Optimization algorithms#

Warning

Some capabilities may require the installation of GEMSEO with all its features and some others may depend on plugins.

Warning

All the features of the wrapped libraries may not be exposed through GEMSEO.

Note

The algorithm settings can be passed to a function of the form

function(..., settings_model: AlgorithmSettings | None = None, **settings: Any)

either one by one:

function(..., setting_name_1=setting_name_1, setting_name_2=setting_name_2, ...)

or using the argument name "settings_model" and the Pydantic model associated with the algorithm:

settings_model = AlgorithmSettings(setting_name_1=setting_name_1, setting_name_2=setting_name_2, ...)
function(..., settings_model=settings_model)

Overview

Display in the table the optimization algorithms that

support equality constraints
support inequality constraints
support float variables
support integer variables
support multiple objective
require gradient evaluations

Algorithm ▲▼	Library ▲▼	Name in GEMSEO ▲▼	Package ▲▼
Augmented_Lagrangian_order_0		Augmented_Lagrangian_order_0	gemseo
Augmented_Lagrangian_order_1		Augmented_Lagrangian_order_1	gemseo
COBYQA	SciPy Local	COBYQA	gemseo
Differential evolution	SciPy Global Optimization	DIFFERENTIAL_EVOLUTION	gemseo
Dual annealing	SciPy Global Optimization	DUAL_ANNEALING	gemseo
Dual simplex	SciPy Linear Programming	DUAL_SIMPLEX	gemseo
HEXALY	Hexaly	HEXALY	gemseo_hexaly
Interior point method	SciPy Linear Programming	INTERIOR_POINT	gemseo
L-BFGS-B	SciPy Local	L-BFGS-B	gemseo
MMA	MMA	MMA	gemseo_mma
mNBI	MNBI	MNBI	gemseo
Multi-start optimization		MultiStart	gemseo
NELDER-MEAD	SciPy Local	NELDER-MEAD	gemseo
BFGS	NLopt	NLOPT_BFGS	gemseo
BOBYQA	NLopt	NLOPT_BOBYQA	gemseo
COBYLA	NLopt	NLOPT_COBYLA	gemseo
MMA	NLopt	NLOPT_MMA	gemseo
NEWUOA	NLopt	NLOPT_NEWUOA	gemseo
SLSQP	NLopt	NLOPT_SLSQP	gemseo
BOBYQA	PDFO	PDFO_BOBYQA	gemseo_pdfo
COBYLA	PDFO	PDFO_COBYLA	gemseo_pdfo
NEWUOA	PDFO	PDFO_NEWUOA	gemseo_pdfo
GA	pymoo	PYMOO_GA	gemseo_pymoo
NSGA2	pymoo	PYMOO_NSGA2	gemseo_pymoo
NSGA3	pymoo	PYMOO_NSGA3	gemseo_pymoo
RNSGA3	pymoo	PYMOO_RNSGA3	gemseo_pymoo
UNSGA3	pymoo	PYMOO_UNSGA3	gemseo_pymoo
PYOPTSPARSE_SLSQP	pyOptSparse	PYOPTSPARSE_SLSQP	gemseo_pyoptsparse
PYOPTSPARSE_SNOPT	pyOptSparse	PYOPTSPARSE_SNOPT	gemseo_pyoptsparse
SBO	gemseo-mlearning	SBO	gemseo_mlearning
SHGO	SciPy Global Optimization	SHGO	gemseo
SLSQP	SciPy Local	SLSQP	gemseo
SMT_EGO	SMT	SMT_EGO	gemseo_mlearning
Branch & Cut algorithm	SciPy Mixed-Integer Linear Programming	Scipy_MILP	gemseo
TNC	SciPy Local	TNC	gemseo

Augmented_Lagrangian_order_0#

Module: gemseo.algos.opt.augmented_lagrangian.augmented_lagrangian_order_0

Augmented Lagrangian algorithm for gradient-less functions.

Pydantic model of the settings for Augmented_Lagrangian_order_0#

from gemseo.settings.opt import Augmented_Lagrangian_order_0_Settings

Required settings

sub_algorithm_name : <class 'str'>

The name of the optimizer used to solve each sub-problem.

Optional settings

enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
gamma : <class 'float'>, optional

The penalty increase factor.

By default it is set to 1.5.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
initial_rho : <class 'float'>, optional

The initial penalty value.

By default it is set to 10.0.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_rho : <class 'float'>, optional

The maximum penalty value.

By default it is set to 10000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
sub_algorithm_settings : collections.abc.Mapping[str, typing.Any], optional

The settings of the optimizer used to solve each sub-problem.

By default it is set to {}.
sub_problem_constraints : collections.abc.Iterable[str], optional

The constraints to keep in the sub-problem.

If empty, all constraints are handled by the Augmented Lagrangian method which implies that the sub-problem is unconstrained.

By default it is set to ().
tau : <class 'float'>, optional

The threshold to increase the penalty.

By default it is set to 0.9.
update_options_callback : typing.Optional[typing.Annotated[typing.Callable[[typing.Any], typing.Any], WithJsonSchema(json_schema={}, mode=None)]], optional

A callable for updating parameters or a function call.

By default it is set to None.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

Augmented_Lagrangian_order_1#

Module: gemseo.algos.opt.augmented_lagrangian.augmented_lagrangian_order_1

Augmented Lagrangian algorithm using gradient information

Pydantic model of the settings for Augmented_Lagrangian_order_1#

from gemseo.settings.opt import Augmented_Lagrangian_order_1_Settings

Required settings

sub_algorithm_name : <class 'str'>

The name of the optimizer used to solve each sub-problem.

Optional settings

enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
gamma : <class 'float'>, optional

The penalty increase factor.

By default it is set to 1.5.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
initial_rho : <class 'float'>, optional

The initial penalty value.

By default it is set to 10.0.
kkt_tol_abs : <class 'float'>, optional

The absolute tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
kkt_tol_rel : <class 'float'>, optional

The relative tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_rho : <class 'float'>, optional

The maximum penalty value.

By default it is set to 10000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
sub_algorithm_settings : collections.abc.Mapping[str, typing.Any], optional

The settings of the optimizer used to solve each sub-problem.

By default it is set to {}.
sub_problem_constraints : collections.abc.Iterable[str], optional

The constraints to keep in the sub-problem.

If empty, all constraints are handled by the Augmented Lagrangian method which implies that the sub-problem is unconstrained.

By default it is set to ().
tau : <class 'float'>, optional

The threshold to increase the penalty.

By default it is set to 0.9.
update_options_callback : typing.Optional[typing.Annotated[typing.Callable[[typing.Any], typing.Any], WithJsonSchema(json_schema={}, mode=None)]], optional

A callable for updating parameters or a function call.

By default it is set to None.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

COBYQA#

Module: gemseo.algos.opt.scipy_local.scipy_local

Derivative-free trust-region SQP method based on quadratic models for constrained optimization.

Pydantic model of the settings for COBYQA#

from gemseo.settings.opt import COBYQA_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-cobyqa.html.

Optional settings

disp : <class 'bool'>, optional

Whether to print convergence messages.

By default it is set to False.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 1e-06.
f_target : <class 'float'>, optional

The target value for the objective function.

The optimization procedure is terminated when the objective function value of a feasible point is less than or equal to this target.

By default it is set to -inf.
final_tr_radius : <class 'float'>, optional

The final trust-region radius.

By default it is set to 1e-06.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
initial_tr_radius : <class 'float'>, optional

The initial trust-region radius.

By default it is set to 1.0.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

DIFFERENTIAL_EVOLUTION#

Module: gemseo.algos.opt.scipy_global.scipy_global

Differential Evolution algorithm

Pydantic model of the settings for DIFFERENTIAL_EVOLUTION#

from gemseo.settings.opt import DIFFERENTIAL_EVOLUTION_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.differential_evolution.html.

Optional settings

atol : <class 'float'>, optional

The absolute tolerance for convergence.

By default it is set to 0.0.
disp : <class 'bool'>, optional

Whether to print convergence messages.

By default it is set to False.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 1e-06.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
init : str | gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[float]], optional

The method to perform the population initialization as a string
or the initial population as an array.

By default it is set to latinhypercube.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 9223372036854775807.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
mutation : float | tuple[float, float], optional

The mutation constant.

