gemseo / algos

design_space module¶

Design space.

A design space is used to represent the optimization’s unknowns, a.k.a. the 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.

class gemseo.algos.design_space.DesignSpace(name='')[source]¶

Bases: MutableMapping

Description of a design space.

It defines a set of variables from their names, sizes, types and bounds.

In addition, it provides the current values of these variables that can be used as the initial solution of an OptimizationProblem.

A DesignSpace has the same API as a dictionary, e.g. variable = design_space["x"], other_design_space["x"] = design_space["x"], del design_space["x"], for name, value in design_space["x"].items(), …

Parameters:

name (str) –

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

By default it is set to “”.

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

Bases: NamedTuple

A design variable.

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

Parameters:

size (int | None) –

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

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

count(value, /)¶

Return number of occurrences of value.

index(value, start=0, stop=9223372036854775807, /)¶

Return first index of value.

Raises ValueError if the value is not present.

l_b: ndarray | None¶: Alias for field number 2

size: int | None¶: Alias for field number 0

u_b: ndarray | None¶: Alias for field number 3

value: ndarray | None¶: Alias for field number 4

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

DesignVariableType¶: alias of _DesignVariableType

add_variable(name, size=1, var_type=_DesignVariableType.FLOAT, l_b=None, u_b=None, value=None)[source]¶

Add a variable to the design space.

Parameters:

name (str) – The name of the variable.
size (int) –
The size of the variable.

By default it is set to 1.
var_type (DesignVariableType | Sequence[DesignVariableType]) –
Either the type of the variable or the types of its components.

By default it is set to “float”.
l_b (float | ndarray | None) – The lower bound of the variable. If None, use \(-\infty\).
u_b (float | ndarray | None) – The upper bound of the variable. If None, use \(+\infty\).
value (float | ndarray | None) – The default value of the variable. If None, do not use a default value.

Raises:

ValueError – Either if the variable already exists or if the size is not a positive integer.

Return type:

None

array_to_dict(x_array)[source]¶

Convert a design array into a dictionary indexed by the variables names.

Parameters:: x_array (ndarray) – A design value expressed as a NumPy array.
Returns:: The design value expressed as a dictionary of NumPy arrays.
Return type:: dict[str, ndarray]

check()[source]¶

Check the state of the design space.

Raises:: ValueError – If the design space is empty.
Return type:: None

check_membership(x_vect, variable_names=None)[source]¶

Check whether the variables satisfy the design space requirements.

Parameters:

x_vect (Mapping[str, ndarray] | ndarray) – The values of the variables.
variable_names (Sequence[str] | None) – The names of the variables. If None, use the names of the variables of the design space.

Raises:

ValueError – Either if the dimension of the values vector is wrong, if the values are not specified as an array or a dictionary, if the values are outside the bounds of the variables or if the component of an integer variable is not an integer.

Return type:

None

clear() → None. Remove all items from D.¶

dict_to_array(design_values, variable_names=None)[source]¶

Convert a mapping of design values into a NumPy array.

Parameters:

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

Returns:

The design values as a NumPy array.

Return type:

ndarray

Notes

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

extend(other)[source]¶

Extend the design space with another design space.

Parameters:: other (DesignSpace) – The design space to be appended to the current one.
Return type:: None

filter(keep_variables, copy=False)[source]¶

Filter the design space to keep a subset of variables.

Parameters:

keep_variables (str | Iterable[str]) – The names of the variables to be kept.
copy (bool) –
If True, then a copy of the design space is filtered, otherwise the design space itself is filtered.

By default it is set to False.

Returns:

Either the filtered original design space or a copy.

Raises:

ValueError – If the variable is not in the design space.

Return type:

DesignSpace

filter_dim(variable, keep_dimensions)[source]¶

Filter the design space to keep a subset of dimensions for a variable.

Parameters:

variable (str) – The name of the variable.
keep_dimensions (Iterable[int]) – The dimensions of the variable to be kept, between \(0\) and \(d-1\) where \(d\) is the number of dimensions of the variable.

Returns:

The filtered design space.

Raises:

ValueError – If a dimension is unknown.

Return type:

DesignSpace

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

Create a design space from a CSV file.

Parameters:

file_path (str | Path) – The path to the CSV file.
header (Iterable[str] | None) – The names of the fields saved in the file. If None, read them in the file.

