str] | None = None, as_dict: Literal[True] = False) dict[str, ndarray]
Return the lower bounds of design variables.
- Parameters:
variable_names – The names of the design variables. If
None
, the lower bounds of all the design variables are returned.as_dict – Whether to return the lower bounds as a dictionary of the form
{variable_name: variable_lower_bound}
.
- Returns:
The lower bounds of the design variables.
- get_pretty_table(fields=None, with_index=False, capitalize=False, simplify=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.
capitalize (bool) –
Whether to capitalize the field names and replace
"_"
by" "
.By default it is set to False.
simplify (bool) –
Whether to return a simplified tabular view.
By default it is set to False.
- Returns:
A tabular view of the design space.
- Return type:
- get_size(name)[source]
Get the size of a variable.
- get_type(name)[source]
Return the type of a variable.
- 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 | None
- get_upper_bounds(variable_names: Sequence[str] | None = None, as_dict: Literal[False] = False) ndarray [source]
- get_upper_bounds(variable_names: Sequence[str] | None = None, as_dict: Literal[True] = False) dict[str, ndarray]
Return the upper bounds of design variables.
- Parameters:
variable_names – The names of the design variables. If
None
, the upper bounds of all the design variables are returned.as_dict – Whether to return the upper bounds as a dictionary of the form
{variable_name: variable_upper_bound}
.
- Returns:
The upper bounds of the design variables.
- get_variables_indexes(variable_names, use_design_space_order=True)[source]
Return the indexes of a design array corresponding to variables names.
- Parameters:
variable_names (Iterable[str]) – The names of the variables.
use_design_space_order (bool) –
Whether to order the indexes according to the order of the variables names in the design space. Otherwise the indexes will be ordered in the same order as the variables names were required.
By default it is set to True.
- Returns:
The indexes of a design array corresponding to the variables names.
- Return type:
NDArray[int]
- 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:
- 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:
- 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
- normalize_grad(g_vect)[source]
Normalize an unnormalized gradient.
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 \(x\).
Then, the normalized gradient reads:
\[\frac{df(x)}{dx_u} = (u_b-l_b)\frac{df(x)}{dx}\]where \(\frac{df(x)}{dx}\) is the unnormalized one.
- 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 (ArrayType) – 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:
ArrayType
- project_into_bounds(x_c, normalized=False)[source]
Project a vector onto the bounds, using a simple coordinate wise approach.
- 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.
- round_vect(x_vect, copy=True)[source]
Round the vector where variables are of integer type.
- set_current_value(value)[source]
Set the current design value.
- Parameters:
value (ndarray | Mapping[str, ndarray] | OptimizationResult) – The value of the current design.
- Raises:
ValueError – If the value has a wrong dimension.
TypeError – If the value is neither a mapping of NumPy arrays, a NumPy array nor an
OptimizationResult
.
- Return type:
None
- set_current_variable(name, current_value)[source]
Set the current value of a single variable.
- 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
- to_csv(output_file, fields=None, header_char='', **table_options)[source]
Export the design space to a CSV file.
- Parameters:
output_file (str | Path) – The path to the file.
fields (Sequence[str] | None) – The fields to be exported. If
None
, export all fields.header_char (str) –
The header character.
By default it is set to “”.
**table_options (Any) – The names and values of additional attributes for the
PrettyTable
view generated byDesignSpace.get_pretty_table()
.
- Return type:
None
- to_file(file_path, **options)[source]
Save the design space.
- Parameters:
file_path (str | Path) – The file path to save the design space. If the extension starts with “hdf”, the design space will be saved in an HDF file.
**options – The keyword reading options.
- to_hdf(file_path, append=False)[source]
Export the design space to an HDF file.
- 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
- unnormalize_grad(g_vect)[source]
Unnormalize a normalized gradient.
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 \(x\).
- 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 (ArrayType) – 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:
ArrayType
- 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.
- normalize: dict[str, ndarray]
The normalization policies of the variables components indexed by the variables names; if True, the component can be normalized.
- variable_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=ProblemType.LINEAR, input_database=None, differentiation_method=DifferentiationMethod.USER_GRAD, fd_step=1e-07, parallel_differentiation=False, use_standardized_objective=True, **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 aDatabase
.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.