If specified as a float it should be in the range [0, 2]. If specified as a tuple(min, max) dithering is employed.

By default it is set to (0.5, 1.0).
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
polish : <class 'bool'>, optional

Whether to polish the best population member at the end.

By default it is set to True.
popsize : <class 'int'>, optional

The multiplier for setting the total population size.

By default it is set to 15.
recombination : <class 'float'>, optional

The recombination constant.

By default it is set to 0.7.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
seed : <class 'int'>, optional

The random seed.

By default it is set to 0.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
strategy : <class 'str'>, optional

The differential evolution strategy to use.

By default it is set to best1bin.
tol : <class 'float'>, optional

The relative tolerance for convergence.

By default it is set to 0.01.
updating : <class 'str'>, optional

The best solution vector updating strategy.

By default it is set to immediate.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
workers : <class 'int'>, optional

The number of parallel workers the population is subdivided in.

By default it is set to 1.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

DUAL_ANNEALING#

Module: gemseo.algos.opt.scipy_global.scipy_global

Dual annealing

Pydantic model of the settings for DUAL_ANNEALING#

from gemseo.settings.opt import DUAL_ANNEALING_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.dual_annealing.html.

Optional settings

accept : <class 'float'>, optional

The acceptance distribution parameter.

The lower the acceptance parameter, the smaller the probability of acceptance.

By default it is set to -5.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 1e-06.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
initial_temp : <class 'float'>, optional

The initial temperature.

Use higher values to facilitates a wider search of the energy landscape.

By default it is set to 5230.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 9223372036854775807.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
no_local_search : <class 'bool'>, optional

Whether to perform local search.

By default it is set to False.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
restart_temp_ratio : <class 'float'>, optional

The temperature ratio under which the reannealing process is triggered.

By default it is set to 2e-05.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
seed : <class 'int'>, optional

The random seed.

By default it is set to 0.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
visit : <class 'float'>, optional

The visiting distribution parameter.

Higher values give the visiting distribution a heavier tail, this makes the algorithm jump to a more distant region.

By default it is set to 2.62.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

DUAL_SIMPLEX#

Module: gemseo.algos.opt.scipy_linprog.scipy_linprog

Linear programming using the HiGHS dual simplex solver.

Pydantic model of the settings for DUAL_SIMPLEX#

from gemseo.settings.opt import DUAL_SIMPLEX_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.linprog-highs-ds.html.

Optional settings

autoscale : <class 'bool'>, optional

Whether to perform auto-scaling of the constraints.

By default it is set to False.
disp : <class 'bool'>, optional

Whether to print convergence messages.

By default it is set to False.
dual_feasibility_tolerance : <class 'float'>, optional

The dual feasability tolerance.

By default it is set to 1e-07.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 0.0.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 0.0.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
presolve : <class 'bool'>, optional

Whether to perform a preliminary analysis on the problem before solving.

It attempts to detect infeasibility, unboundedness or problem simplifications.

By default it is set to True.
primal_feasibility_tolerance : <class 'float'>, optional

The primal feasability tolerance.

By default it is set to 1e-07.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
rr : <class 'bool'>, optional

Whether to remove linearly dependent equality-constraints.

By default it is set to True.
rr_method : typing.Optional[typing.Literal['SVD', 'pivot', 'ID']], optional

The method to remove redundancy, either 'SVD', 'pivot' or 'ID'.

If None, use “SVD” if the matrix is nearly full rank. If not, uses “pivot”. The behavior of this default is subject to change without prior notice.

By default it is set to None.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
simplex_dual_edge_weight_strategy : <class 'str'>, optional

Strategy for simplex dual edge weights.

Available strategies: dantzig, devex, steepest and steepest-devex.

By default it is set to steepest-devex.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 0.0.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 0.0.

HEXALY#

Note

The plugin gemseo_hexaly is required.

Module: gemseo_hexaly.algos.opt.hexaly.hexaly

Commercial black-box Hexaly library. It relies on a global mixed-integer solver.

Pydantic model of the settings for HEXALY#

from gemseo.settings.opt import HexalySettings

More details about the algorithm and its settings on https://www.hexaly.com/docs/last/index.html.

Optional settings

activate_surrogate : <class 'bool'>, optional

Whether to activate the internal surrogate model.

By default it is set to False.
callback : gemseo_hexaly.algos.opt.hexaly._core.hexaly_callback.HexalyCallback | None, optional

The callback function called during the optimization algorithm.
If None, no callback is given to the Hexaly solver.

By default it is set to None.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 0.0.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 0.0.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
nb_threads : <class 'int'>, optional

The number of threads used by Hexaly.
If 0, the number of threads is automatically adapted to your computer and to your optimization model..

By default it is set to 0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
seed : <class 'int'>, optional

The random seed for the optimizer.

By default it is set to 0.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
verbosity : <class 'int'>, optional

The verbosity level of the optimizer.
0: All the traces are disabled. 1: Normal verbosity. This is the default level. 2: Detailed verbosity. Displays statistics during the search.

By default it is set to 0.
warm_start : <class 'bool'>, optional

Whether to consider the current value of the design space
as the initial solution.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 0.0.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 0.0.

INTERIOR_POINT#

Module: gemseo.algos.opt.scipy_linprog.scipy_linprog

Linear programming using the HiGHS interior point solver.

Pydantic model of the settings for INTERIOR_POINT#

from gemseo.settings.opt import INTERIOR_POINT_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.linprog-highs-ipm.html.

Optional settings

autoscale : <class 'bool'>, optional

Whether to perform auto-scaling of the constraints.

By default it is set to False.
disp : <class 'bool'>, optional

Whether to print convergence messages.

By default it is set to False.
dual_feasibility_tolerance : <class 'float'>, optional

The tolerance on the feasibility of the dual problem.

By default it is set to 1e-07.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 0.0.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 0.0.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
ipm_optimality_tolerance : <class 'float'>, optional

Optimality tolerance.

By default it is set to 1e-08.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
presolve : <class 'bool'>, optional

Whether to perform a preliminary analysis on the problem before solving.

It attempts to detect infeasibility, unboundedness or problem simplifications.

By default it is set to True.
primal_feasibility_tolerance : <class 'float'>, optional

The tolerance on the feasibility of the primal problem.

By default it is set to 1e-07.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
rr : <class 'bool'>, optional

Whether to remove linearly dependent equality-constraints.

By default it is set to True.
rr_method : typing.Optional[typing.Literal['SVD', 'pivot', 'ID']], optional

The method to remove redundancy, either 'SVD', 'pivot' or 'ID'.

If None, use “SVD” if the matrix is nearly full rank. If not, uses “pivot”. The behavior of this default is subject to change without prior notice.

By default it is set to None.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 0.0.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 0.0.

L-BFGS-B#

Module: gemseo.algos.opt.scipy_local.scipy_local

Limited-memory BFGS algorithm implemented in the SciPy library

Pydantic model of the settings for L-BFGS-B#

from gemseo.settings.opt import L_BFGS_B_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-lbfgsb.html.

Optional settings

disp : <class 'bool'>, optional

Whether to print convergence messages.

By default it is set to False.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 1e-06.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
gtol : <class 'float'>, optional

The precision goal for the projected gradient value to stop the algorithm.

By default it is set to 1e-06.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
iprint : <class 'int'>, optional

The flag to control the frequency of output.

Default is no output.

By default it is set to -1.
kkt_tol_abs : <class 'float'>, optional

The absolute tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
kkt_tol_rel : <class 'float'>, optional

The relative tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
maxcor : <class 'int'>, optional

The maximum number of corrections for the limited memory matrix.

By default it is set to 20.
maxls : <class 'int'>, optional

The maximum number of line search steps per iteration.

By default it is set to 20.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

MMA#

Note

The plugin gemseo_mma is required.

Module: gemseo_mma.opt.mma

The Method of Moving Asymptotes

Pydantic model of the settings for MMA#

from gemseo.settings.opt import MMASvanbergSettings

Optional settings

asymptotes_distance_amplification_coefficient : <class 'float'>, optional

The amplification factor for successful iterations.

By default it is set to 1.2.
asymptotes_distance_reduction_coefficient : <class 'float'>, optional

The decremental factor for unsuccessful iterations.

By default it is set to 0.7.
conv_tol : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

If provided, control all other convergence tolerances.

Otherwise, the other convergence tolerances are used.

