# Optimization algorithms¶

Warning

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

Note

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

Algorithm ▲▼ |
Library ▲▼ |
Name in GEMSEO ▲▼ |
Package ▲▼ |
Handle equality constraints ▲▼ |
Handle inequality constraints ▲▼ |
Handle float variables ▲▼ |
Handle integer variables ▲▼ |
Handle multiobjective ▲▼ |
Require gradient ▲▼ |
---|---|---|---|---|---|---|---|---|---|

Augmented_Lagrangian_order_0 | Augmented_Lagrangian_order_0 | gemseo | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ | |

Augmented_Lagrangian_order_1 | Augmented_Lagrangian_order_1 | gemseo | ✓ | ✓ | ✓ | ✗ | ✗ | ✓ | |

Differential evolution | SciPy | DIFFERENTIAL_EVOLUTION | gemseo | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ |

Dual annealing | SciPy | DUAL_ANNEALING | gemseo | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ |

HiGHS | SciPy | HIGHS | gemseo | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ |

Dual simplex | SciPy | HIGHS_DUAL_SIMPLEX | gemseo | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ |

Interior point method | SciPy | HIGHS_INTERIOR_POINT | gemseo | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ |

L-BFGS-B | SciPy | L-BFGS-B | gemseo | ✗ | ✗ | ✓ | ✗ | ✗ | ✓ |

Linear interior point | SciPy | LINEAR_INTERIOR_POINT | gemseo | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ |

MMA | MMA | MMA | gemseo_mma | ✗ | ✓ | ✓ | ✗ | ✗ | ✓ |

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 | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ |

PSEVEN | pSeven | PSEVEN | gemseo_pseven | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ |

Feasible direction | pSeven | PSEVEN_FD | gemseo_pseven | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ |

MOM | pSeven | PSEVEN_MOM | gemseo_pseven | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ |

NCG | pSeven | PSEVEN_NCG | gemseo_pseven | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ |

NLS | pSeven | PSEVEN_NLS | gemseo_pseven | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ |

POWELL | pSeven | PSEVEN_POWELL | gemseo_pseven | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ |

QP | pSeven | PSEVEN_QP | gemseo_pseven | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ |

SQ2P | pSeven | PSEVEN_SQ2P | gemseo_pseven | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ |

SQP | pSeven | PSEVEN_SQP | gemseo_pseven | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ |

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 | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ |

Revised simplex | SciPy | REVISED_SIMPLEX | gemseo | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ |

SBO | gemseo-mlearning | SBO | gemseo_mlearning | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ |

SHGO | SciPy | SHGO | gemseo | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ |

Simplex | SciPy | SIMPLEX | gemseo | ✓ | ✓ | ✓ | ✗ | ✗ | ✗ |

SLSQP | SciPy | SLSQP | gemseo | ✓ | ✓ | ✓ | ✗ | ✗ | ✓ |

Branch & Cut algorithm | SciPy | Scipy_MILP | gemseo | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ |

TNC | SciPy | TNC | gemseo | ✗ | ✗ | ✓ | ✗ | ✗ | ✓ |

## Augmented_Lagrangian_order_0¶

Module: `gemseo.algos.opt.augmented_lagrangian.order_0`

Augmented Lagrangian algorithm for gradient-less functions.

- Required parameters
**sub_solver_algorithm**:*str*The name of the optimization algorithm used to solve each sub-poblem.

- Optional parameters
**ftol_abs**:*float, optional*A stop criteria, the absolute tolerance on the objective function. If abs(f(xk)-f(xk+1))<= ftol_rel: stop.

By default it is set to 1e-09.

**ftol_rel**:*float, optional*A stop criteria, the relative tolerance on the objective function. If abs(f(xk)-f(xk+1))/abs(f(xk))<= ftol_rel: stop.

By default it is set to 1e-09.

**gamma**:*float, optional*The increase of the penalty term.

By default it is set to 1.5.

**initial_rho**:*float, optional*The initial value of the penalty.

By default it is set to 10.0.

**kkt_tol_abs**:*float | None, optional*The absolute tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**kkt_tol_rel**:*float | None, optional*The relative tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**max_iter**:*int, optional*The maximum number of iterations, i.e. unique calls to f(x).

By default it is set to 999.

**max_rho**:*float, optional*The max penalty value.

By default it is set to 10000.

**normalize_design_space**:*bool, optional*Whether to scale the variables into

`[0, 1]`

.By default it is set to True.

**stop_crit_n_x**:*int, optional*The minimum number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**sub_problem_constraints**:*Iterable[str], optional*The constraints to keep in the sub-problem. If

`empty`

all constraints are dealt by the Augmented Lagrange, which means that the sub-problem is unconstrained.By default it is set to ().

**sub_problem_options**:*Mapping[str, Any] | None, optional*The options passed to the sub-problem optimization solver.

By default it is set to None.

