gemseo / algos / opt

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mnbi module

Modified Normal Boundary Intersection (mNBI) algorithm.

Based on [Shu07].

class gemseo.algos.opt.mnbi.BetaSubOptimOutput(f_min, x_min, w, database, n_calls)[source]

Bases: NamedTuple

An output from a beta sub optimization.

Create new instance of BetaSubOptimOutput(f_min, x_min, w, database, n_calls)

Parameters:

  • f_min (RealArray) –

  • x_min (RealArray) –

  • w (RealArray) –

  • database (Database) –

  • n_calls (int) –

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.

database: Database

The database of the main problem.

f_min: RealArray

The coordinates in the objective space of the sub-optimization result.

n_calls: int

The number of calls to the main objective function by the optimizer during the sub-optimization.

w: RealArray

The vector w used to compute the values of beta that can be skipped in the following sub-optimizations.

x_min: RealArray

The coordinates in the design space of the sub-optimization result.

class gemseo.algos.opt.mnbi.IndividualSubOptimOutput(f_min, x_min, database, n_calls)[source]

Bases: NamedTuple

An output from a sub optimization.

Create new instance of IndividualSubOptimOutput(f_min, x_min, database, n_calls)

Parameters:

  • f_min (RealArray) –

  • x_min (RealArray) –

  • database (Database) –

  • n_calls (int) –

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.

database: Database

The database of the main problem.

f_min: RealArray

The value of f at the design value minimizing f_i.

n_calls: int

The number of calls to f.

x_min: RealArray

The value of the design variables minimizing f_i.

class gemseo.algos.opt.mnbi.MNBI[source]

Bases: OptimizationLibrary

MNBI optimizer.

This algorithm computes the Pareto front of a multi-objective optimization problem by decomposing it into a series of constrained single-objective problems. Considering the following problem:

\[\begin{split}\begin{align} & \min_{x \in D} f(x),\\ & g(x) \leq 0,\\ & h(x) = 0 \end{align}\end{split}\]

the algorithm first finds the individual optima \((x_i^\ast)_{i=1..m}\) of the \(m\) components of the objective function \(f\). The corresponding anchor points \((f(x_i^\ast))_{i=1..m}\) are stored in a matrix \(\Phi\).

The simplex formed by the convex hull of the anchor points can be expressed as \(\Phi \beta\), where \(\beta = \{ (b_1, ..., b_m)^T | \sum_{i=1}^m b_i =1 \}\).

Given a list of vectors \(\beta\), mNBI will solve the following single-objective problems:

\[\begin{split}\begin{align} & \max_{x \in D, t \in \mathbb{R}} t,\\ & \Phi \beta + t \hat{n} \geq f(x),\\ & g(x) \leq 0,\\ & h(x) = 0 \end{align}\end{split}\]

where \(\hat{n}\) is a quasi-normal vector to the \(\Phi \beta\) simplex pointing towards the origin of the objective space. If \((x^{*}, t^{*})\) is a solution of this problem, \(x^{*}\) is proven to be at least weakly Pareto-dominant.

Let \(w = \Phi \beta + t^{*} \hat{n}\), and \(\pi\) denote the projection (in the direction of \(\hat{n}\)) on the simplex formed by the convex hull of the anchor points. If not all constraints \(\Phi \beta + t^{*} \hat{n} \geq f(x^{*})\) are active, \(x^{*}\) will weakly dominate the solution of the sub-problem for all values \(\beta_{dom}\) that verify:

\[\Phi \beta_{dom} \in \pi[(f(x^{*}) + \mathbb{R}_m^{+}) \cap (w - \mathbb{R}_m^{+})]\]

Therefore, the corresponding sub-optimizations are redundant and can be skipped to reduce run time.

Notes

The missing current values of the DesignSpace attached to the OptimizationProblem are automatically initialized with the method DesignSpace.initialize_missing_current_values().

class ApproximationMode(value)

Bases: StrEnum

The approximation derivation modes.

CENTERED_DIFFERENCES = 'centered_differences'

The centered differences method used to approximate the Jacobians by perturbing each variable with a small real number.

COMPLEX_STEP = 'complex_step'

The complex step method used to approximate the Jacobians by perturbing each variable with a small complex number.

FINITE_DIFFERENCES = 'finite_differences'

The finite differences method used to approximate the Jacobians by perturbing each variable with a small real number.

class DifferentiationMethod(value)

Bases: StrEnum

The differentiation methods.