By default it is set to None.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-14.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-08.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.01.
initial_asymptotes_distance : <class 'float'>, optional

The initial asymptotes distance from the current design variable
value.

By default it is set to 0.5.
kkt_tol_abs : <class 'float'>, optional

The absolute tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
kkt_tol_rel : <class 'float'>, optional

The relative tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_asymptote_distance : <class 'float'>, optional

The maximum distance of the asymptotes from the current design variable
value.

By default it is set to 10.0.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_optimization_step : <class 'float'>, optional

The maximum optimization step.

By default it is set to 0.1.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
min_asymptote_distance : <class 'float'>, optional

The minimum distance of the asymptotes from the current design variable
value.

By default it is set to 0.01.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
tol : <class 'float'>, optional

The tolerance of convergence used in MMA to be compared with the KKT
residual.

By default it is set to 0.01.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-14.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-08.

MNBI#

Module: gemseo.algos.opt.mnbi.mnbi

Modified Normal Boundary Intersection (mNBI) method

Pydantic model of the settings for MNBI#

from gemseo.settings.opt import MNBI_Settings

Required settings

sub_optim_algo : <class 'str'>

The optimization algorithm used to solve the sub-optimization problems.

Optional settings

custom_anchor_points : collections.abc.Sequence[gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]]], optional

The bounding points of the custom phi simplex for the optimization.

By default it is set to ().
custom_phi_betas : collections.abc.Sequence[gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]]], optional

The custom values of \(\Phi \beta\) to be used in the optimization.

By default it is set to ().
debug : <class 'bool'>, optional

Whether to output the sub-optimization optima in a database hdf file.

By default it is set to False.
debug_file_path : str | pathlib.Path, optional

The path to the debug file if debug mode is active.

By default it is set to debug_history.h5.
doe_algo : <class 'str'>, optional

The design of experiments algo for the target points on the Pareto front.

A fullfactorial DOE is used default as these tend to be low dimensions, usually not more than 3 objectives for a given problem. This setting is relevant only for problems with more than 2 objectives.

By default it is set to PYDOE_FULLFACT.
doe_algo_settings : collections.abc.Mapping[str, typing.Any], optional

The settings for the DOE algorithm.

By default it is set to {}.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 0.0.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 0.0.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
n_processes : <class 'int'>, optional

The maximum number of processes used to parallelize the sub-optimizations.

By default it is set to 1.
n_sub_optim : <class 'int'>, optional

The number of sub-optimizations points.

mNBI generates n_sub_optim points on the Pareto front between the n-objective individual minima. This value must be strictly greater than the number of objectives of the problem.

By default it is set to 1.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

The mNBI algorithm does not allow to normalize the design space at the top level, only the sub-optimizations accept design space normalization. To do this, pass the setting normalize_design_space to sub_optim_algo_settings.

By default it is set to False.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
skip_betas : <class 'bool'>, optional

Whether to skip the sub-optimizations of relevant.

The sub-optimizations are skipped if they correspond to values of beta for which the theoretical result has already been found.

By default it is set to True.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
sub_optim_algo_settings : collections.abc.Mapping[str, typing.Any], optional

The settings for the sub optimization algorithm.

By default it is set to {}.
sub_optim_max_iter : <class 'int'>, optional

The maximum number of iterations of the sub-optimization algorithms.

If 0, the max_iter value is used.

By default it is set to 0.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 0.0.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 0.0.

MultiStart#

Module: gemseo.algos.opt.multi_start.multi_start

The optimization algorithm multistart generates starting points using a DOE algorithmand run a sub-optimization algorithm from each starting point.Depending on the sub-optimization algorithm,``multistart`` can handle integer design variables,equality and inequality constraintsas well as multi-objective functions.

Pydantic model of the settings for MultiStart#

from gemseo.settings.opt import MultiStart_Settings

Optional settings

doe_algo_name : <class 'str'>, optional

The name of the DOE algorithm.

The DOE algorthm is used to generate the sub-optimizations starting points.

By default it is set to LHS.
doe_algo_settings : collections.abc.Mapping[str, typing.Any], optional

The settings of the DOE algorithm.

By default it is set to {}.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 0.0.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 0.0.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
multistart_file_path : str | pathlib.Path

The database file path to save the local optima.

If empty, do not save the local optima.

By default it is set to .
n_processes : <class 'int'>, optional

The maximum number of processes used to parallelize the sub-optimizations.

By default it is set to 1.
n_start : <class 'int'>, optional

The number of sub-optimizations.

By default it is set to 5.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to False.
opt_algo_max_iter : <class 'int'>, optional

The maximum number of iterations for each sub-optimization.

If 0, this number is int(max_iter/n_start).

By default it is set to 0.
opt_algo_name : <class 'str'>, optional

The name of the sub-optimization algorithm.

By default it is set to SLSQP.
opt_algo_settings : collections.abc.Mapping[str, typing.Any], optional

The settings of the sub-optimization algorithm.

By default it is set to {}.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 0.0.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 0.0.

NELDER-MEAD#

Module: gemseo.algos.opt.scipy_local.scipy_local

Nelder-Mead algorithm implemented in the SciPy library

Pydantic model of the settings for NELDER-MEAD#

from gemseo.settings.opt import NELDER_MEAD_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-neldermead.html.

Optional settings

adaptive : <class 'bool'>, optional

Whether to adapt the algorithm parameters to dimensionality of problem.

By default it is set to False.
disp : <class 'bool'>, optional

Whether to print convergence messages.

By default it is set to False.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 1e-06.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
initial_simplex : collections.abc.Sequence[float] | gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[float]] | None, optional

The initial simplex.

If provided, the expected shape is (N+1, N) where N is the problem dimension.

By default it is set to None.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
return_all : <class 'bool'>, optional

Whether to return a list of the best solution at each of the iterations.

By default it is set to False.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

NLOPT_BFGS#

Module: gemseo.algos.opt.nlopt.nlopt

Broyden-Fletcher-Goldfarb-Shanno method (BFGS) implemented in the NLOPT library

Pydantic model of the settings for NLOPT_BFGS#

from gemseo.settings.opt import NLOPT_BFGS_Settings

More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#low-storage-bfgs.

Optional settings

enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-14.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-08.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
kkt_tol_abs : <class 'float'>, optional

The absolute tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
kkt_tol_rel : <class 'float'>, optional

The relative tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : int | None, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to None.
stopval : <class 'float'>, optional

The objective value at which the optimization will stop.

By default it is set to -inf.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-14.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-08.

NLOPT_BOBYQA#

Module: gemseo.algos.opt.nlopt.nlopt

Bound Optimization BY Quadratic Approximation (BOBYQA) implemented in the NLOPT library

Pydantic model of the settings for NLOPT_BOBYQA#

from gemseo.settings.opt import NLOPT_BOBYQA_Settings

More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#bobyqa.

Optional settings

enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-14.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-08.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
init_step : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

The initial step size for derivative-free algorithms.

It can be an array of the initial steps for each dimension, or a single number if the same step will be used for all of them.

For derivative-free local-optimization algorithms, the optimizer must somehow decide on some initial step size to perturb x by when it begins the optimization. This step size should be big enough so that the value of the objective significantly changes, but not too big if you want to find the local optimum nearest to x.

By default it is set to 0.25.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : int | None, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to None.
stopval : <class 'float'>, optional

The objective value at which the optimization will stop.

By default it is set to -inf.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-14.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-08.

NLOPT_COBYLA#

Module: gemseo.algos.opt.nlopt.nlopt

Constrained Optimization BY Linear Approximations (COBYLA) implemented in the NLOPT library

Pydantic model of the settings for NLOPT_COBYLA#

from gemseo.settings.opt import NLOPT_COBYLA_Settings

More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#cobyla-constrained-optimization-by-linear-approximations.

Optional settings

enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-14.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-08.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
init_step : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

The initial step size for derivative-free algorithms.

It can be an array of the initial steps for each dimension, or a single number if the same step will be used for all of them.

For derivative-free local-optimization algorithms, the optimizer must somehow decide on some initial step size to perturb x by when it begins the optimization. This step size should be big enough so that the value of the objective significantly changes, but not too big if you want to find the local optimum nearest to x.

By default it is set to 0.25.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : int | None, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to None.
stopval : <class 'float'>, optional

The objective value at which the optimization will stop.

By default it is set to -inf.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-14.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-08.