**tau**:*float, optional*The threshold for the penalty term increase.

By default it is set to 0.9.

**xtol_abs**:*float, optional*A stop criteria, absolute tolerance on the design variables. If norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-09.

**xtol_rel**:*float, optional*A stop criteria, the relative tolerance on the design variables. If norm(xk-xk+1)/norm(xk)<= xtol_rel: stop.

By default it is set to 1e-09.

## Augmented_Lagrangian_order_1¶

Module: `gemseo.algos.opt.augmented_lagrangian.order_1`

Augmented Lagrangian algorithm using gradient information.

- Required parameters
**sub_solver_algorithm**:*str*The name of the optimization algorithm used to solve each sub-poblem.

- Optional parameters
**ftol_abs**:*float, optional*A stop criteria, the absolute tolerance on the objective function. If abs(f(xk)-f(xk+1))<= ftol_rel: stop.

By default it is set to 1e-09.

**ftol_rel**:*float, optional*A stop criteria, the relative tolerance on the objective function. If abs(f(xk)-f(xk+1))/abs(f(xk))<= ftol_rel: stop.

By default it is set to 1e-09.

**gamma**:*float, optional*The increase of the penalty term.

By default it is set to 1.5.

**initial_rho**:*float, optional*The initial value of the penalty.

By default it is set to 10.0.

**kkt_tol_abs**:*float | None, optional*The absolute tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**kkt_tol_rel**:*float | None, optional*The relative tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**max_iter**:*int, optional*The maximum number of iterations, i.e. unique calls to f(x).

By default it is set to 999.

**max_rho**:*float, optional*The max penalty value.

By default it is set to 10000.

**normalize_design_space**:*bool, optional*Whether to scale the variables into

`[0, 1]`

.By default it is set to True.

**stop_crit_n_x**:*int, optional*The minimum number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**sub_problem_constraints**:*Iterable[str], optional*The constraints to keep in the sub-problem. If

`empty`

all constraints are dealt by the Augmented Lagrange, which means that the sub-problem is unconstrained.By default it is set to ().

**sub_problem_options**:*Mapping[str, Any] | None, optional*The options passed to the sub-problem optimization solver.

By default it is set to None.

**tau**:*float, optional*The threshold for the penalty term increase.

By default it is set to 0.9.

**xtol_abs**:*float, optional*A stop criteria, absolute tolerance on the design variables. If norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-09.

**xtol_rel**:*float, optional*A stop criteria, the relative tolerance on the design variables. If norm(xk-xk+1)/norm(xk)<= xtol_rel: stop.

By default it is set to 1e-09.

## DIFFERENTIAL_EVOLUTION¶

Module: `gemseo.algos.opt.lib_scipy_global`

Differential Evolution algorithm

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

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to f(x).

- Optional parameters
**atol**:*float, optional*The absolute tolerance for convergence.

By default it is set to 0.0.

**eq_tolerance**:*float, optional*The tolerance on equality constraints.

By default it is set to 1e-06.

**ftol_abs**:*float, optional*A stop criteria, the absolute tolerance on the objective function. If abs(f(xk)-f(xk+1))<= ftol_rel: stop.

By default it is set to 1e-09.

**ftol_rel**:*float, optional*A stop criteria, the relative tolerance on the objective function. If abs(f(xk)-f(xk+1))/abs(f(xk))<= ftol_rel: stop.

By default it is set to 1e-09.

**ineq_tolerance**:*float, optional*The tolerance on inequality constraints.

By default it is set to 1e-06.

**init**:*str, optional*Either the type of population initialization to be used or an array specifying the initial population.

By default it is set to latinhypercube.

**max_time**:*float, optional*The maximum runtime in seconds. The value 0 disables the cap on the runtime.

By default it is set to 0.0.

**normalize_design_space**:*bool, optional*If

`True`

, variables are scaled in [0, 1].By default it is set to True.

**polish**:*bool, optional*Whether to use the L-BFGS-B algorithm to polish the best population member at the end.

By default it is set to True.

**popsize**:*int, optional*A multiplier for setting the total population size. The population has popsize * len(x) individuals.

By default it is set to 15.

**recombination**:*float, optional*The recombination constant.

By default it is set to 0.7.

**seed**:*int, optional*The seed to be used for repeatable minimizations. If

`None`

, the`numpy.random.RandomState`

singleton is used.By default it is set to 0.

**stop_crit_n_x**:*int, optional*The number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**strategy**:*str, optional*The differential evolution strategy to use.

By default it is set to best1bin.

**tol**:*float, optional*The relative tolerance for convergence.

By default it is set to 0.01.

**updating**:*str, optional*The strategy to update the solution vector. If

`"immediate"`

, the best solution vector is continuously updated within a single generation. With`"deferred"`

, the best solution vector is updated once per generation. Only`"deferred"`

is compatible with parallelization, and the`"workers"`

keyword can over-ride this option.By default it is set to immediate.