**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 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 toDatabase.store()
.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 aNormDBFunction
, which unnormalizes thex_vect
before evaluation.The unnormalized
x_vect
and the result of the evaluation are stored in theOptimizationProblem.database
.The previous step triggers the
OptimizationProblem.new_iter_listeners
, which calls the observables with the unnormalizedx_vect
.The observables themselves are wrapped as a
NormDBFunction
byOptimizationProblem.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 ofobjective_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
andjacobian_names
isNone
then compute the Jacobian matrices (or gradients) of the functions that are selected for evaluation (witheval_obj
,constraint_names
,eval_observables
and``observable_names``). IfFalse
andjacobian_names
isNone
then no Jacobian matrix is evaluated. Ifjacobian_names
is notNone
then the value ofeval_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
andobservable_names
isNone
then all the observables are evaluated. IfFalse
andobservable_names
isNone
then no observable is evaluated. Ifobservable_names
is notNone
then the value ofeval_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
andeval_observables
isTrue
then all the observables are evaluated. IfNone
andeval_observables
isFalse
then no observable is evaluated.jacobian_names (Iterable[str] | None) – The names of the functions whose Jacobian matrices (or gradients) to compute. If
None
andeval_jac
isTrue
then compute the Jacobian matrices (or gradients) of the functions that are selected for evaluation (witheval_obj
,constraint_names
,eval_observables
and``observable_names``). IfNone
andeval_jac
isFalse
then no Jacobian matrix is computed.
- Returns:
The output values of the functions of interest, as well as their Jacobian matrices if
eval_jac
isTrue
.- Raises:
ValueError – If a name in
jacobian_names
is not the name of a function of the problem.- Return type:
- 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)[source]
Import an optimization history from an HDF file.
- Parameters:
- Returns:
The read optimization problem.
- Return type:
- get_active_ineq_constraints(x_vect, tol=1e-06)[source]
For each constraint, indicate if its different components are active.
- Parameters:
- Returns:
For each constraint, a boolean indicator of activation of its different components.
- Return type:
- 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.
- 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_best_infeasible_point()[source]
Retrieve the best infeasible point within a given tolerance.
- get_constraint_names()[source]
Retrieve the names of the constraints.
- get_constraints_number()[source]
Retrieve the number of constraints.
- Returns:
The number of constraints.
- Return type:
- get_data_by_names(names, as_dict=True, filter_non_feasible=False)[source]
Return the data for specific names of variables.
- Parameters:
- Returns:
The data related to the variables.
- Return type:
- get_design_variable_names()[source]
Retrieve the names of the design variables.
- get_dimension()[source]
Retrieve the total number of design variables.
- Returns:
The dimension of the design space.
- Return type:
- 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:
- 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:
- get_feasible_points()[source]
Retrieve the feasible points within a given tolerance.
This tolerance is defined by
OptimizationProblem.eq_tolerance
for equality constraints andOptimizationProblem.ineq_tolerance
for inequality ones.
- 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:
- get_function_names(names)[source]
Return the names of the functions stored in the database.
- 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:
- 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:
- 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:
- 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:
- get_nonproc_objective()[source]
Retrieve the non-processed objective function.
- Return type:
- get_number_of_unsatisfied_constraints(design_variables, values=mappingproxy({}))[source]
Return the number of scalar constraints not satisfied by design variables.
- Parameters:
- Returns:
The number of unsatisfied scalar constraints.
- Return type:
- get_objective_name(standardize=True)[source]
Retrieve the name of the objective function.
- 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:
- 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:
- get_scalar_constraint_names()[source]
Return the names of the scalar constraints.
- 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.
- get_x0_normalized(cast_to_real=False, as_dict=False)[source]
Return the initial values of the design variables after normalization.
- Parameters:
- Returns:
The current values of the design variables normalized between 0 and 1 from their lower and upper bounds.
- Return type:
- has_constraints()[source]
Check if the problem has equality or inequality constraints.
- Returns:
True if the problem has equality or inequality constraints.
- Return type:
- has_eq_constraints()[source]
Check if the problem has equality constraints.
- Returns:
True if the problem has equality constraints.
- Return type:
- has_ineq_constraints()[source]
Check if the problem has inequality constraints.
- Returns:
True if the problem has inequality constraints.
- Return type:
- has_nonlinear_constraints()[source]
Check if the problem has non-linear constraints.
- Returns:
True if the problem has equality or inequality constraints.
- Return type:
- 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:
- 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:
- 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:
- 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
orDataset.INPUT_GROUP
for the design variables andDataset.FUNCTION_GROUP
orDataset.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
andDataset.FUNCTION_GROUP
as groups. Otherwise, useDataset.INPUT_GROUP
andDataset.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:
- to_hdf(file_path, append=False)[source]
Export the optimization problem to an HDF file.
- 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 theDatabase
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_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'
- deactivate_progress_bar()[source]
Deactivate the progress bar.
- Return type:
None
- driver_has_option(option_name)
Check the existence of an option.
- 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:
- filter_adapted_algorithms(problem)
Filter the algorithms capable of solving the problem.
- 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:
- 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:
- 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:
- 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:
- 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
- requires_gradient(driver_name)[source]
Check if a driver requires the gradient.
- 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.
- 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.