The GEMSEO concepts¶
Design space¶
A design space is used to represent the optimization’s unknowns,
a.k.a. design variables. A DesignSpace
describes
this design space at a given state, in terms of names, sizes, types, bounds
and current values of the design variables. Variables can easily be added to
the DesignSpace
using the DesignSpace.add_variable()
method
or removed using the DesignSpace.remove_variable()
method. We can also
filter the design variables using the DesignSpace.filter()
method.
Getters and setters are also available to get or set the value of a given
variable property. Lastly, an instance of DesignSpace
can be stored
in a txt or HDF file.
Classes:

Class that describes the design space at a given state: 
 class gemseo.algos.design_space.DesignSpace(hdf_file=None)[source]
Class that describes the design space at a given state:
the names/sizes/types/bounds of the variables and the initial solution of the optimization problem
Constructor.
Methods:
add_variable
(name[, size, var_type, l_b, …])Add a variable to the design space.
array_to_dict
(x_array)Split the current point into a dictionary with variables names.
check
()Check the state of the design space.
check_membership
(x_vect[, variables_names])Checks whether the input variables satisfy the design space requirements.
dict_to_array
(x_dict[, all_vars, all_var_list])Aggregate a point as dictionary into array.
export_hdf
(file_path[, append])Export to hdf file.
export_to_txt
(output_file[, fields, header_char])Exports the design space to a text file.
extend
(other)Extend the design space with another design space.
filter
(keep_variables[, copy])Filter the design space to keep a sublist of variables.
filter_dim
(variable, keep_dimensions)Filters the design space to keep a sublist of dimensions for a given variable.
get_active_bounds
([x_vec, tol])Determine which bound constraints of the current point are active.
get_current_x
([variables_names])Gets the current point in the design space.
Get the current point in the design space.
Returns the current point normalized.
get_indexed_var_name
(variable_name)Return a list of the variables names with their indices such as.
Return a list of the variables names with their indices such as.
get_lower_bound
(name)Gets the lower bound of a variable.
get_lower_bounds
([variables_names])Generates an array of the variables’ lower bounds.
get_pretty_table
([fields])Builds a PrettyTable object from the design space data.
get_size
(name)Get the size of a variable Return None if the variable is not known.
get_type
(name)Get the type of a variable Return None if the variable is not known.
get_upper_bound
(name)Gets the upper bound of a variable.
get_upper_bounds
([variables_names])Generates an array of the variables’ upper bounds.
get_variables_indexes
(variables_names)Return the indexes of a design array corresponding to the variables names.
Tests if current_x is defined.
import_hdf
(file_path)Imports design space from hdf file.
normalize_vect
(x_vect[, minus_lb])Normalizes a vector of the design space.
project_into_bounds
(x_c[, normalized])Projects x_c onto the bounds, using a simple coordinate wise approach.
read_from_txt
(input_file[, header])Parses a csv file to read the DesignSpace.
remove_variable
(name)Remove a variable (and bounds and types) from the design space.
round_vect
(x_vect)Rounds the vector where variables are of integer type.
set_current_variable
(name, current_value)Set the current value of a single variable.
set_current_x
(current_x)Set the current point.
set_lower_bound
(name, lower_bound)Set a new lower bound for variable name.
set_upper_bound
(name, upper_bound)Set a new upper bound for variable name.
Casts the current value to complex.
unnormalize_vect
(x_vect[, minus_lb, no_check])Unnormalizes a normalized vector of the design space.
 add_variable(name, size=1, var_type='float', l_b=None, u_b=None, value=None)[source]
Add a variable to the design space.
 Parameters
name – param size: (Default value = 1)
var_type – Default value = FLOAT)
l_b – Default value = None)
u_b – Default value = None)
value – Default value = None)
size – (Default value = 1)
 array_to_dict(x_array)[source]
Split the current point into a dictionary with variables names.
 Parameters
x_array – x array to be converted to a dict of array
 check()[source]
Check the state of the design space.
 check_membership(x_vect, variables_names=None)[source]
Checks whether the input variables satisfy the design space requirements.
 Parameters
x_vect (dict or array) – design variables
variables_names – names of the variables to be checked
 dict_to_array(x_dict, all_vars=True, all_var_list=None)[source]
Aggregate a point as dictionary into array.
 Parameters
x_dict – point as dictionary
all_vars – if True, all variables shall be in x_dict
all_var_list – list of whole set of variables, if None, use self.variables_names
 export_hdf(file_path, append=False)[source]
Export to hdf file.
