opt_problem module¶
Optimization problem.
The OptimizationProblem
class operates on a DesignSpace
defining:
an initial guess \(x_0\) for the design variables,
the bounds \(l_b \\leq x \\leq u_b\) of the design variables.
A (possible vector) objective function with a MDOFunction
type
is set using the objective
attribute.
If the optimization problem looks for the maximum of this objective function,
the OptimizationProblem.change_objective_sign()
changes the objective function sign
because the optimization drivers seek to minimize this objective function.
Equality and inequality constraints are also MDOFunction
instances
provided to the OptimizationProblem
by means of its OptimizationProblem.add_constraint()
method.
The OptimizationProblem
allows to evaluate the different functions
for a given design parameters vector
(see OptimizationProblem.evaluate_functions()
).
Note that this evaluation step relies on an automated scaling of function wrt the bounds
so that optimizers and DOE algorithms work
with inputs scaled between 0 and 1 for all the variables.
The OptimizationProblem
has also a Database
that stores the calls to all the functions
so that no function is called twice with the same inputs.
Concerning the derivatives computation,
the OptimizationProblem
automates
the generation of the finite differences or complex step wrappers on functions,
when the analytical gradient is not available.
Lastly,
various getters and setters are available,
as well as methods to export the Database
to a HDF file or to a Dataset
for future postprocessing.
Classes:

An optimization problem. 
 class gemseo.algos.opt_problem.OptimizationProblem(design_space, pb_type='nonlinear', input_database=None, differentiation_method='user', fd_step=1e07, parallel_differentiation=False, **parallel_differentiation_options)[source]¶
Bases:
object
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 a
MDOFunction
, which can be a vector,
execute it from an algorithm provided by a
DriverLib
, 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. nonproc_objective¶
The nonprocessed objective function.
 Type
 constraints¶
The constraints.
 Type
List(MDOFunction)
 nonproc_constraints¶
The nonprocessed constraints.
 Type
List(MDOFunction)
 observables¶
The observables.
 Type
List(MDOFunction)
 new_iter_observables¶
The observables to be called at each new iterate.
 Type
List(MDOFunction)
 nonproc_observables¶
The nonprocessed observables.
 Type
List(MDOFunction)
 nonproc_new_iter_observables¶
The nonprocessed observables to be called at each new iterate.
 Type
List(MDOFunction)
 minimize_objective¶
If True, maximize the objective.
 Type
bool
 fd_step¶
The finite differences step.
 Type
float
 pb_type¶
The type of optimization problem.
 Type
str
 ineq_tolerance¶
The tolerance for the inequality constraints.
 Type
float
 eq_tolerance¶
The tolerance for the equality constraints.
 Type
float
 solution¶
The solution of the optimization problem.
 design_space¶
The design space on which the optimization problem is solved.
 Type
 stop_if_nan¶
If True, the optimization stops when a function returns NaN.
 Type
bool
 preprocess_options¶
The options to preprocess the functions.
 Type
Dict
 Parameters
design_space (DesignSpace) – The design space on which the functions are evaluated.
pb_type (str) –
The type of the optimization problem among
OptimizationProblem.AVAILABLE_PB_TYPES
.By default it is set to nonlinear.
input_database (Optional[Union[str,Database]]) –
A database to initialize that of the optimization problem. If None, the optimization problem starts from an empty database.
By default it is set to None.
differentiation_method (str) –
The default differentiation method to be applied to the functions of the optimization problem.
By default it is set to user.
fd_step (float) –
The step to be used by the stepbased differentiation methods.
By default it is set to 1e07.
parallel_differentiation (bool) –
Whether to approximate the derivatives in parallel.
By default it is set to False.
**parallel_differentiation_options (Union[int,bool]) – The options to approximate the derivatives in parallel.
 Return type
None
Attributes:
The differentiation method.
The dimension of the design space.
Whether the optimization problem is monoobjective.
The objective function.
Whether to approximate the derivatives in parallel.