**workers**:*int, optional*The number of processes for parallel execution.

By default it is set to 1.

**xtol_abs**:*float, optional*A stop criteria, the absolute tolerance on the design variables. If norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-09.

**xtol_rel**:*float, optional*A stop criteria, the relative tolerance on the design variables. If norm(xk-xk+1)/norm(xk)<= xtol_rel: stop.

By default it is set to 1e-09.

## DUAL_ANNEALING¶

Module: `gemseo.algos.opt.lib_scipy_global`

Dual annealing

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

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to f(x).

- Optional parameters
**ftol_abs**:*float, optional*By default it is set to 1e-09.

**ftol_rel**:*float, optional*By default it is set to 1e-09.

**max_time**:*float, optional*The maximum runtime in seconds. The value 0 disables the cap on the runtime.

By default it is set to 0.0.

**normalize_design_space**:*bool, optional*If

`True`

, variables are scaled in [0, 1].By default it is set to True.

**seed**:*int, optional*The seed to be used for repeatable minimizations. If

`None`

, the`numpy.random.RandomState`

singleton is used.By default it is set to 0.

**stop_crit_n_x**:*int, optional*The number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**xtol_abs**:*float, optional*A stop criteria, the absolute tolerance on the design variables. If norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-09.

**xtol_rel**:*float, optional*By default it is set to 1e-09.

## HIGHS¶

Module: `gemseo.algos.opt.lib_scipy_linprog`

Linear programming using the HiGHS solvers. A choice is automatically made between the dual simplex and the interior-point method.

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

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to the objective function.

- Optional parameters
**disp**:*bool, optional*Whether to print convergence messages.

By default it is set to False.

**normalize_design_space**:*bool, optional*If

`True`

, scales variables in [0, 1].By default it is set to True.

## HIGHS_DUAL_SIMPLEX¶

Module: `gemseo.algos.opt.lib_scipy_linprog`

Linear programming using the HiGHS dual simplex solver.

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

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to the objective function.

- Optional parameters
**disp**:*bool, optional*Whether to print convergence messages.

By default it is set to False.

**normalize_design_space**:*bool, optional*If

`True`

, scales variables in [0, 1].By default it is set to True.

## HIGHS_INTERIOR_POINT¶

Module: `gemseo.algos.opt.lib_scipy_linprog`

Linear programming using the HiGHS interior point solver.

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

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to the objective function.

- Optional parameters
**disp**:*bool, optional*Whether to print convergence messages.

By default it is set to False.

**normalize_design_space**:*bool, optional*If

`True`

, scales variables in [0, 1].By default it is set to True.

## L-BFGS-B¶

Module: `gemseo.algos.opt.lib_scipy`

Limited-memory BFGS algorithm implemented in SciPy library

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

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to f(x).

- Optional parameters
**disp**:*int, optional*The display information flag.

By default it is set to 0.

**ftol_abs**:*float, optional*By default it is set to 1e-09.

**ftol_rel**:*float, optional*By default it is set to 1e-09.

**kkt_tol_abs**:*float | None, optional*The absolute tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**kkt_tol_rel**:*float | None, optional*The relative tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**max_ls_step_nb**:*int, optional*The maximum number of line search steps per iteration.

By default it is set to 20.

**max_time**:*float, optional*The maximum runtime in seconds, disabled if 0.

By default it is set to 0.

**maxcor**:*int, optional*The maximum BFGS updates.

By default it is set to 20.

**normalize_design_space**:*int, optional*If

`True`

, scales variables to [0, 1].By default it is set to True.

**pg_tol**:*float, optional*A stop criteria on the projected gradient norm.

By default it is set to 1e-05.

**xtol_abs**:*float, optional*A stop criteria, absolute tolerance on the design variables. If norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-09.

**xtol_rel**:*float, optional*By default it is set to 1e-09.

## LINEAR_INTERIOR_POINT¶

Module: `gemseo.algos.opt.lib_scipy_linprog`

Linear programming by the interior-point method implemented in the SciPy library

More details about the algorithm and its options on https://docs.scipy.org/doc/scipy/reference/optimize.linprog-interior-point.html.

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to the objective function.

- Optional parameters
**disp**:*bool, optional*Whether to print convergence messages.

By default it is set to False.

**normalize_design_space**:*bool, optional*If

`True`

, scales variables in [0, 1].By default it is set to True.

## MMA¶

Note

The plugin gemseo_mma is required.

Module: `gemseo_mma.opt.lib_mma`

- Required parameters
**max_iter**:*int*The maximum number of iterations.

- Optional parameters
**asymptotes_distance_amplification_coefficient**:*float, optional*The amplification factor for successful iterations.