 Parameters
file_path – path to file to write
append – if True, appends the data in the file
 export_to_txt(output_file, fields=None, header_char='', **table_options)[source]
Exports the design space to a text file.
 Parameters
output_file – output file path
fields – list of fields to export, by default all
 extend(other)[source]
Extend the design space with another design space.
 Parameters
other (DesignSpace) – design space to be appended
 filter(keep_variables, copy=False)[source]
Filter the design space to keep a sublist of variables.
 Parameters
keep_variables (str of list(str)) – the list of variables to keep
copy (bool) – if True then a copy of the design space is filtered, otherwise the design space itself is filtered
 Returns
the filtered design space (or a copy)
 Return type
 filter_dim(variable, keep_dimensions)[source]
Filters the design space to keep a sublist of dimensions for a given variable.
 Parameters
variable – the variable
keep_dimensions – the list of dimension to keep
 get_active_bounds(x_vec=None, tol=1e08)[source]
Determine which bound constraints of the current point are active.
 Parameters
x_vec – the point at which we check the bounds
tol – tolerance of comparison of a scalar with a bound (Default value = 1e8)
 get_current_x(variables_names=None)[source]
Gets the current point in the design space.
 Parameters
variables_names (list(str)) – names of the required variables, optional
 Returns
the x vector as array
 Return type
ndarray
 get_current_x_dict()[source]
Get the current point in the design space.
 Returns
the x vector as a dict, keys are the variable names values are the variable vales as np array
 get_current_x_normalized()[source]
Returns the current point normalized.
 Returns
the x vector as array normalized by the bounds
 get_indexed_var_name(variable_name)[source]
Return a list of the variables names with their indices such as.
[x!0,x!1,y,z!0,z!1]
 Parameters
variable_name (str) – name of the variable
 Returns
names of the variable components
 Return type
list(str)
 get_indexed_variables_names()[source]
Return a list of the variables names with their indices such as.
[x!0,x!1,y,z!0,z!1]
 Returns
names of all the variables components
 Return type
list(str)
 get_lower_bound(name)[source]
Gets the lower bound of a variable.
 Parameters
name – variable name
 Returns
variable lower bound (possibly infinite)
 get_lower_bounds(variables_names=None)[source]
Generates an array of the variables’ lower bounds.
 Parameters
variables_names – names of the variables of which the lower bounds are required
 get_pretty_table(fields=None)[source]
Builds a PrettyTable object from the design space data.
 Parameters
fields – list of fields to export, by default all
 Returns
the pretty table object
 get_size(name)[source]
Get the size of a variable Return None if the variable is not known.
 Parameters
name – name of the variable
 get_type(name)[source]
Get the type of a variable Return None if the variable is not known.
 Parameters
name – name of the variable
 get_upper_bound(name)[source]
Gets the upper bound of a variable.
 Parameters
name – variable name
 Returns
variable upper bound (possibly infinite)
 get_upper_bounds(variables_names=None)[source]
Generates an array of the variables’ upper bounds.
 Parameters
variables_names – names of the variables of which the upper bounds are required
 get_variables_indexes(variables_names)[source]
Return the indexes of a design array corresponding to the variables names.
 Parameters
variables_names (list(str)) – names of the variables
 Returns
indexes of a design array corresponding to the variables names
 Return type
ndarray
 has_current_x()[source]
Tests if current_x is defined.
 Returns
True if current_x is defined
 import_hdf(file_path)[source]
Imports design space from hdf file.
 Parameters
file_path –
 normalize_vect(x_vect, minus_lb=True)[source]
Normalizes a vector of the design space. Unbounded variables are not normalized.
 Parameters
x_vect (ndarray) – design variables
minus_lb – if True, remove lower bounds at normalization
 Returns
normalized vector
 project_into_bounds(x_c, normalized=False)[source]
Projects x_c onto the bounds, using a simple coordinate wise approach.
 Parameters
normalized (bool) – if True then the vector is assumed to be normalized
x_c – x vector (np array)
 Returns
projected x_c
 static read_from_txt(input_file, header=None)[source]
Parses a csv file to read the DesignSpace.
 Parameters
input_file – returns: s: the design space
header – fields list, or by default, read in the file
 Returns
the design space
 remove_variable(name)[source]
Remove a variable (and bounds and types) from the design space.
 Parameters
name – name of the variable to remove
 round_vect(x_vect)[source]
Rounds the vector where variables are of integer type.
 Parameters
x_vect – design variables to round
 set_current_variable(name, current_value)[source]
Set the current value of a single variable.