CENTERED_DIFFERENCES = 'centered_differences'
COMPLEX_STEP = 'complex_step'
FINITE_DIFFERENCES = 'finite_differences'
USER_GRAD = 'user'
algorithm_handles_eqcstr(algo_name)

Check if an algorithm handles equality constraints.

Parameters:

algo_name (str) – The name of the algorithm.

Returns:

Whether the algorithm handles equality constraints.

Return type:

bool

algorithm_handles_ineqcstr(algo_name)

Check if an algorithm handles inequality constraints.

Parameters:

algo_name (str) – The name of the algorithm.

Returns:

Whether the algorithm handles inequality constraints.

Return type:

bool

clear_listeners()

Remove the listeners from the database.

Return type:

None

deactivate_progress_bar()

Deactivate the progress bar.

Return type:

None

driver_has_option(option_name)

Check the existence of an option.

Parameters:

option_name (str) – The name of the option.

Returns:

Whether the option exists.

Return type:

bool

ensure_bounds(orig_func, normalize=True)

Project the design vector onto the design space before execution.

Parameters:

  • orig_func – The original function.

  • normalize (bool) –

    Whether to use the normalized design space.

    By default it is set to True.

Returns:

A function calling the original function with the input data projected onto the design space.

execute(problem, algo_name=None, eval_obs_jac=False, skip_int_check=False, **options)

Execute the driver.

Parameters:

  • problem (OptimizationProblem) – The problem to be solved.

  • algo_name (str | None) – The name of the algorithm. If None, use the algo_name attribute which may have been set by the factory.

  • eval_obs_jac (bool) –

    Whether to evaluate the Jacobian of the observables.

    By default it is set to False.

  • skip_int_check (bool) –

    Whether to skip the integer variable handling check of the selected algorithm.

    By default it is set to False.

  • **options (DriverLibOptionType) – The options for the algorithm.

Returns:

The optimization result.

Raises:

ValueError – If algo_name was not either set by the factory or given as an argument.

Return type:

OptimizationResult

filter_adapted_algorithms(problem)

Filter the algorithms capable of solving the problem.

Parameters:

problem (Any) – The problem to be solved.

Returns:

The names of the algorithms adapted to this problem.

Return type:

list[str]

finalize_iter_observer()

Finalize the iteration observer.

Return type:

None

get_optimum_from_database(message=None, status=None)

Return the optimization result from the database.

Return type:

OptimizationResult

get_right_sign_constraints()

Transform the problem constraints into their opposite sign counterpart.

This is done if the algorithm requires positive constraints.

get_x0_and_bounds_vects(normalize_ds, as_dict=False)

Return the initial design variable values and their lower and upper bounds.

Parameters:

  • normalize_ds (bool) – Whether to normalize the design variables.

  • as_dict (bool) –

    Whether to return dictionaries instead of NumPy arrays.

    By default it is set to False.

Returns:

The initial values of the design variables, their lower bounds, and their upper bounds.

Return type:

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

init_iter_observer(max_iter, message='')

Initialize the iteration observer.

It will handle the stopping criterion and the logging of the progress bar.

Parameters:

  • max_iter (int) – The maximum number of iterations.

  • message (str) –

    The message to display at the beginning of the progress bar status.

    By default it is set to “”.

Raises:

ValueError – If max_iter is lower than one.

Return type:

None

init_options_grammar(algo_name)

Initialize the options’ grammar.

Parameters:

algo_name (str) – The name of the algorithm.

Return type:

JSONGrammar

is_algo_requires_positive_cstr(algo_name)

Check if an algorithm requires positive constraints.

Parameters:

algo_name (str) – The name of the algorithm.

Returns:

Whether the algorithm requires positive constraints.

Return type:

bool

classmethod is_algorithm_suited(algorithm_description, problem)

Check if an algorithm is suited to a problem according to its description.

Parameters:

  • algorithm_description (AlgorithmDescription) – The description of the algorithm.

  • problem (Any) – The problem to be solved.

Returns:

Whether the algorithm is suited to the problem.

Return type:

bool

new_iteration_callback(x_vect)

Verify the design variable and objective value stopping criteria.

Parameters:

x_vect (ndarray) – The design variables values.

Raises:

  • FtolReached – If the defined relative or absolute function tolerance is reached.

  • XtolReached – If the defined relative or absolute x tolerance is reached.

Return type:

None

requires_gradient(driver_name)

Check if a driver requires the gradient.

