# 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:

 DesignSpace([hdf_file]) 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 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. 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. 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 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

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

DesignSpace

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=1e-08)[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 = 1e-8)

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

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 post-processing.

Classes:

 OptimizationProblem(design_space[, pb_type, …]) An optimization problem.
class gemseo.algos.opt_problem.OptimizationProblem(design_space, pb_type='non-linear', input_database=None, differentiation_method='user', fd_step=1e-07)[source]

An optimization problem.

Create an optimization problem from:

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

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

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

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

Attributes
• nonproc_objective (MDOFunction) – The non-processed objective function.

• constraints (List(MDOFunction)) – The constraints.

• nonproc_constraints (List(MDOFunction)) – The non-processed 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 non-processed observables.

• nonproc_new_iter_observables (List(MDOFunction)) – The non-processed 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 pre-process 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 step-based 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 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 non-processed constraints. Retrieve the non-processed 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 non-linear 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, …]) Pre-process all the functions and eventually the gradien. repr_constraint(func, ctype[, value, positive]) Express a constraint as a string expression.

Attributes:

 dimension The dimension of the design space. objective The objective function.

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 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 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 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 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 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 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]

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 pre-processed 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 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 and Database.FUNCTION_GROUP or an input-output naming, with Database.INPUT_GROUP and Database.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

gemseo.core.dataset.Dataset

get_active_ineq_constraints(x_vect, tol=1e-06)[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 and OptimizationProblem.ineq_tolerance for inequality ones.

Returns

The values of the design variables and objective function for the feasible points.

Return type

Tuple[List[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 non-processed constraints.

Returns

The non-processed constraints.

Return type
get_nonproc_objective()[source]

Retrieve the non-processed objective function.

Return type

gemseo.core.function.MDOFunction

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

gemseo.core.function.MDOFunction

get_optimum()[source]

Return the optimum solution within a given feasibility tolerances.

Returns

The optimum result, defined by:

• the value of the objective function,

• the value of the design variables,

• the indicator of feasibility of the optimal solution,

• the value of the constraints,

• the value of the gradients of the constraints.

Return type

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 non-linear constraints.

Returns

True if the problem has equality or inequality constraints.

Return type

bool

classmethod import_hdf(file_path, x_tolerance=0.0)[source]

Import an optimization history from an HDF file.

Parameters
• file_path (str) – The file containing the optimization history.

• x_tolerance (float) – The tolerance on the design variables when reading the file.

Returns

Return type

gemseo.algos.opt_problem.OptimizationProblem

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]

Pre-process 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. ProgressBar(*_, **__) Extend tqdm progress bar with better time units. TqdmToLogger([initial_value, newline]) 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:

 algorithms 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

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

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 non-TTY.

• 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 non-zero 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. 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 string-based progress bar given some parameters Intelligent scientific notation (.3g). format_sizeof(num[, suffix, divisor]) Formats a number (greater than unity) with SI Order of Magnitude prefixes. 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 in-place updating of a line of characters. 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 : file-like 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:

 format_dict Public API for read-only 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.

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 read-only 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 string-based 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 non-zero 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) – Post-postfix [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/ progress-indicator-during-pandas-operations-python>

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 in-place updating of a line of characters. Note that if the string is longer than a line, then in-place 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 : file-like 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:
...         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 the IO object. detach Separate the underlying buffer from the TextIOBase and return it. Returns underlying file descriptor if one exists. Flush write buffers, if applicable. Retrieve the entire contents of the object. Return whether this is an ‘interactive’ stream. read([size]) Read at most size characters, returned as a string. 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. Returns True if the IO object can be seeked. Tell the current file position. truncate([pos]) Truncate size to pos. Returns True if the IO object can be written. write(buf) Write buffer. writelines(lines, /) Write a list of lines to stream.

Attributes:

 encoding Encoding of the text stream. errors The error setting of the decoder or encoder. newlines
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 read-only and non-blocking 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 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.

Returns True if the IO object can be read.

Returns an empty string if EOF is hit immediately.

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.