 Parameters
name – name of the variable
current_value – current value of the variable
 set_current_x(current_x)[source]
Set the current point.
 Parameters
current_x – the current design vector
 set_lower_bound(name, lower_bound)[source]
Set a new lower bound for variable name.
 Parameters
name – name of the variable
lower_bound – lower bound
 set_upper_bound(name, upper_bound)[source]
Set a new upper bound for variable name.
 Parameters
name – name of the variable
upper_bound – upper bound
 to_complex()[source]
Casts the current value to complex.
 unnormalize_vect(x_vect, minus_lb=True, no_check=False)[source]
Unnormalizes a normalized vector of the design space.
 Parameters
x_vect (ndarray) – design variables
minus_lb – if True, remove lower bounds at normalization
no_check – if True, don’t check that values are in [0,1]
 Returns
normalized vector
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)[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 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. Attributes
nonproc_objective (MDOFunction) – The nonprocessed objective function.
constraints (List(MDOFunction)) – The constraints.
nonproc_constraints (List(MDOFunction)) – The nonprocessed constraints.
observables (List(MDOFunction)) – The observables.
new_iter_observables (List(MDOFunction)) – The observables to be called at each new iterate.
nonproc_observables (List(MDOFunction)) – The nonprocessed observables.
nonproc_new_iter_observables (List(MDOFunction)) – The nonprocessed observables to be called at each new iterate.
minimize_objective (bool) – If True, maximize the objective.
fd_step (float) – The finite differences step.
differentiation_method (str) – The type differentiation method.
pb_type (str) – The type of optimization problem.
ineq_tolerance (float) – The tolerance for the inequality constraints.
eq_tolerance (float) – The tolerance for the equality constraints.
database (Database) – The database to store the optimization problem data.
solution – The solution of the optimization problem.
design_space (DesignSpace) – The design space on which the optimization problem is solved.
stop_if_nan (bool) – If True, the optimization stops when a function returns NaN.
preprocess_options (Dict) – The options to preprocess the functions.
 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
.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.
differentiation_method (str) – The default differentiation method to be applied to the functions of the optimization problem.
fd_step (float) – The step to be used by the stepbased differentiation methods.
 Return type
None
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_new_iter_listener
(listener_func)Add a listener to be called when a new iteration is stored to the database.
add_observable
(obs_func[, new_iter])Add a function to be observed.
add_store_listener
(listener_func)Add a listener to be called when an item is stored to the database.
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.
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.
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.
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.
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.
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.
is_point_feasible
(out_val[, constraints])Check if a point is feasible.
preprocess_functions
([normalize, …])Preprocess all the functions and eventually the gradien.
repr_constraint
(func, ctype[, value, positive])Express a constraint as a string expression.
Attributes:
The dimension of the design space.
The objective function.
 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.
each_store (bool) – If True, then callback at every call to
Database.store
.
 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.
cstr_type (Optional[str]) – The type of the constraint. Either equality or inequality.
positive (bool) – If True, then the inequality constraint is positive.
 Return type
None
 add_eq_constraint(cstr_func, value=None)[source]
Add an equality constraint to the optimization problem.
 Parameters
cstr_func (gemseo.core.function.MDOFunction) – The constraint.
value (Optional[float]) – 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 (Optional[value]) – The value for which the constraint is active. If None, this value is 0.
positive (bool) – If True, then the inequality constraint is positive.
 Return type
None
 add_new_iter_listener(listener_func)[source]
Add a listener to be called when a new iteration is stored to the database.
 Parameters
listener_func (Callable) – The function to be called.
 Raises
TypeError – If the argument is not a callable
 Return type
None
 add_observable(obs_func, new_iter=True)[source]
Add a function to be observed.
 Parameters
obs_func (gemseo.core.function.MDOFunction) – An observable to be observed.
new_iter (bool) – If True, then the observable will be called at each new iterate.
 Return type
None
 add_store_listener(listener_func)[source]
Add a listener to be called when an item is stored to the database.
 Parameters
listener_func (Callable) – The function to be called.
 Raises
TypeError – If the argument is not a callable
 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’)
groups (tuple of ndarray) – if None, a single output constraint is produced otherwise, one output per group is produced.
 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
 clear_listeners()[source]
Clear all the listeners.
 Return type
None
 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.
eval_jac (bool) – If True, then the Jacobian is evaluated
eval_obj (bool) – If True, then the objective function is evaluated
normalize (bool) – If True, then input vector is considered normalized
no_db_no_norm (bool) – If True, then do not use the preprocessed functions, so we have no database, nor normalization.