NLOPT_MMA#

Module: gemseo.algos.opt.nlopt.nlopt

Method of Moving Asymptotes (MMA)implemented in the NLOPT library

Pydantic model of the settings for NLOPT_MMA#

from gemseo.settings.opt import NLOPT_MMA_Settings

More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#mma-method-of-moving-asymptotes-and-ccsa.

Optional settings

enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-14.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-08.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
inner_maxeval : <class 'int'>, optional

The maximum number of inner iterations of the algorithm.

The value 0 means that there is no limit.

By default it is set to 0.
kkt_tol_abs : <class 'float'>, optional

The absolute tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
kkt_tol_rel : <class 'float'>, optional

The relative tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : int | None, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to None.
stopval : <class 'float'>, optional

The objective value at which the optimization will stop.

By default it is set to -inf.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-14.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-08.

NLOPT_NEWUOA#

Module: gemseo.algos.opt.nlopt.nlopt

NEWUOA + bound constraints implemented in the NLOPT library

Pydantic model of the settings for NLOPT_NEWUOA#

from gemseo.settings.opt import NLOPT_NEWUOA_Settings

More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#newuoa-bound-constraints.

Optional settings

enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-14.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-08.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
init_step : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

The initial step size for derivative-free algorithms.

It can be an array of the initial steps for each dimension, or a single number if the same step will be used for all of them.

For derivative-free local-optimization algorithms, the optimizer must somehow decide on some initial step size to perturb x by when it begins the optimization. This step size should be big enough so that the value of the objective significantly changes, but not too big if you want to find the local optimum nearest to x.

By default it is set to 0.25.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : int | None, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to None.
stopval : <class 'float'>, optional

The objective value at which the optimization will stop.

By default it is set to -inf.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-14.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-08.

NLOPT_SLSQP#

Module: gemseo.algos.opt.nlopt.nlopt

Sequential Least-Squares Quadratic Programming (SLSQP) implemented in the NLOPT library

Pydantic model of the settings for NLOPT_SLSQP#

from gemseo.settings.opt import NLOPT_SLSQP_Settings

More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#slsqp.

Optional settings

enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-14.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-08.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
kkt_tol_abs : <class 'float'>, optional

The absolute tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
kkt_tol_rel : <class 'float'>, optional

The relative tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : int | None, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to None.
stopval : <class 'float'>, optional

The objective value at which the optimization will stop.

By default it is set to -inf.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-14.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-08.

PDFO_BOBYQA#

Note

The plugin gemseo_pdfo is required.

Module: gemseo_pdfo.pdfo

Bound Optimization By Quadratic Approximation

Pydantic model of the settings for PDFO_BOBYQA#

from gemseo.settings.opt import PDFO_BOBYQA_Settings

More details about the algorithm and its settings on https://www.pdfo.net/.

Optional settings

chkfunval : <class 'bool'>, optional

A flag used when debugging. If both debug
and chkfunval are True, an extra function/constraint evaluation would be performed to check whether the returned values of the objective function and constraint match the returned x.

By default it is set to False.
classical : <class 'bool'>, optional

The flag indicating whether to call the classical Powell
code or not.

By default it is set to False.
debug : <class 'bool'>, optional

The debugging flag.

By default it is set to False.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
ensure_bounds : <class 'bool'>, optional

Whether to project the design vector
onto the design space before execution.

By default it is set to True.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftarget : <class 'float'>, optional

The target value of the objective function. If a feasible
iterate achieves an objective function value lower or equal to ftarget, the algorithm stops immediately.

By default it is set to -inf.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-12.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-12.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 500.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.
normalize_design_space : <class 'bool'>, optional

None

By default it is set to (FieldInfo(annotation=bool, required=False, default=True, description='Whether to normalize the design space variables between 0 and 1.'),).
quiet : <class 'bool'>, optional

The flag of quietness of the interface. If True,
the output message will not be printed.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
rhobeg : <class 'float'>, optional

The initial value of the trust region radius.

By default it is set to 0.5.
rhoend : <class 'float'>, optional

The final value of the trust region radius. Indicates
the accuracy required in the final values of the variables.

By default it is set to 1e-06.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scale : <class 'bool'>, optional

The flag indicating whether to scale the problem according to
the bound constraints.

By default it is set to False.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-12.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-12.

PDFO_COBYLA#

Note

The plugin gemseo_pdfo is required.

Module: gemseo_pdfo.pdfo

Constrained Optimization By Linear Approximations

Pydantic model of the settings for PDFO_COBYLA#

from gemseo.settings.opt import PDFO_COBYLA_Settings

More details about the algorithm and its settings on https://www.pdfo.net/.

Optional settings

chkfunval : <class 'bool'>, optional

A flag used when debugging. If both debug
and chkfunval are True, an extra function/constraint evaluation would be performed to check whether the returned values of the objective function and constraint match the returned x.

By default it is set to False.
classical : <class 'bool'>, optional

The flag indicating whether to call the classical Powell
code or not.

By default it is set to False.
debug : <class 'bool'>, optional

The debugging flag.

By default it is set to False.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
ensure_bounds : <class 'bool'>, optional

Whether to project the design vector
onto the design space before execution.

By default it is set to True.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftarget : <class 'float'>, optional

The target value of the objective function. If a feasible
iterate achieves an objective function value lower or equal to ftarget, the algorithm stops immediately.

By default it is set to -inf.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-12.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-12.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 500.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.
normalize_design_space : <class 'bool'>, optional

None

By default it is set to (FieldInfo(annotation=bool, required=False, default=True, description='Whether to normalize the design space variables between 0 and 1.'),).
quiet : <class 'bool'>, optional

The flag of quietness of the interface. If True,
the output message will not be printed.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
rhobeg : <class 'float'>, optional

The initial value of the trust region radius.

By default it is set to 0.5.
rhoend : <class 'float'>, optional

The final value of the trust region radius. Indicates
the accuracy required in the final values of the variables.

By default it is set to 1e-06.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scale : <class 'bool'>, optional

The flag indicating whether to scale the problem according to
the bound constraints.

By default it is set to False.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-12.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-12.

PDFO_NEWUOA#

Note

The plugin gemseo_pdfo is required.

Module: gemseo_pdfo.pdfo

NEWUOA

Pydantic model of the settings for PDFO_NEWUOA#

from gemseo.settings.opt import PDFO_NEWUOA_Settings

More details about the algorithm and its settings on https://www.pdfo.net/.

Optional settings

chkfunval : <class 'bool'>, optional

A flag used when debugging. If both debug
and chkfunval are True, an extra function/constraint evaluation would be performed to check whether the returned values of the objective function and constraint match the returned x.

By default it is set to False.
classical : <class 'bool'>, optional

The flag indicating whether to call the classical Powell
code or not.

By default it is set to False.
debug : <class 'bool'>, optional

The debugging flag.

By default it is set to False.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
ensure_bounds : <class 'bool'>, optional

Whether to project the design vector
onto the design space before execution.

By default it is set to True.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftarget : <class 'float'>, optional

The target value of the objective function. If a feasible
iterate achieves an objective function value lower or equal to ftarget, the algorithm stops immediately.

By default it is set to -inf.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-12.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-12.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 500.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.
normalize_design_space : <class 'bool'>, optional

None

By default it is set to (FieldInfo(annotation=bool, required=False, default=True, description='Whether to normalize the design space variables between 0 and 1.'),).
quiet : <class 'bool'>, optional

The flag of quietness of the interface. If True,
the output message will not be printed.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
rhobeg : <class 'float'>, optional

The initial value of the trust region radius.

By default it is set to 0.5.
rhoend : <class 'float'>, optional

The final value of the trust region radius. Indicates
the accuracy required in the final values of the variables.

By default it is set to 1e-06.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scale : <class 'bool'>, optional

The flag indicating whether to scale the problem according to
the bound constraints.

By default it is set to False.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-12.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-12.

PYMOO_GA#

Note

The plugin gemseo_pymoo is required.

Module: gemseo_pymoo.algos.opt.pymoo

Genetic Algorithm (GA) implemented in the Pymoo library

Pydantic model of the settings for PYMOO_GA#

from gemseo.settings.opt import GASettings

More details about the algorithm and its settings on https://www.pymoo.org/algorithms/soo/ga.html.