The options to approximate the derivatives in parallel.
Methods:
add_callback
(callback_func[, each_new_iter, ...])Add a callback function after each store operation or new iteration.
add_constraint
(cstr_func[, value, ...])Add a constraint (equality and inequality) to the optimization problem.
add_eq_constraint
(cstr_func[, value])Add an equality constraint to the optimization problem.
add_ineq_constraint
(cstr_func[, value, positive])Add an inequality constraint to the optimization problem.
add_observable
(obs_func[, new_iter])Add a function to be observed.
aggregate_constraint
(constr_id[, method, groups])Aggregates a constraint to generate a reduced dimension constraint.
Change the objective function sign in order to minimize its opposite.
check
()Check if the optimization problem is ready for run.
check_format
(input_function)Check that a function is an instance of
MDOFunction
.Clear all the listeners.
evaluate_functions
([x_vect, eval_jac, ...])Compute the objective and the constraints.
execute_observables_callback
(last_x)The callback function to be passed to the database.
export_hdf
(file_path[, append])Export the optimization problem to an HDF file.
export_to_dataset
([name, by_group, ...])Export the database of the optimization problem to a
Dataset
.get_active_ineq_constraints
(x_vect[, tol])For each constraint, indicate if its different components are active.
Retrieve all the functions of the optimization problem.
Retrieve the names of all the function of the optimization problem.
Retrieve the best infeasible point within a given tolerance.
Retrieve the names of the constraints.
Retrieve the number of constraints.
get_data_by_names
(names[, as_dict, ...])Return the data for specific names of variables.
Retrieve the names of the design variables.
Retrieve the total number of design variables.
Retrieve all the equality constraints.
Retrieve the number of equality constraints.
Retrieve the total dimension of the equality constraints.
Retrieve the feasible points within a given tolerance.
Return the dimensions of the outputs of the problem functions.
Retrieve all the inequality constraints.
Retrieve the number of inequality constraints.
Retrieve the total dimension of the inequality constraints.
Retrieve the nonprocessed constraints.
Retrieve the nonprocessed objective function.
Return the number of scalar constraints not satisfied by design variables.
Retrieve the name of the objective function.
get_observable
(name)Retrieve an observable from its name.
Return the optimum solution within a given feasibility tolerances.
Return the names of the scalar constraints.
get_violation_criteria
(x_vect)Compute a violation measure associated to an iteration.
Return the current values of the design variables after normalization.
Check if the problem has equality or inequality constraints.
Check if the problem has equality constraints.
Check if the problem has inequality constraints.
Check if the problem has nonlinear constraints.
import_hdf
(file_path[, x_tolerance])Import an optimization history from an HDF file.
Check if the maximum amount of iterations has been reached.
is_point_feasible
(out_val[, constraints])Check if a point is feasible.
preprocess_functions
([normalize, ...])Preprocess all the functions and eventually the gradient.
repr_constraint
(func, ctype[, value, positive])Express a constraint as a string expression.
 AVAILABLE_PB_TYPES = ['linear', 'nonlinear']¶
 COMPLEX_STEP = 'complex_step'¶
 CONSTRAINTS_GROUP = 'constraints'¶
 DESIGN_SPACE_ATTRS = ['u_bounds', 'l_bounds', 'x_0', 'x_names', 'dimension']¶
 DESIGN_SPACE_GROUP = 'design_space'¶
 DESIGN_VAR_NAMES = 'x_names'¶
 DESIGN_VAR_SIZE = 'x_size'¶
 DIFFERENTIATION_METHODS = ['user', 'complex_step', 'finite_differences', 'no_derivatives']¶
 FINITE_DIFFERENCES = 'finite_differences'¶
 FUNCTIONS_ATTRS = ['objective', 'constraints']¶
 GGOBI_FORMAT = 'ggobi'¶
 HDF5_FORMAT = 'hdf5'¶
 LINEAR_PB = 'linear'¶
 NON_LINEAR_PB = 'nonlinear'¶
 NO_DERIVATIVES = 'no_derivatives'¶
 OBJECTIVE_GROUP = 'objective'¶
 OPTIM_DESCRIPTION = ['minimize_objective', 'fd_step', 'differentiation_method', 'pb_type', 'ineq_tolerance', 'eq_tolerance']¶
 OPT_DESCR_GROUP = 'opt_description'¶
 SOLUTION_GROUP = 'solution'¶
 USER_GRAD = 'user'¶
 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 to
Database.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 (Optional[value]) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
cstr_type (Optional[str]) –
The type of the constraint. Either equality or inequality.