 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]]
 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.
 Return type
None
 export_to_dataset(name, 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 (str) – A name to be given to the dataset.
by_group (bool) – If True, then store the data by group. Otherwise, store them by variables.
categorize (bool) – If True, then distinguish between the different groups of variables.
opt_naming (bool) – If True, then use an optimization naming.
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.
 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.
 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_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_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_nonproc_objective()[source]
Retrieve the nonprocessed objective function.
 Return type
 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_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.
 Returns
The read optimization problem.
 Return type
 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.function.MDOFunction]]) – 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
 property objective
The objective function.
 preprocess_functions(normalize=True, use_database=True, round_ints=True)[source]
Preprocess all the functions and eventually the gradien.
Required to wrap the objective function and constraints with the database and eventually the gradients by complex step or finite differences.
 Parameters
normalize (bool) – If True, then the functions are normalized.
use_database (bool) – If True, then the functions are wrapped in the database.
round_ints (bool) – If True, then round the integer variables.
 Return type
None
 static repr_constraint(func, ctype, value=None, positive=False)[source]
Express a constraint as a string expression.
 Parameters
func (gemseo.core.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.
positive (bool) – If True, then the inequality constraint is positive.
 Returns
A string representation of the constraint.
 Return type
str
Driver library¶
A driver library aims to solve an DriverLib
using a particular algorithm from a particular family of numerical methods.
This algorithm will be in charge of evaluating the objective and constraints
functions at different points of the design space, using the
DriverLib.execute()
method.
The most famous kinds of numerical methods to solve an optimization problem
are optimization algorithms and design of experiments (DOE). A DOE driver
browses the design space agnostically, i.e. without taking into
account the function evaluations. On the contrary, an optimization algorithm
uses this information to make the journey through design space
as relevant as possible in order to reach as soon as possible the optimum.
These families are implemented in DOELibrary
and OptimizationLibrary
.
Classes:
Abstract class for DOE & optimization libraries interfaces. 


Extend tqdm progress bar with better time units. 

Redirect tqdm output to the gemseo logger. 
 class gemseo.algos.driver_lib.DriverLib[source]
Abstract class for DOE & optimization libraries interfaces.
Lists available methods in the library for the proposed problem to be solved.
To integrate an optimization package, inherit from this class and put your file in gemseo.algos.doe or gemseo.algo.opt packages.
Constructor.
Attributes:
Return the available algorithms.
Methods:
driver_has_option
(option_key)Checks if the option key exists.
ensure_bounds
(orig_func[, normalize])Project the design vector onto the design space before execution.
execute
(problem[, algo_name])Executes the driver.
filter_adapted_algorithms
(problem)Filters the algorithms capable of solving the problem.
Finalize the iteration observer.
get_optimum_from_database
([message, status])Retrieves the optimum from the database and builds an optimization result object from it.
get_x0_and_bounds_vects
(normalize_ds)Gets x0, bounds, normalized or not depending on algo options, all as numpy arrays.
init_iter_observer
(max_iter, message)Initialize the iteration observer.
init_options_grammar
(algo_name)Initializes the options grammar.
is_algo_requires_grad
(algo_name)Returns True if the algorithm requires a gradient evaluation.
is_algorithm_suited
(algo_dict, problem)Checks if the algorithm is suited to the problem according to its algo dict.
Callback called at each new iteration, ie every time a design vector that is not already in the database is proposed by the optimizer.
 property algorithms
Return the available algorithms.
 driver_has_option(option_key)[source]
Checks if the option key exists.
 Parameters
option_key – the name of the option
 Returns
True if the option is in the grammar
 ensure_bounds(orig_func, normalize=True)[source]
Project the design vector onto the design space before execution.
 Parameters
orig_func – the original function
normalize – if True, use the normalized design space
 Returns
the wrapped function
 execute(problem, algo_name=None, **options)[source]
Executes the driver.
 Parameters
problem – the problem to be solved
algo_name – name of the algorithm if None, use self.algo_name which may have been set by the factory (Default value = None)
options – the options dict for the algorithm
 filter_adapted_algorithms(problem)[source]
Filters the algorithms capable of solving the problem.
 Parameters
problem – the opt_problem to be solved
 Returns
the list of adapted algorithms names
 finalize_iter_observer()[source]
Finalize the iteration observer.
 get_optimum_from_database(message=None, status=None)[source]
Retrieves the optimum from the database and builds an optimization result object from it.