Optional settings

crossover : <MagicMock name='Crossover.__or__()' id='126849001444256'>, optional

The crossover operator used to create offsprings. If None, the algorithm's default is used.

By default it is set to None.
eliminate_duplicates : <class 'bool'>, optional

If True, eliminate duplicates after merging the parent and the offspring population.

By default it is set to True.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The equality tolerance.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
hv_tol_abs : <class 'float'>, optional

hv_tol_abs: A stop criterion, absolute tolerance on the hypervolume convergence check. If norm(xk-xk+1)<= hv_tol_abs: stop.

By default it is set to 1e-09.
hv_tol_rel : <class 'float'>, optional

A stop criterion, the relative tolerance on the hypervolume convergence check. If norm(xk-xk+1)/norm(xk)<= hv_tol_rel: stop.

By default it is set to 1e-09.
ineq_tolerance : <class 'float'>, optional

The inequality tolerance.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_gen : <class 'int'>, optional

The maximum number of generations.

By default it is set to 10000000.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 999.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
mutation : <MagicMock name='Mutation.__or__()' id='126848970018736'>, optional

The mutation operator. If None, the algorithm's default is used.

By default it is set to None.
n_offsprings : typing.Optional[typing.Annotated[int, Ge(ge=0)]], optional

Number of offspring that are created through mating. If None, it will be set equal to the population size.

By default it is set to None.
n_processes : <class 'int'>, optional

Number of processes for multiprocess problems.

By default it is set to 1.
normalize_design_space : <class 'bool'>, optional

If True, scale the variables to the range [0, 1].

By default it is set to True.
pop_size : <class 'int'>, optional

The population size.

By default it is set to 100.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
sampling : typing.Any | None, optional

The sampling process that generates the initial population. If None, the algorithm's default is used

By default it is set to None.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
seed : <class 'int'>, optional

The random seed to be used.

By default it is set to 1.
selection : <MagicMock name='Selection.__or__()' id='126848944415008'>, optional

The mating selection operator. If None, the algorithm's default is used.

By default it is set to None.
stop_crit_n_hv : <class 'int'>, optional

The number of generations to account for during the criterion check on the hypervolume indicator.

By default it is set to 5.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

PYMOO_NSGA2#

Note

The plugin gemseo_pymoo is required.

Module: gemseo_pymoo.algos.opt.pymoo

Non-Dominated Sorting Genetic Algorithm II (NSGA2) implemented in the Pymoo library

Pydantic model of the settings for PYMOO_NSGA2#

from gemseo.settings.opt import NSGA2Settings

More details about the algorithm and its settings on https://www.pymoo.org/algorithms/moo/nsga2.html.

Optional settings

crossover : <MagicMock name='Crossover.__or__()' id='126849001444256'>, optional

The crossover operator used to create offsprings. If None, the algorithm's default is used.

By default it is set to None.
eliminate_duplicates : <class 'bool'>, optional

If True, eliminate duplicates after merging the parent and the offspring population.

By default it is set to True.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The equality tolerance.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
hv_tol_abs : <class 'float'>, optional

hv_tol_abs: A stop criterion, absolute tolerance on the hypervolume convergence check. If norm(xk-xk+1)<= hv_tol_abs: stop.

By default it is set to 1e-09.
hv_tol_rel : <class 'float'>, optional

A stop criterion, the relative tolerance on the hypervolume convergence check. If norm(xk-xk+1)/norm(xk)<= hv_tol_rel: stop.

By default it is set to 1e-09.
ineq_tolerance : <class 'float'>, optional

The inequality tolerance.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_gen : <class 'int'>, optional

The maximum number of generations.

By default it is set to 10000000.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 999.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
mutation : <MagicMock name='Mutation.__or__()' id='126848970018736'>, optional

The mutation operator. If None, the algorithm's default is used.

By default it is set to None.
n_offsprings : typing.Optional[typing.Annotated[int, Ge(ge=0)]], optional

Number of offspring that are created through mating. If None, it will be set equal to the population size.

By default it is set to None.
n_processes : <class 'int'>, optional

Number of processes for multiprocess problems.

By default it is set to 1.
normalize_design_space : <class 'bool'>, optional

If True, scale the variables to the range [0, 1].

By default it is set to True.
pop_size : <class 'int'>, optional

The population size.

By default it is set to 100.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
sampling : typing.Any | None, optional

The sampling process that generates the initial population. If None, the algorithm's default is used

By default it is set to None.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
seed : <class 'int'>, optional

The random seed to be used.

By default it is set to 1.
selection : <MagicMock name='Selection.__or__()' id='126848944415008'>, optional

The mating selection operator. If None, the algorithm's default is used.

By default it is set to None.
stop_crit_n_hv : <class 'int'>, optional

The number of generations to account for during the criterion check on the hypervolume indicator.

By default it is set to 5.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

PYMOO_NSGA3#

Note

The plugin gemseo_pymoo is required.

Module: gemseo_pymoo.algos.opt.pymoo

Non-Dominated Sorting Genetic Algorithm III (NSGA3) implemented in the Pymoo library

Pydantic model of the settings for PYMOO_NSGA3#

from gemseo.settings.opt import NSGA3Settings

More details about the algorithm and its settings on https://www.pymoo.org/algorithms/moo/nsga3.html.

Optional settings

crossover : <MagicMock name='Crossover.__or__()' id='126849001444256'>, optional

The crossover operator used to create offsprings. If None, the algorithm's default is used.

By default it is set to None.
eliminate_duplicates : <class 'bool'>, optional

If True, eliminate duplicates after merging the parent and the offspring population.

By default it is set to True.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The equality tolerance.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
hv_tol_abs : <class 'float'>, optional

hv_tol_abs: A stop criterion, absolute tolerance on the hypervolume convergence check. If norm(xk-xk+1)<= hv_tol_abs: stop.

By default it is set to 1e-09.
hv_tol_rel : <class 'float'>, optional

A stop criterion, the relative tolerance on the hypervolume convergence check. If norm(xk-xk+1)/norm(xk)<= hv_tol_rel: stop.

By default it is set to 1e-09.
ineq_tolerance : <class 'float'>, optional

The inequality tolerance.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_gen : <class 'int'>, optional

The maximum number of generations.

By default it is set to 10000000.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 999.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
mutation : <MagicMock name='Mutation.__or__()' id='126848970018736'>, optional

The mutation operator. If None, the algorithm's default is used.

By default it is set to None.
n_offsprings : typing.Optional[typing.Annotated[int, Ge(ge=0)]], optional

Number of offspring that are created through mating. If None, it will be set equal to the population size.

By default it is set to None.
n_partitions : <class 'int'>, optional

The number of gaps between two consecutive points along an objective axis.

By default it is set to 20.
n_points : typing.Optional[typing.Annotated[int, Gt(gt=0)]], optional

The number of points on the unit simplex.

By default it is set to None.
n_processes : <class 'int'>, optional

Number of processes for multiprocess problems.

By default it is set to 1.
normalize_design_space : <class 'bool'>, optional

If True, scale the variables to the range [0, 1].

By default it is set to True.
partitions : gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]] | None, optional

The custom partitions.

By default it is set to None.
pop_size : <class 'int'>, optional

The population size.

By default it is set to 100.
ref_dirs_name : gemseo_pymoo.algos.opt._base_scaled_pymoo_algorithms_settings.RefDirsNames | None

The reference directions.

By default it is set to .
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
sampling : typing.Any | None, optional

The sampling process that generates the initial population. If None, the algorithm's default is used

By default it is set to None.
scaling_1 : float | None, optional

The scaling of the first simplex.

By default it is set to None.
scaling_2 : float | None, optional

The scaling of the second simplex.

By default it is set to None.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
seed : <class 'int'>, optional

The random seed to be used.

By default it is set to 1.
selection : <MagicMock name='Selection.__or__()' id='126848944415008'>, optional

The mating selection operator. If None, the algorithm's default is used.

By default it is set to None.
stop_crit_n_hv : <class 'int'>, optional

The number of generations to account for during the criterion check on the hypervolume indicator.

By default it is set to 5.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

PYMOO_RNSGA3#

Note

The plugin gemseo_pymoo is required.

Module: gemseo_pymoo.algos.opt.pymoo

Reference Point Based NSGA III implemented in the Pymoo library

Pydantic model of the settings for PYMOO_RNSGA3#

from gemseo.settings.opt import RNSGA3Settings

More details about the algorithm and its settings on https://www.pymoo.org/algorithms/moo/rnsga3.html.