By default it is set to None.
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 (gemseo.core.mdofunctions.mdo_function.MDOFunction) – The constraint.
value (Optional[float]) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
 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 (Optional[value]) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
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.
 Parameters
obs_func (gemseo.core.mdofunctions.mdo_function.MDOFunction) – An observable to be observed.
new_iter (bool) –
If True, then the observable will be called at each new iterate.
By default it is set to True.
 Return type
None
 aggregate_constraint(constr_id, method='max', groups=None, **options)[source]¶
Aggregates a constraint to generate a reduced dimension constraint.
 Parameters
constr_id (int) – index of the constraint in self.constraints
method (str or callable, that takes a function and returns a function) –
aggregation method, among (‘max’,’KS’, ‘IKS’)
By default it is set to max.
groups (tuple of ndarray) –
if None, a single output constraint is produced otherwise, one output per group is produced.
By default it is set to 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 – The function to be tested.
 Raises
TypeError – If the function is not a
MDOFunction
. Return type
None
 property differentiation_method¶
The differentiation method.
 property dimension¶
The dimension of the design space.
 evaluate_functions(x_vect=None, eval_jac=False, eval_obj=True, normalize=True, no_db_no_norm=False)[source]¶
Compute the objective and the constraints.
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 (Optional[numpy.ndarray]) –
The input vector at which the functions must be evaluated; if None, x_0 is used.
By default it is set to None.
eval_jac (bool) –
If True, then the Jacobian is evaluated
By default it is set to False.
eval_obj (bool) –
If True, then the objective function is evaluated
By default it is set to True.
normalize (bool) –
If True, then input vector is considered normalized
By default it is set to True.
no_db_no_norm (bool) –
If True, then do not use the preprocessed functions, so we have no database, nor normalization.
By default it is set to False.
 Returns
The functions values and/or the Jacobian values according to the passed arguments.
 Raises
ValueError – If both no_db_no_norm and normalize are True.
 Return type
Tuple[Dict[str, Union[float, numpy.ndarray]], Dict[str, numpy.ndarray]]
 execute_observables_callback(last_x)[source]¶
The callback function to be passed to the database.
Call all the observables with the last design variables values as argument.
 Parameters
last_x (numpy.ndarray) – The design variables values from the last evaluation.
 Return type
None
 export_hdf(file_path, append=False)[source]¶
Export the optimization problem to an HDF file.
 Parameters
file_path (str) – The file to store the data.
append (bool) –
If True, then the data are appended to the file if not empty.
By default it is set to False.
 Return type
None
 export_to_dataset(name=None, by_group=True, categorize=True, opt_naming=True, export_gradients=False)[source]¶
Export the database of the optimization problem to a
Dataset
.The variables can be classified into groups, separating the design variables and functions (objective function and constraints). This classification can use either an optimization naming, with
Database.DESIGN_GROUP
andDatabase.FUNCTION_GROUP
or an inputoutput naming, withDatabase.INPUT_GROUP
andDatabase.OUTPUT_GROUP
 Parameters
name (Optional[str]) –
A name to be given to the dataset. If None, use the name of the
database
.By default it is set to None.
by_group (bool) –
If True, then store the data by group. Otherwise, store them by variables.
By default it is set to True.
categorize (bool) –
If True, then distinguish between the different groups of variables.
By default it is set to True.
opt_naming (bool) –
If True, then use an optimization naming.