 Parameters
message – Default value = None)
status – Default value = None)
 get_x0_and_bounds_vects(normalize_ds)[source]
Gets x0, bounds, normalized or not depending on algo options, all as numpy arrays.
 Parameters
normalize_ds – if True, normalizes all input vars that are not integers, according to design space normalization policy
 Returns
x, lower bounds, 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 – maximum number of calls
message – message to display at the beginning
 init_options_grammar(algo_name)[source]
Initializes the options grammar.
 Parameters
algo_name – name of the algorithm
 is_algo_requires_grad(algo_name)[source]
Returns True if the algorithm requires a gradient evaluation.
 Parameters
algo_name – name of the algorithm
 static is_algorithm_suited(algo_dict, problem)[source]
Checks if the algorithm is suited to the problem according to its algo dict.
 Parameters
algo_dict – the algorithm characteristics
problem – the opt_problem to be solved
 new_iteration_callback()[source]
Callback called at each new iteration, ie every time a design vector that is not already in the database is proposed by the optimizer.
Iterates the progress bar, implements the stop criteria.
 class gemseo.algos.driver_lib.ProgressBar(*_, **__)[source]
Extend tqdm progress bar with better time units.
Use hour, day or week for slower processes.
 Parameters
iterable (iterable, optional) – Iterable to decorate with a progressbar. Leave blank to manually manage the updates.
desc (str, optional) – Prefix for the progressbar.
total (int or float, optional) – The number of expected iterations. If unspecified, len(iterable) is used if possible. If float(“inf”) or as a last resort, only basic progress statistics are displayed (no ETA, no progressbar). If gui is True and this parameter needs subsequent updating, specify an initial arbitrary large positive number, e.g. 9e9.
leave (bool, optional) – If [default: True], keeps all traces of the progressbar upon termination of iteration. If None, will leave only if position is 0.
file (io.TextIOWrapper or io.StringIO, optional) – Specifies where to output the progress messages (default: sys.stderr). Uses file.write(str) and file.flush() methods. For encoding, see write_bytes.
ncols (int, optional) – The width of the entire output message. If specified, dynamically resizes the progressbar to stay within this bound. If unspecified, attempts to use environment width. The fallback is a meter width of 10 and no limit for the counter and statistics. If 0, will not print any meter (only stats).
mininterval (float, optional) – Minimum progress display update interval [default: 0.1] seconds.
maxinterval (float, optional) – Maximum progress display update interval [default: 10] seconds. Automatically adjusts miniters to correspond to mininterval after long display update lag. Only works if dynamic_miniters or monitor thread is enabled.
miniters (int or float, optional) – Minimum progress display update interval, in iterations. If 0 and dynamic_miniters, will automatically adjust to equal mininterval (more CPU efficient, good for tight loops). If > 0, will skip display of specified number of iterations. Tweak this and mininterval to get very efficient loops. If your progress is erratic with both fast and slow iterations (network, skipping items, etc) you should set miniters=1.
ascii (bool or str, optional) – If unspecified or False, use unicode (smooth blocks) to fill the meter. The fallback is to use ASCII characters ” 123456789#”.
disable (bool, optional) – Whether to disable the entire progressbar wrapper [default: False]. If set to None, disable on nonTTY.
unit (str, optional) – String that will be used to define the unit of each iteration [default: it].
unit_scale (bool or int or float, optional) – If 1 or True, the number of iterations will be reduced/scaled automatically and a metric prefix following the International System of Units standard will be added (kilo, mega, etc.) [default: False]. If any other nonzero number, will scale total and n.
dynamic_ncols (bool, optional) – If set, constantly alters ncols and nrows to the environment (allowing for window resizes) [default: False].
smoothing (float, optional) – Exponential moving average smoothing factor for speed estimates (ignored in GUI mode). Ranges from 0 (average speed) to 1 (current/instantaneous speed) [default: 0.3].
bar_format (str, optional) –
Specify a custom bar string formatting. May impact performance. [default: ‘{l_bar}{bar}{r_bar}’], where l_bar=’{desc}: {percentage:3.0f}%’ and r_bar=’ {n_fmt}/{total_fmt} [{elapsed}<{remaining}, ‘
’{rate_fmt}{postfix}]’
 Possible vars: l_bar, bar, r_bar, n, n_fmt, total, total_fmt,
percentage, elapsed, elapsed_s, ncols, nrows, desc, unit, rate, rate_fmt, rate_noinv, rate_noinv_fmt, rate_inv, rate_inv_fmt, postfix, unit_divisor, remaining, remaining_s, eta.