Optional settings

crossover : <MagicMock name='Crossover.__or__()' id='126849001444256'>, optional

The crossover operator used to create offsprings. If None, the algorithm's default is used.

By default it is set to None.
eliminate_duplicates : <class 'bool'>, optional

If True, eliminate duplicates after merging the parent and the offspring population.

By default it is set to True.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The equality tolerance.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
hv_tol_abs : <class 'float'>, optional

hv_tol_abs: A stop criterion, absolute tolerance on the hypervolume convergence check. If norm(xk-xk+1)<= hv_tol_abs: stop.

By default it is set to 1e-09.
hv_tol_rel : <class 'float'>, optional

A stop criterion, the relative tolerance on the hypervolume convergence check. If norm(xk-xk+1)/norm(xk)<= hv_tol_rel: stop.

By default it is set to 1e-09.
ineq_tolerance : <class 'float'>, optional

The inequality tolerance.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_gen : <class 'int'>, optional

The maximum number of generations.

By default it is set to 10000000.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 999.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
mu : <class 'float'>, optional

The scaling of the reference lines used during survival selection.

By default it is set to 0.1.
mutation : <MagicMock name='Mutation.__or__()' id='126848970018736'>, optional

The mutation operator. If None, the algorithm's default is used.

By default it is set to None.
n_offsprings : typing.Optional[typing.Annotated[int, Ge(ge=0)]], optional

Number of offspring that are created through mating. If None, it will be set equal to the population size.

By default it is set to None.
n_processes : <class 'int'>, optional

Number of processes for multiprocess problems.

By default it is set to 1.
normalize_design_space : <class 'bool'>, optional

If True, scale the variables to the range [0, 1].

By default it is set to True.
pop_per_ref_point : <class 'int'>, optional

The size of the population used for each reference point.

By default it is set to 1.
pop_size : <class 'int'>, optional

The population size.

By default it is set to 100.
ref_points : gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]] | None, optional

The reference points (Aspiration Points) as a NumPy array where each row represents a point and each column a variable.

By default it is set to None.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
sampling : typing.Any | None, optional

The sampling process that generates the initial population. If None, the algorithm's default is used

By default it is set to None.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
seed : <class 'int'>, optional

The random seed to be used.

By default it is set to 1.
selection : <MagicMock name='Selection.__or__()' id='126848944415008'>, optional

The mating selection operator. If None, the algorithm's default is used.

By default it is set to None.
stop_crit_n_hv : <class 'int'>, optional

The number of generations to account for during the criterion check on the hypervolume indicator.

By default it is set to 5.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

PYMOO_UNSGA3#

Note

The plugin gemseo_pymoo is required.

Module: gemseo_pymoo.algos.opt.pymoo

Unified NSGA III implemented in the Pymoo library

Pydantic model of the settings for PYMOO_UNSGA3#

from gemseo.settings.opt import UNSGA3Settings

More details about the algorithm and its settings on https://www.pymoo.org/algorithms/moo/unsga3.html.

Optional settings

crossover : <MagicMock name='Crossover.__or__()' id='126849001444256'>, optional

The crossover operator used to create offsprings. If None, the algorithm's default is used.

By default it is set to None.
eliminate_duplicates : <class 'bool'>, optional

If True, eliminate duplicates after merging the parent and the offspring population.

By default it is set to True.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The equality tolerance.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
hv_tol_abs : <class 'float'>, optional

hv_tol_abs: A stop criterion, absolute tolerance on the hypervolume convergence check. If norm(xk-xk+1)<= hv_tol_abs: stop.

By default it is set to 1e-09.
hv_tol_rel : <class 'float'>, optional

A stop criterion, the relative tolerance on the hypervolume convergence check. If norm(xk-xk+1)/norm(xk)<= hv_tol_rel: stop.

By default it is set to 1e-09.
ineq_tolerance : <class 'float'>, optional

The inequality tolerance.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_gen : <class 'int'>, optional

The maximum number of generations.

By default it is set to 10000000.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 999.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
mutation : <MagicMock name='Mutation.__or__()' id='126848970018736'>, optional

The mutation operator. If None, the algorithm's default is used.

By default it is set to None.
n_offsprings : typing.Optional[typing.Annotated[int, Ge(ge=0)]], optional

Number of offspring that are created through mating. If None, it will be set equal to the population size.

By default it is set to None.
n_partitions : <class 'int'>, optional

The number of gaps between two consecutive points along an objective axis.

By default it is set to 20.
n_points : typing.Optional[typing.Annotated[int, Gt(gt=0)]], optional

The number of points on the unit simplex.

By default it is set to None.
n_processes : <class 'int'>, optional

Number of processes for multiprocess problems.

By default it is set to 1.
normalize_design_space : <class 'bool'>, optional

If True, scale the variables to the range [0, 1].

By default it is set to True.
partitions : gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]] | None, optional

The custom partitions.

By default it is set to None.
pop_size : <class 'int'>, optional

The population size.

By default it is set to 100.
ref_dirs_name : gemseo_pymoo.algos.opt._base_scaled_pymoo_algorithms_settings.RefDirsNames | None

The reference directions.

By default it is set to .
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
sampling : typing.Any | None, optional

The sampling process that generates the initial population. If None, the algorithm's default is used

By default it is set to None.
scaling_1 : float | None, optional

The scaling of the first simplex.

By default it is set to None.
scaling_2 : float | None, optional

The scaling of the second simplex.

By default it is set to None.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
seed : <class 'int'>, optional

The random seed to be used.

By default it is set to 1.
selection : <MagicMock name='Selection.__or__()' id='126848944415008'>, optional

The mating selection operator. If None, the algorithm's default is used.

By default it is set to None.
stop_crit_n_hv : <class 'int'>, optional

The number of generations to account for during the criterion check on the hypervolume indicator.

By default it is set to 5.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

PYOPTSPARSE_SLSQP#

Note

The plugin gemseo_pyoptsparse is required.

Module: gemseo_pyoptsparse.algos.opt.py_opt_sparse

Sequential Least-Squares Quadratic Programming (SLSQP) implemented in pyOptSparse library

Pydantic model of the settings for PYOPTSPARSE_SLSQP#

from gemseo.settings.opt import SLSQP_Settings

More details about the algorithm and its settings on https://mdolab-pyoptsparse.readthedocs-hosted.com.

Optional settings

enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-06.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-06.
i_file : <class 'str'>, optional

Output file path

By default it is set to SLSQP.out.
i_out : <class 'int'>, optional

Output unit number

By default it is set to 60.
i_print : <class 'int'>, optional

Output Level (<0 - None, 0 - Screen, 1 - File)

By default it is set to -1.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
kkt_tol_abs : <class 'float'>, optional

The absolute tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
kkt_tol_rel : <class 'float'>, optional

The relative tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
options_file : str | None, optional

The file name where all options are written.

By default it is set to None.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-06.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-06.

PYOPTSPARSE_SNOPT#

Note

The plugin gemseo_pyoptsparse is required.

Module: gemseo_pyoptsparse.algos.opt.py_opt_sparse

SNOPT implemented in PyOptSparse library

Pydantic model of the settings for PYOPTSPARSE_SNOPT#

from gemseo.settings.opt import SNOPT_Settings

More details about the algorithm and its settings on https://mdolab-pyoptsparse.readthedocs-hosted.com.

Optional settings

backup_basis_file : int | None, optional

None

By default it is set to None.
central_difference_interval : float | None, optional

None

By default it is set to None.
check_frequency : int | None, optional

None

By default it is set to None.
crash_option : int | None, optional

None

By default it is set to None.
crash_tolerance : float | None, optional

None

By default it is set to None.
debug_level : int | None, optional

None

By default it is set to None.
derivative_linesearch : dict[str, typing.Any] | None, optional

None

By default it is set to None.
difference_interval : float | None, optional

None

By default it is set to None.
dump_file : int | None, optional

None

By default it is set to None.
elastic_mode : str | None, optional

None

By default it is set to None.
elastic_weight : <class 'float'>, optional

The initial elastic weight associated to the elastic mode activation.