Returns:

The design space defined in the file.

Raises:

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

Return type:

DesignSpace

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

Create a design space from a file.

Parameters:

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

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

Returns:

The design space defined in the file.

Return type:

DesignSpace

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

Create a design space from an HDF file.

Parameters:

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

By default it is set to “”.

Returns:

The design space defined in the file.

Return type:

DesignSpace

get(k[, d]) → D[k] if k in D, else d. d defaults to None.¶

get_active_bounds(x_vec=None, tol=1e-08)[source]¶

Determine which bound constraints of a design value are active.

Parameters:

x_vec (ndarray | None) – The design value at which to check the bounds. If None, use the current design value.
tol (float) –
The tolerance of comparison of a scalar with a bound.

By default it is set to 1e-08.

Returns:

Whether the components of the lower and upper bound constraints are active, the first returned value representing the lower bounds and the second one the upper bounds, e.g.

(
    {
        "x": array(are_x_lower_bounds_active),
        "y": array(are_y_lower_bounds_active),
    },
    {
        "x": array(are_x_upper_bounds_active),
        "y": array(are_y_upper_bounds_active),
    },
)

where:

are_x_lower_bounds_active = [True, False]
are_x_upper_bounds_active = [False, False]
are_y_lower_bounds_active = [False]
are_y_upper_bounds_active = [True]

Return type:

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

get_current_value(variable_names=None, complex_to_real=False, as_dict=False, normalize=False)[source]¶

Return the current design value.

If the names of the variables are empty then an empty data is returned.

Parameters:

variable_names (Sequence[str] | None) – The names of the design variables. If None, use all the design variables.
complex_to_real (bool) –
Whether to cast complex numbers to real ones.

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

By default it is set to False.
normalize (bool) –
Whether to normalize the design values in \([0,1]\) with the bounds of the variables.

By default it is set to False.

Returns:

The current design value.

Raises:

ValueError – If names in variable_names are not in the design space.

Return type:

ndarray | dict[str, ndarray]

Warning

For performance purposes, get_current_value() does not return a copy of the current value. This means that modifying the returned object will make the DesignSpace inconsistent (the current design value stored as a NumPy array and the current design value stored as a dictionary of NumPy arrays will be different). To modify the returned object without impacting the DesignSpace, you shall copy this object and modify the copy.

Examples using DesignSpace¶

Example for exterior penalty applied to the Sobieski test case.

Parameter space

Comparing sensitivity indices

Correlation analysis

Morris analysis

Sobol’ analysis

Sobol' analysis

Empirical estimation of statistics

Analytical test case # 2

Analytical test case # 3

Examples for constraint aggregation

Pareto front on the Binh and Korn problem using a BiLevel formulation

Create a DOE Scenario

Create an MDO Scenario

Gantt Chart

Store observables

A from scratch example on the Sellar problem

Application: Sobieski’s Super-Sonic Business Jet (MDO)

Application: Sobieski's Super-Sonic Business Jet (MDO)

GEMSEO in 10 minutes

MDO formulations for a toy example in aerostructure

Design space

Post-processing

Scenario

Multistart optimization

Diagonal design of experiments

Scalable diagonal discipline

Scalable problem

BiLevel-based DOE on the Sobieski SSBJ test case

BiLevel-based MDO on the Sobieski SSBJ test case

IDF-based MDO on the Sobieski SSBJ test case

MDF-based DOE on the Sobieski SSBJ test case

MDF-based MDO on the Sobieski SSBJ test case

Change the seed of a DOE

Simple disciplinary DOE example on the Sobieski SSBJ test case

Use a design of experiments from a file

Use a design of experiments from an array

Create a surrogate discipline

Plug a surrogate discipline in a Scenario

Calibration of a polynomial regression

Machine learning algorithm selection example

Polynomial regression

RBF regression

Random forest regression

Save and Load

Scaling

Solve a 2D L-shape topology optimization problem

Solve a 2D MBB topology optimization problem

Solve a 2D short cantilever topology optimization problem

DesignSpace creation and manipulation

DesignSpace import and export from disk

Objective and constraints history

Optimization History View

Parallel coordinates

Pareto front

Quadratic approximations

Examples using _DesignVariableType¶

Examples for constraint aggregation

Use a design of experiments from a file

Use a design of experiments from an array