Note that a trailing “: ” is automatically removed after {desc} if the latter is empty.
initial (int or float, optional) – The initial counter value. Useful when restarting a progress bar [default: 0]. If using float, consider specifying {n:.3f} or similar in bar_format, or specifying unit_scale.
position (int, optional) – Specify the line offset to print this bar (starting from 0) Automatic if unspecified. Useful to manage multiple bars at once (eg, from threads).
postfix (dict or *, optional) – Specify additional stats to display at the end of the bar. Calls set_postfix(**postfix) if possible (dict).
unit_divisor (float, optional) – [default: 1000], ignored unless unit_scale is True.
write_bytes (bool, optional) – If (default: None) and file is unspecified, bytes will be written in Python 2. If True will also write bytes. In all other cases will default to unicode.
lock_args (tuple, optional) – Passed to refresh for intermediate output (initialisation, iterating, and updating).
nrows (int, optional) – The screen height. If specified, hides nested bars outside this bound. If unspecified, attempts to use environment height. The fallback is 20.
colour (str, optional) – Bar colour (e.g. ‘green’, ‘#00ff00’).
delay (float, optional) – Don’t display until [default: 0] seconds have elapsed.
gui (bool, optional) – WARNING: internal parameter  do not use. Use tqdm.gui.tqdm(…) instead. If set, will attempt to use matplotlib animations for a graphical output [default: False].
 Returns
out
 Return type
decorated iterator.
Methods:
clear
([nolock])Clear current bar display.
close
()Cleanup and (if leave=False) close the progressbar.
display
([msg, pos])Use self.sp to display msg in the specified pos.
external_write_mode
([file, nolock])Disable tqdm within context and refresh tqdm when exits.
Formats a number of seconds as a clock time, [H:]MM:SS
format_meter
(n, total, elapsed, **kwargs)Return a stringbased progress bar given some parameters
format_num
(n)Intelligent scientific notation (.3g).
format_sizeof
(num[, suffix, divisor])Formats a number (greater than unity) with SI Order of Magnitude prefixes.
get_lock
()Get the global lock.
pandas
(**tqdm_kwargs)Registers the current tqdm class with
refresh
([nolock, lock_args])Force refresh the display of this bar.
reset
([total])Resets to 0 iterations for repeated use.
set_description
([desc, refresh])Set/modify description of the progress bar.
set_description_str
([desc, refresh])Set/modify description without ‘: ‘ appended.
set_lock
(lock)Set the global lock.
set_postfix
([ordered_dict, refresh])Set/modify postfix (additional stats) with automatic formatting based on datatype.
set_postfix_str
([s, refresh])Postfix without dictionary expansion, similar to prefix handling.
status_printer
(file)Manage the printing and inplace updating of a line of characters.
unpause
()Restart tqdm timer from last print time.
update
([n])Manually update the progress bar, useful for streams such as reading files.
wrapattr
(stream, method[, total, bytes])stream : filelike object. method : str, “read” or “write”. The result of read() and the first argument of write() should have a len().
write
(s[, file, end, nolock])Print a message via tqdm (without overlap with bars).
Attributes:
Public API for readonly member access.
 clear(nolock=False)
Clear current bar display.
 close()
Cleanup and (if leave=False) close the progressbar.
 display(msg=None, pos=None)
Use self.sp to display msg in the specified pos.
Consider overloading this function when inheriting to use e.g.: self.some_frontend(**self.format_dict) instead of self.sp.
 Parameters
msg (str, optional. What to display (default: repr(self)).) –
pos (int, optional. Position to moveto) – (default: abs(self.pos)).
 classmethod external_write_mode(file=None, nolock=False)
Disable tqdm within context and refresh tqdm when exits. Useful when writing to standard output stream
 property format_dict
Public API for readonly member access.
 static format_interval(t)
Formats a number of seconds as a clock time, [H:]MM:SS
 Parameters
t (int) – Number of seconds.
 Returns
out – [H:]MM:SS
 Return type
str
 classmethod format_meter(n, total, elapsed, **kwargs)[source]
Return a stringbased progress bar given some parameters
 Parameters
n (int or float) – Number of finished iterations.
total (int or float) – The expected total number of iterations. If meaningless (None), only basic progress statistics are displayed (no ETA).
elapsed (float) – Number of seconds passed since start.
ncols (int, optional) – The width of the entire output message. If specified, dynamically resizes {bar} to stay within this bound [default: None]. If 0, will not print any bar (only stats). The fallback is {bar:10}.
prefix (str, optional) – Prefix message (included in total width) [default: ‘’]. Use as {desc} in bar_format string.