By default it is set to 10000.0.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
expand_frequency : int | None, optional

None

By default it is set to None.
factorization_frequency : int | None, optional

None

By default it is set to None.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-06.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-06.
function_precision : float | None, optional

None

By default it is set to None.
hessian_flush : int | None, optional

None

By default it is set to None.
hessian_frequency : int | None, optional

None

By default it is set to None.
hessian_full_memory : dict[str, typing.Any] | None, optional

None

By default it is set to None.
hessian_limited_memory : dict[str, typing.Any] | None, optional

None

By default it is set to None.
hessian_updates : <class 'int'>, optional

Iteration frequency to start again the hessian updating process

By default it is set to 10.
i_print : <class 'int'>, optional

Print file output unit

By default it is set to 0.
i_summ : <class 'int'>, optional

Summary file output unit

By default it is set to 0.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
infinite_bound : float | None, optional

None

By default it is set to None.
insert_file : int | None, optional

None

By default it is set to None.
kkt_tol_abs : <class 'float'>, optional

The absolute tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
kkt_tol_rel : <class 'float'>, optional

The relative tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
linesearch_tolerance : <class 'float'>, optional

Accuracy to control a steplength with the direction of search at each iteration

By default it is set to 0.9.
load_file : int | None, optional

None

By default it is set to None.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
lu_complete_pivoting : dict[str, typing.Any] | None, optional

None

By default it is set to None.
lu_factor_tolerance : float | None, optional

None

By default it is set to None.
lu_partial_pivoting : dict[str, typing.Any] | None, optional

None

By default it is set to None.
lu_rook_pivoting : dict[str, typing.Any] | None, optional

None

By default it is set to None.
lu_singularity_tolerance : float | None, optional

None

By default it is set to None.
lu_update_tolerance : float | None, optional

None

By default it is set to None.
major_optimality_tolerance : <class 'float'>, optional

None

By default it is set to 1e-06.
major_print_level : int | None, optional

None

By default it is set to None.
major_step_limit : <class 'float'>, optional

Limitation of the change in design variables during a linesearch

By default it is set to 2.0.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
minor_feasibility_tolerance : <class 'float'>, optional

Fesibility tolerance of the minor problem

By default it is set to 1e-06.
minor_iterations_limit : <class 'int'>, optional

The iterations limit for the minor problem

By default it is set to 10000.
minor_print_level : int | None, optional

None

By default it is set to None.
new_basis_file : int | None, optional

None

By default it is set to None.
new_superbasics_limit : int | None, optional

None

By default it is set to None.
nonderivative_linesearch : dict[str, typing.Any] | None, optional

None

By default it is set to None.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
objective_row : int | None, optional

None

By default it is set to None.
old_basis_file : int | None, optional

None

By default it is set to None.
options_file : str | None, optional

The file name where all options are written.

By default it is set to None.
partial_price : int | None, optional

None

By default it is set to None.
penalty_parameter : float | None, optional

None

By default it is set to None.
pivot_tolerance : float | None, optional

None

By default it is set to None.
print_file : <class 'str'>, optional

None

By default it is set to SNOPT_print.out.
print_frequency : int | None, optional

None

By default it is set to None.
proximal_iterations_limit : <class 'int'>, optional

The iterations limit for solving the proximal point problem

By default it is set to 10000.
proximal_point_method : <class 'int'>, optional

The method for the proximal point procedure

By default it is set to 1.
punch_file : int | None, optional

None

By default it is set to None.
reduced_hessian_dimension : int | None, optional

None

By default it is set to None.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
save_frequency : int | None, optional

None

By default it is set to None.
save_major_iteration_variables : list[str], optional

The SNOPT internal variables that must be saved into the optimization database (specific to PyOptSparse wrapper).

By default it is set to [].
scale_option : int | None, optional

None

By default it is set to None.
scale_tolerance : float | None, optional

None

By default it is set to None.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
solution : str | None, optional

None

By default it is set to None.
solution_file : int | None, optional

None

By default it is set to None.
start_constraint_check_at_column : int | None, optional

None

By default it is set to None.
start_objective_check_at_column : int | None, optional

None

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
summary_file : <class 'str'>, optional

None

By default it is set to SNOPT_summary.out.
summary_frequency : int | None, optional

None

By default it is set to None.
superbasics_limit : int | None, optional

None

By default it is set to None.
suppress_options_listing : dict[str, typing.Any] | None, optional

None

By default it is set to None.
system_information : str | None, optional

None

By default it is set to None.
timing_level : int | None, optional

None

By default it is set to None.
unbounded_objective : float | None, optional

None

By default it is set to None.
unbounded_step_size : float | None, optional

None

By default it is set to None.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
user_character_workspace : int | None, optional

None

By default it is set to None.
user_integer_workspace : int | None, optional

None

By default it is set to None.
user_real_workspace : int | None, optional

None

By default it is set to None.
verify_level : int | None, optional

None

By default it is set to None.
violation_limit : <class 'float'>, optional

The absolute limit on the magnitude of the maximum constraint violation after the linesearch

By default it is set to 10.0.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-06.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-06.

SBO#

Note

The plugin gemseo_mlearning is required.

Module: gemseo_mlearning.algos.opt.surrogate_based_optimization

GEMSEO in-house surrogate-based optimizer.

Pydantic model of the settings for SBO#

from gemseo.settings.opt import SBOSettings

Optional settings

acquisition_algorithm : <class 'str'>

The name of the algorithm to optimize the data acquisition criterion.
If empty, use the default algorithm with its default settings.

By default it is set to .
acquisition_settings : collections.abc.Mapping[str, typing.Union[str, float, int, bool, list[str], numpy.ndarray, collections.abc.Iterable[collections.abc.Callable[[int, typing.Any], None]], collections.abc.Mapping[str, typing.Any]]], optional

The settings of the algorithm
to optimize the data acquisition criterion. Ignored when acquisition_algorithm is empty.

By default it is set to {}.
batch_size : <class 'int'>, optional

The number of points to be acquired in parallel.

By default it is set to 1.
criterion : <enum 'AcquisitionCriterion'>, optional

The acquisition criterion.

By default it is set to EI.
doe_algorithm : <class 'str'>, optional

The name of the DOE algorithm for the initial sampling.
This argument is ignored when regression_algorithm is a [BaseRegressor][gemseo.mlearning.regression.algos.base_regressor.BaseRegressor].

By default it is set to OT_OPT_LHS.
doe_settings : collections.abc.Mapping[str, typing.Union[str, float, int, bool, list[str], numpy.ndarray, collections.abc.Iterable[collections.abc.Callable[[int, typing.Any], None]], collections.abc.Mapping[str, typing.Any]]], optional

The settings of the DOE algorithm for the initial sampling.
This argument is ignored when regression_algorithm is a [BaseRegressor][gemseo.mlearning.regression.algos.base_regressor.BaseRegressor].

By default it is set to {}.
doe_size : <class 'int'>, optional

Either the initial DOE size or 0 if it is inferred from doe_settings.
This argument is ignored when regression_algorithm is a [BaseRegressor][gemseo.mlearning.regression.algos.base_regressor.BaseRegressor].

By default it is set to 10.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 0.0.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 0.0.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
mc_size : <class 'int'>, optional

The sample size to estimate the acquisition criteria in parallel.

By default it is set to 10000.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to False.
regression_algorithm : str | gemseo.mlearning.regression.algos.base_regressor.BaseRegressor, optional

The regression algorithm.
Either the name of the regression algorithm approximating the objective function over the design space or the regression algorithm itself.

By default it is set to OTGaussianProcessRegressor.
regression_file_path : str | pathlib.Path

The path to the file to save the regression model.
If empty, do not save the regression model.

By default it is set to .
regression_settings : collections.abc.Mapping[str, typing.Optional[typing.Any]], optional

The settings of the regression algorithm.
This argument is ignored when regression_algorithm is a [BaseRegressor][gemseo.mlearning.regression.algos.base_regressor.BaseRegressor].

By default it is set to {}.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 0.0.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 0.0.

SHGO#

Module: gemseo.algos.opt.scipy_global.scipy_global

Simplicial homology global optimization

Pydantic model of the settings for SHGO#

from gemseo.settings.opt import SHGO_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.shgo.html.

Optional settings

enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 1e-06.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
iters : <class 'int'>, optional

The number of iterations used to construct the simplicial complex.

By default it is set to 1.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 9223372036854775807.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
n : <class 'int'>, optional

The number of samples used to construct the simplicial complex.