Parameters:

driver_name (str) – The name of the driver.

Returns:

Whether the driver requires the gradient.

Return type:

bool

EQ_TOLERANCE = 'eq_tolerance'
EVAL_OBS_JAC_OPTION = 'eval_obs_jac'
F_TOL_ABS = 'ftol_abs'
F_TOL_REL = 'ftol_rel'
INEQ_TOLERANCE = 'ineq_tolerance'
LIBRARY_NAME: ClassVar[str | None] = None

The name of the interfaced library.

LS_STEP_NB_MAX = 'max_ls_step_nb'
LS_STEP_SIZE_MAX = 'max_ls_step_size'
MAX_DS_SIZE_PRINT = 40
MAX_FUN_EVAL = 'max_fun_eval'
MAX_ITER = 'max_iter'
MAX_TIME = 'max_time'
NORMALIZE_DESIGN_SPACE_OPTION = 'normalize_design_space'
OPTIONS_DIR: ClassVar[str | Path] = 'options'

The name of the directory containing the files of the grammars of the options.

OPTIONS_MAP: ClassVar[dict[str, str]] = {}

The names of the options in GEMSEO mapping to those in the wrapped library.

PG_TOL = 'pg_tol'
ROUND_INTS_OPTION = 'round_ints'
SCALING_THRESHOLD: Final[str] = 'scaling_threshold'
STOP_CRIT_NX = 'stop_crit_n_x'
USE_DATABASE_OPTION = 'use_database'
USE_ONE_LINE_PROGRESS_BAR: ClassVar[bool] = False

Whether to use a one line progress bar.

VERBOSE = 'verbose'
X_TOL_ABS = 'xtol_abs'
X_TOL_REL = 'xtol_rel'
activate_progress_bar: ClassVar[bool] = True

Whether to activate the progress bar in the optimization log.

algo_name: str | None

The name of the algorithm used currently.

property algorithms: list[str]

The available algorithms.

descriptions: dict[str, AlgorithmDescription]

The description of the algorithms contained in the library.

internal_algo_name: str | None

The internal name of the algorithm used currently.

It typically corresponds to the name of the algorithm in the wrapped library if any.

opt_grammar: JSONGrammar | None

The grammar defining the options of the current algorithm.

problem: OptimizationProblem

The optimization problem the driver library is bonded to.

class gemseo.algos.opt.mnbi.MNBIAlgorithmDescription(algorithm_name, internal_algorithm_name, library_name='MNBI', description='', website='', handle_integer_variables=True, require_gradient=False, handle_equality_constraints=True, handle_inequality_constraints=True, handle_multiobjective=True, positive_constraints=False, problem_type=ProblemType.NON_LINEAR)[source]

Bases: OptimizationAlgorithmDescription

The description of the MNBI optimization algorithm.

Parameters:

  • algorithm_name (str) –

  • internal_algorithm_name (str) –

  • library_name (str) –

    By default it is set to “MNBI”.

  • description (str) –

    By default it is set to “”.

  • website (str) –

    By default it is set to “”.

  • handle_integer_variables (bool) –

    By default it is set to True.

  • require_gradient (bool) –

    By default it is set to False.

  • handle_equality_constraints (bool) –

    By default it is set to True.

  • handle_inequality_constraints (bool) –

    By default it is set to True.

  • handle_multiobjective (bool) –

    By default it is set to True.

  • positive_constraints (bool) –

    By default it is set to False.

  • problem_type (ProblemType) –

    By default it is set to “non-linear”.

algorithm_name: str

The name of the algorithm in GEMSEO.

description: str = ''

A description of the algorithm.

handle_equality_constraints: bool = True

Whether the optimization algorithm handles equality constraints.

handle_inequality_constraints: bool = True

Whether the optimization algorithm handles inequality constraints.

handle_integer_variables: bool = True

Whether the optimization algorithm handles integer variables.

handle_multiobjective: bool = True

Whether the optimization algorithm handles multiple objectives.

internal_algorithm_name: str

The name of the algorithm in the wrapped library.

library_name: str = 'MNBI'

The name of the wrapped library.

positive_constraints: bool = False

Whether the optimization algorithm requires positive constraints.

problem_type: ProblemType = 'non-linear'

The type of problem (see OptimizationProblem.ProblemType).

require_gradient: bool = False

Whether the optimization algorithm requires the gradient.

website: str = ''

The website of the wrapped library or algorithm.