ascii (bool, optional or str, optional) – If not set, use unicode (smooth blocks) to fill the meter [default: False]. The fallback is to use ASCII characters ” 123456789#”.
unit (str, optional) – The iteration unit [default: ‘it’].
unit_scale (bool or int or float, optional) – If 1 or True, the number of iterations will be printed with an appropriate SI metric prefix (k = 10^3, M = 10^6, etc.) [default: False]. If any other nonzero number, will scale total and n.
rate (float, optional) – Manual override for iteration rate. If [default: None], uses n/elapsed.
bar_format (str, optional) –
Specify a custom bar string formatting. May impact performance. [default: ‘{l_bar}{bar}{r_bar}’], where l_bar=’{desc}: {percentage:3.0f}%’ and r_bar=’ {n_fmt}/{total_fmt} [{elapsed}<{remaining}, ‘
’{rate_fmt}{postfix}]’
 Possible vars: l_bar, bar, r_bar, n, n_fmt, total, total_fmt,
percentage, elapsed, elapsed_s, ncols, nrows, desc, unit, rate, rate_fmt, rate_noinv, rate_noinv_fmt, rate_inv, rate_inv_fmt, postfix, unit_divisor, remaining, remaining_s, eta.
Note that a trailing “: ” is automatically removed after {desc} if the latter is empty.
postfix (*, optional) – Similar to prefix, but placed at the end (e.g. for additional stats). Note: postfix is usually a string (not a dict) for this method, and will if possible be set to postfix = ‘, ‘ + postfix. However other types are supported (#382).
unit_divisor (float, optional) – [default: 1000], ignored unless unit_scale is True.
initial (int or float, optional) – The initial counter value [default: 0].
colour (str, optional) – Bar colour (e.g. ‘green’, ‘#00ff00’).
 Returns
out
 Return type
Formatted meter and stats, ready to display.
 static format_num(n)
Intelligent scientific notation (.3g).
 Parameters
n (int or float or Numeric) – A Number.
 Returns
out – Formatted number.
 Return type
str
 static format_sizeof(num, suffix='', divisor=1000)
Formats a number (greater than unity) with SI Order of Magnitude prefixes.
 Parameters
num (float) – Number ( >= 1) to format.
suffix (str, optional) – Postpostfix [default: ‘’].
divisor (float, optional) – Divisor between prefixes [default: 1000].
 Returns
out – Number with Order of Magnitude SI unit postfix.
 Return type
str
 classmethod get_lock()
Get the global lock. Construct it if it does not exist.
 classmethod pandas(**tqdm_kwargs)
 Registers the current tqdm class with
pandas.core. ( frame.DataFrame  series.Series  groupby.(generic.)DataFrameGroupBy  groupby.(generic.)SeriesGroupBy ).progress_apply
A new instance will be create every time progress_apply is called, and each instance will automatically close() upon completion.
 Parameters
tqdm_kwargs (arguments for the tqdm instance) –
Examples
>>> import pandas as pd >>> import numpy as np >>> from tqdm import tqdm >>> from tqdm.gui import tqdm as tqdm_gui >>> >>> df = pd.DataFrame(np.random.randint(0, 100, (100000, 6))) >>> tqdm.pandas(ncols=50) # can use tqdm_gui, optional kwargs, etc >>> # Now you can use `progress_apply` instead of `apply` >>> df.groupby(0).progress_apply(lambda x: x**2)
References
<https://stackoverflow.com/questions/18603270/ progressindicatorduringpandasoperationspython>
 refresh(nolock=False, lock_args=None)
Force refresh the display of this bar.
 Parameters
nolock (bool, optional) – If True, does not lock. If [default: False]: calls acquire() on internal lock.
lock_args (tuple, optional) – Passed to internal lock’s acquire(). If specified, will only display() if acquire() returns True.
 reset(total=None)
Resets to 0 iterations for repeated use.
Consider combining with leave=True.
 Parameters
total (int or float, optional. Total to use for the new bar.) –
 set_description(desc=None, refresh=True)
Set/modify description of the progress bar.
 Parameters
desc (str, optional) –
refresh (bool, optional) – Forces refresh [default: True].
 set_description_str(desc=None, refresh=True)
Set/modify description without ‘: ‘ appended.
 classmethod set_lock(lock)
Set the global lock.
 set_postfix(ordered_dict=None, refresh=True, **kwargs)
Set/modify postfix (additional stats) with automatic formatting based on datatype.