By default it is set to 100.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
options : collections.abc.Mapping[str, typing.Any], optional

The options for the local optimization algorithm.

By default it is set to {}.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
sampling_method : <class 'str'>, optional

The sampling method.

By default it is set to simplicial.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
workers : <class 'int'>, optional

The number workers to parallelize on.

By default it is set to 1.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

SLSQP#

Module: gemseo.algos.opt.scipy_local.scipy_local

Sequential Least-Squares Quadratic Programming (SLSQP) implemented in the SciPy library

Pydantic model of the settings for SLSQP#

from gemseo.settings.opt import SLSQP_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-slsqp.html.

Optional settings

disp : <class 'bool'>, optional

Whether to print convergence messages.

By default it is set to False.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 1e-06.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
iprint : <class 'int'>, optional

The flag to control the frequency of output.

Default is no output.

By default it is set to -1.
kkt_tol_abs : <class 'float'>, optional

The absolute tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
kkt_tol_rel : <class 'float'>, optional

The relative tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

SMT_EGO#

Note

The plugin gemseo_mlearning is required.

Module: gemseo_mlearning.algos.opt.smt.smt_ego

Efficient Global Optimization

Pydantic model of the settings for SMT_EGO#

from gemseo.settings.opt import SMTEGOSettings

More details about the algorithm and its settings on https://smt.readthedocs.io/en/latest/_src_docs/applications/ego.html.

Optional settings

criterion : <enum 'AcquisitionCriterion'>, optional

The acquisition criterion.

By default it is set to EI.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
enable_tunneling : <class 'bool'>, optional

Whether to enable the penalization of points that have been already evaluated in EI criterion.

By default it is set to False.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 0.0.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 0.0.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
n_doe : <class 'int'>, optional

The number of points of the initial LHS DOE to train the surrogate.

By default it is set to 10.
n_max_optim : <class 'int'>, optional

The maximum number of iterations for each sub-optimization.

By default it is set to 20.
n_parallel : <class 'int'>, optional

The number of points to be acquired in parallel; if 1, acquire points sequentially.

By default it is set to 1.
n_start : <class 'int'>, optional

The number of sub-optimizations.

By default it is set to 50.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
qEI : <enum 'ParallelStrategy'>, optional

The strategy to acquire points in parallel.

By default it is set to KBUB.
random_state : <class 'int'>, optional

The Numpy RandomState object or seed number which controls random draws.

By default it is set to 1.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
surrogate : <MagicMock name='SurrogateModel.__ror__()' id='126849253433344'>, optional

The SMT Kriging-based surrogate model used internally; either an instance of the surrogate before training or its class name.

By default it is set to KRG.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 0.0.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 0.0.

Scipy_MILP#

Module: gemseo.algos.opt.scipy_milp.scipy_milp

Mixed-integer linear programming

Pydantic model of the settings for Scipy_MILP#

from gemseo.settings.opt import SciPyMILP_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.milp.html.

Optional settings

disp : <class 'bool'>, optional

Whether to print optimization status during optimization.

By default it is set to False.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 0.01.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 0.0.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 0.0.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
mip_rel_gap : <class 'float'>, optional

The termination criterion for MIP solver.

The solver will terminate when the gap between the primal objective value and the dual objective bound, scaled by the primal objective value, is <= mip_rel_gap.

By default it is set to 0.0.
node_limit : <class 'int'>, optional

The maximum number of nodes to solve before stopping.

By default it is set to 1000.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
presolve : <class 'bool'>, optional

Whether to perform a preliminary analysis on the problem before solving.

It attempts to detect infeasibility, unboundedness or problem simplifications.

By default it is set to True.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 0.0.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 0.0.

TNC#

Module: gemseo.algos.opt.scipy_local.scipy_local

Truncated Newton (TNC) algorithm implemented in SciPy library

Pydantic model of the settings for TNC#

from gemseo.settings.opt import TNC_Settings

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-tnc.html.

Optional settings

accuracy : <class 'float'>, optional

The relative precision for finite difference calculations.

By default it is set to 0.0.
disp : <class 'bool'>, optional

Whether to print convergence messages.

By default it is set to False.
enable_progress_bar : bool | None, optional

Whether to enable the progress bar in the optimization log.

If None, use the global value of enable_progress_bar (see the configure function to change it globally).

By default it is set to None.
eq_tolerance : <class 'float'>, optional

The tolerance on the equality constraints.

By default it is set to 1e-06.
eta : <class 'float'>, optional

The severity of the line search.

By default it is set to -1.
ftol_abs : <class 'float'>, optional

The absolute tolerance on the objective function.

By default it is set to 1e-09.
ftol_rel : <class 'float'>, optional

The relative tolerance on the objective function.

By default it is set to 1e-09.
gtol : <class 'float'>, optional

The precision goal for the projected gradient value to stop the algorithm.

By default it is set to 1e-06.
ineq_tolerance : <class 'float'>, optional

The tolerance on the inequality constraints.

By default it is set to 0.0001.
kkt_tol_abs : <class 'float'>, optional

The absolute tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
kkt_tol_rel : <class 'float'>, optional

The relative tolerance on the KKT residual norm.

If inf this criterion is not activated.

By default it is set to inf.
log_problem : <class 'bool'>, optional

Whether to log the definition and result of the problem.

By default it is set to True.
max_iter : <class 'int'>, optional

The maximum number of iterations.

By default it is set to 1000.
max_time : <class 'float'>, optional

The maximum runtime in seconds, disabled if 0.

By default it is set to 0.0.
maxCGit : <class 'int'>, optional

The maximum number of hessian-vector evaluations per main iteration.

By default it is set to -1.
minfev : <class 'float'>, optional

The minimum function value estimate.

By default it is set to 0.0.
normalize_design_space : <class 'bool'>, optional

Whether to normalize the design space variables between 0 and 1.

By default it is set to True.
offset : float | None, optional

The value to subtract from each variable.

If None, the offsets are (up+low)/2 for interval bounded variables and x for the others.

By default it is set to None.
rescale : <class 'float'>, optional

The log10 scaling factor used to trigger the objectiv function rescaling.

By default it is set to 1.3.
reset_iteration_counters : <class 'bool'>, optional

Whether to reset the iteration counters before each execution.

By default it is set to True.
round_ints : <class 'bool'>, optional

Whether to round the integer variables.

By default it is set to True.
scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

The threshold on the reference function value that triggers scaling.

If None, do not scale the functions.

By default it is set to None.
stepmx : <class 'float'>, optional

The maximum step for the line search (may be increased during call).

By default it is set to 0.0.
stop_crit_n_x : <class 'int'>, optional

The minimum number of design vectors to consider in the stopping criteria.

By default it is set to 3.
store_jacobian : <class 'bool'>, optional

Whether to store the Jacobian matrices in the database.

This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

By default it is set to True.
use_database : <class 'bool'>, optional

Whether to wrap the functions in the database.

By default it is set to True.
use_one_line_progress_bar : <class 'bool'>, optional

Whether to log the progress bar on a single line.

By default it is set to False.
xtol_abs : <class 'float'>, optional

The absolute tolerance on the design parameters.

By default it is set to 1e-09.
xtol_rel : <class 'float'>, optional

The relative tolerance on the design parameters.

By default it is set to 1e-09.

Optimization algorithms#

Overview

Augmented_Lagrangian_order_0#

Augmented_Lagrangian_order_1#

COBYQA#

DIFFERENTIAL_EVOLUTION#

DUAL_ANNEALING#

DUAL_SIMPLEX#

HEXALY#

INTERIOR_POINT#

L-BFGS-B#

MMA#

MNBI#

MultiStart#

NELDER-MEAD#

NLOPT_BFGS#

NLOPT_BOBYQA#

NLOPT_COBYLA#

NLOPT_MMA#

NLOPT_NEWUOA#

NLOPT_SLSQP#

PDFO_BOBYQA#

PDFO_COBYLA#

PDFO_NEWUOA#

PYMOO_GA#

PYMOO_NSGA2#

PYMOO_NSGA3#

PYMOO_RNSGA3#

PYMOO_UNSGA3#

PYOPTSPARSE_SLSQP#

PYOPTSPARSE_SNOPT#

SBO#

SHGO#

SLSQP#

SMT_EGO#

Scipy_MILP#

TNC#

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