By default it is set to True.
export_gradients (bool) –
If True, then export also 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.
 Returns
A dataset built from the database of the optimization problem.
 Return type
 get_active_ineq_constraints(x_vect, tol=1e06)[source]¶
For each constraint, indicate if its different components are active.
 Parameters
x_vect (numpy.ndarray) – The vector of design variables.
tol (float) –
The tolerance for deciding whether a constraint is active.
By default it is set to 1e06.
 Returns
For each constraint, a boolean indicator of activation of its different components.
 Return type
Dict[str, numpy.ndarray]
 get_all_functions()[source]¶
Retrieve all the functions of the optimization problem.
These functions are the constraints, the objective function and the observables.
 Returns
All the functions of the optimization problem.
 Return type
 get_all_functions_names()[source]¶
Retrieve the names of all the function of the optimization problem.
These functions are the constraints, the objective function and the observables.
 Returns
The names of all the functions of the optimization problem.
 Return type
List[str]
 get_best_infeasible_point()[source]¶
Retrieve the best infeasible point within a given tolerance.
 Returns
The best infeasible point expressed as the design variables values, the objective function value, the feasibility of the point and the functions values.
 Return type
Tuple[Optional[numpy.ndarray], Optional[numpy.ndarray], bool, Dict[str, numpy.ndarray]]
 get_constraints_names()[source]¶
Retrieve the names of the constraints.
 Returns
The names of the constraints.
 Return type
List[str]
 get_constraints_number()[source]¶
Retrieve the number of constraints.
 Returns
The number of constraints.
 Return type
int
 get_data_by_names(names, as_dict=True, filter_non_feasible=False)[source]¶
Return the data for specific names of variables.
 Parameters
names (Union[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 nonfeasible points from the data.
By default it is set to False.
 Returns
The data related to the variables.
 Return type
Union[numpy.ndarray, Dict[str, numpy.ndarray]]
 get_design_variable_names()[source]¶
Retrieve the names of the design variables.
 Returns
The names of the design variables.
 Return type
List[str]
 get_dimension()[source]¶
Retrieve the total number of design variables.
 Returns
The dimension of the design space.
 Return type
int
 get_eq_constraints()[source]¶
Retrieve all the equality constraints.
 Returns
The equality constraints.
 Return type
 get_eq_constraints_number()[source]¶
Retrieve the number of equality constraints.
 Returns
The number of equality constraints.
 Return type
int
 get_eq_cstr_total_dim()[source]¶
Retrieve the total dimension of the equality constraints.
This dimension is the sum of all the outputs dimensions of all the equality constraints.
 Returns
The total dimension of the equality constraints.
 Return type
int
 get_feasible_points()[source]¶
Retrieve the feasible points within a given tolerance.
This tolerance is defined by
OptimizationProblem.eq_tolerance
for equality constraints andOptimizationProblem.ineq_tolerance
for inequality ones. Returns
The values of the design variables and objective function for the feasible points.
 Return type
Tuple[List[numpy.ndarray], List[Dict[str, Union[float, List[int]]]]]
 get_functions_dimensions()[source]¶
Return the dimensions of the outputs of the problem functions.
 Returns
The dimensions of the outputs of the problem functions. The dictionary keys are the functions names and the values are the functions dimensions.
 Return type
Dict[str, int]
 get_ineq_constraints()[source]¶
Retrieve all the inequality constraints.
 Returns
The inequality constraints.
 Return type
 get_ineq_constraints_number()[source]¶
Retrieve the number of inequality constraints.
 Returns
The number of inequality constraints.
 Return type
int
 get_ineq_cstr_total_dim()[source]¶
Retrieve the total dimension of the inequality constraints.
This dimension is the sum of all the outputs dimensions of all the inequality constraints.
 Returns
The total dimension of the inequality constraints.
 Return type
int
 get_nonproc_constraints()[source]¶
Retrieve the nonprocessed constraints.
 Returns
The nonprocessed constraints.