 Parameters
ordered_dict (dict or OrderedDict, optional) –
refresh (bool, optional) – Forces refresh [default: True].
kwargs (dict, optional) –
 set_postfix_str(s='', refresh=True)
Postfix without dictionary expansion, similar to prefix handling.
 static status_printer(file)
Manage the printing and inplace updating of a line of characters. Note that if the string is longer than a line, then inplace updating may not work (it will print a new line at each refresh).
 unpause()
Restart tqdm timer from last print time.
 update(n=1)
Manually update the progress bar, useful for streams such as reading files. E.g.: >>> t = tqdm(total=filesize) # Initialise >>> for current_buffer in stream: … … … t.update(len(current_buffer)) >>> t.close() The last line is highly recommended, but possibly not necessary if t.update() will be called in such a way that filesize will be exactly reached and printed.
 Parameters
n (int or float, optional) – Increment to add to the internal counter of iterations [default: 1]. If using float, consider specifying {n:.3f} or similar in bar_format, or specifying unit_scale.
 Returns
out – True if a display() was triggered.
 Return type
bool or None
 classmethod wrapattr(stream, method, total=None, bytes=True, **tqdm_kwargs)
stream : filelike object. method : str, “read” or “write”. The result of read() and
the first argument of write() should have a len().
>>> with tqdm.wrapattr(file_obj, "read", total=file_obj.size) as fobj: ... while True: ... chunk = fobj.read(chunk_size) ... if not chunk: ... break
 classmethod write(s, file=None, end='\n', nolock=False)
Print a message via tqdm (without overlap with bars).
 class gemseo.algos.driver_lib.TqdmToLogger(initial_value='', newline='\n')[source]
Redirect tqdm output to the gemseo logger.
Methods:
close
()Close the IO object.
Separate the underlying buffer from the TextIOBase and return it.
fileno
()Returns underlying file descriptor if one exists.
flush
()Flush write buffers, if applicable.
getvalue
()Retrieve the entire contents of the object.
isatty
()Return whether this is an ‘interactive’ stream.
read
([size])Read at most size characters, returned as a string.
readable
()Returns True if the IO object can be read.
readline
([size])Read until newline or EOF.
readlines
([hint])Return a list of lines from the stream.
seek
(pos[, whence])Change stream position.
seekable
()Returns True if the IO object can be seeked.
tell
()Tell the current file position.
truncate
([pos])Truncate size to pos.
writable
()Returns True if the IO object can be written.
write
(buf)Write buffer.
writelines
(lines, /)Write a list of lines to stream.
Attributes:
Encoding of the text stream.
The error setting of the decoder or encoder.
 close()
Close the IO object.
Attempting any further operation after the object is closed will raise a ValueError.
This method has no effect if the file is already closed.
 detach()
Separate the underlying buffer from the TextIOBase and return it.
After the underlying buffer has been detached, the TextIO is in an unusable state.
 encoding
Encoding of the text stream.
Subclasses should override.
 errors
The error setting of the decoder or encoder.
Subclasses should override.
 fileno()
Returns underlying file descriptor if one exists.
OSError is raised if the IO object does not use a file descriptor.
 flush()
Flush write buffers, if applicable.
This is not implemented for readonly and nonblocking streams.
 getvalue()
Retrieve the entire contents of the object.
 isatty()
Return whether this is an ‘interactive’ stream.
Return False if it can’t be determined.
 newlines
 read(size= 1, /)
Read at most size characters, returned as a string.
If the argument is negative or omitted, read until EOF is reached. Return an empty string at EOF.
 readable()
Returns True if the IO object can be read.
 readline(size= 1, /)
Read until newline or EOF.
Returns an empty string if EOF is hit immediately.
 readlines(hint= 1, /)
Return a list of lines from the stream.
hint can be specified to control the number of lines read: no more lines will be read if the total size (in bytes/characters) of all lines so far exceeds hint.
 seek(pos, whence=0, /)
Change stream position.
 Seek to character offset pos relative to position indicated by whence:
0 Start of stream (the default). pos should be >= 0; 1 Current position  pos must be 0; 2 End of stream  pos must be 0.
Returns the new absolute position.
 seekable()
Returns True if the IO object can be seeked.
 tell()
Tell the current file position.
 truncate(pos=None, /)
Truncate size to pos.
The pos argument defaults to the current file position, as returned by tell(). The current file position is unchanged. Returns the new absolute position.
 writable()
Returns True if the IO object can be written.
 write(buf)[source]
Write buffer.
 writelines(lines, /)
Write a list of lines to stream.
Line separators are not added, so it is usual for each of the lines provided to have a line separator at the end.