 Return type
 get_number_of_unsatisfied_constraints(design_variables)[source]¶
Return the number of scalar constraints not satisfied by design variables.
 Parameters
design_variables (numpy.ndarray) – The design variables.
 Returns
The number of unsatisfied scalar constraints.
 Return type
int
 get_objective_name()[source]¶
Retrieve the name of the objective function.
 Returns
The name of the objective function.
 Return type
str
 get_observable(name)[source]¶
Retrieve an observable from its name.
 Parameters
name (str) – The name of the observable.
 Returns
The observable.
 Raises
ValueError – If the observable cannot be found.
 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.
 Return type
Tuple[numpy.ndarray, numpy.ndarray, bool, Dict[str, numpy.ndarray], Dict[str, numpy.ndarray]]
 get_scalar_constraints_names()[source]¶
Return the names of the scalar constraints.
 Returns
The names of the scalar constraints.
 Return type
List[str]
 get_violation_criteria(x_vect)[source]¶
Compute a violation measure associated to an iteration.
For each constraint, when it is violated, add the absolute distance to zero, in L2 norm.
If 0, all constraints are satisfied
 Parameters
x_vect (numpy.ndarray) – The vector of the design variables values.
 Returns
The feasibility of the point and the violation measure.
 Return type
Tuple[bool, float]
 get_x0_normalized()[source]¶
Return the current values of the design variables after normalization.
 Returns
The current values of the design variables normalized between 0 and 1 from their lower and upper bounds.
 Return type
numpy.ndarray
 has_constraints()[source]¶
Check if the problem has equality or inequality constraints.
 Returns
True if the problem has equality or inequality constraints.
 has_eq_constraints()[source]¶
Check if the problem has equality constraints.
 Returns
True if the problem has equality constraints.
 Return type
bool
 has_ineq_constraints()[source]¶
Check if the problem has inequality constraints.
 Returns
True if the problem has inequality constraints.
 Return type
bool
 has_nonlinear_constraints()[source]¶
Check if the problem has nonlinear constraints.
 Returns
True if the problem has equality or inequality constraints.
 Return type
bool
 classmethod import_hdf(file_path, x_tolerance=0.0)[source]¶
Import an optimization history from an HDF file.
 Parameters
file_path (str) – The file containing the optimization history.
x_tolerance (float) –
The tolerance on the design variables when reading the file.
By default it is set to 0.0.
 Returns
The read optimization problem.
 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
bool
 property is_mono_objective¶
Whether the optimization problem is monoobjective.
 is_point_feasible(out_val, constraints=None)[source]¶
Check if a point is feasible.
Note
If the value of a constraint is absent from this point, then this constraint will be considered satisfied.
 Parameters
out_val (Dict[str, numpy.ndarray]) – The values of the objective function, and eventually constraints.
constraints (Optional[Iterable[gemseo.core.mdofunctions.mdo_function.MDOFunction]]) –
The constraints whose values are to be tested. If None, then take all constraints of the problem.
By default it is set to None.
 Returns
The feasibility of the point.
 Return type
bool
 property objective¶
The objective function.
 property parallel_differentiation¶
Whether to approximate the derivatives in parallel.
 property parallel_differentiation_options¶
The options to approximate the derivatives in parallel.
 preprocess_functions(normalize=True, use_database=True, round_ints=True)[source]¶
Preprocess 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
normalize (bool) –
Whether to unnormalize the input vector of the function before evaluate it.
By default it is set to True.
use_database (bool) –
If True, then the functions are wrapped in the database.
By default it is set to True.
round_ints (bool) –
If True, then round the integer variables.
By default it is set to True.
 Return type
None
 static repr_constraint(func, ctype, value=None, positive=False)[source]¶
Express a constraint as a string expression.
 Parameters
func (gemseo.core.mdofunctions.mdo_function.MDOFunction) – The constraint function.
ctype (str) – The type of the constraint. Either equality or inequality.
value (Optional[float]) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
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