By default it is set to 1.2.

**asymptotes_distance_reduction_coefficient**:*float, optional*The decremental factor for unsuccessful iterations.

By default it is set to 0.7.

**conv_tol**:*float | None, optional*If provided control all other convergence tolerances.

By default it is set to None.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.01.

**initial_asymptotes_distance**:*float, optional*The initial asymptotes distance from the current design variable value.

By default it is set to 0.5.

**max_asymptote_distance**:*float, optional*The maximum distance of the asymptotes from the current design variable value.

By default it is set to 10.0.

**max_optimization_step**:*float, optional*The maximum optimization step.

By default it is set to 0.1.

**min_asymptote_distance**:*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**:*bool, optional*If True, normalize the design variables between 0 and 1.

By default it is set to True.

**tol**:*float, optional*tolerance of convergence used in MMA to be compared with kkt residual.

By default it is set to 0.01.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## NLOPT_BFGS¶

Module: `gemseo.algos.opt.lib_nlopt`

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

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

- Required parameters
**max_iter**:*int*The maximum number of iterations.

- Optional parameters
**ctol_abs**:*float, optional*The absolute tolerance on the constraints.

By default it is set to 1e-06.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**init_step**:*float, optional*The initial step size \(r\) for derivative-free algorithms. Increasing the initial step size will make the initial DOE of size \(d+1\) take wider steps in the design variables. In details, given a \(d\)-length design vector initialized to \(x_0\), the first value of the design vector will be the initial one \(x^{(1)}=x_0\), the second one will be \(x^{(2)}=x^{(1)}+(r(\max(x_1)-\min(x_1)),0,\ldots,0)\), …, the \(d+1\)-th one will be \(x^{(d+1)}=x^{d}+(0,\ldots,0,r(\max(x_d)-\min(x_d)))\). Note that in a normalized design space, \(\min(x_i)=0\) and \(\max(x_i)=1\).

By default it is set to 0.25.

**kkt_tol_abs**:*float | None, optional*The absolute tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**kkt_tol_rel**:*float | None, optional*The relative tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**max_time**:*float, optional*The maximum runtime in seconds. The value 0 means no runtime limit.

By default it is set to 0.0.

**normalize_design_space**:*bool, optional*If

`True`

, normalize the design variables between 0 and 1.By default it is set to True.

**stop_crit_n_x**:*int | None, optional*The minimum number of design vectors to take into account in the stopping criteria.

By default it is set to None.

**stopval**:*float | None, optional*The objective value at which the optimization will stop. Stop minimizing when an objective value \(\leq\) stopval is found, or stop maximizing when a value \(\geq\) stopval is found. If

`None`

, this termination condition will not be active.By default it is set to None.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## NLOPT_BOBYQA¶

Module: `gemseo.algos.opt.lib_nlopt`

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

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

- Required parameters
**max_iter**:*int*The maximum number of iterations.

- Optional parameters
**ctol_abs**:*float, optional*The absolute tolerance on the constraints.

By default it is set to 1e-06.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**init_step**:*float, optional*The initial step size \(r\) for derivative-free algorithms. Increasing the initial step size will make the initial DOE of size \(d+1\) take wider steps in the design variables. In details, given a \(d\)-length design vector initialized to \(x_0\), the first value of the design vector will be the initial one \(x^{(1)}=x_0\), the second one will be \(x^{(2)}=x^{(1)}+(r(\max(x_1)-\min(x_1)),0,\ldots,0)\), …, the \(d+1\)-th one will be \(x^{(d+1)}=x^{d}+(0,\ldots,0,r(\max(x_d)-\min(x_d)))\). Note that in a normalized design space, \(\min(x_i)=0\) and \(\max(x_i)=1\).

By default it is set to 0.25.

**kkt_tol_abs**:*float | None, optional*The absolute tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**kkt_tol_rel**:*float | None, optional*The relative tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**max_time**:*float, optional*The maximum runtime in seconds. The value 0 means no runtime limit.

By default it is set to 0.0.

**normalize_design_space**:*bool, optional*If

`True`

, normalize the design variables between 0 and 1.By default it is set to True.

**stop_crit_n_x**:*int | None, optional*The minimum number of design vectors to take into account in the stopping criteria.

By default it is set to None.

**stopval**:*float | None, optional*The objective value at which the optimization will stop. Stop minimizing when an objective value \(\leq\) stopval is found, or stop maximizing when a value \(\geq\) stopval is found. If

`None`

, this termination condition will not be active.By default it is set to None.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## NLOPT_COBYLA¶

Module: `gemseo.algos.opt.lib_nlopt`

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

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

- Required parameters
**max_iter**:*int*The maximum number of iterations.

- Optional parameters
**ctol_abs**:*float, optional*The absolute tolerance on the constraints.

By default it is set to 1e-06.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**init_step**:*float, optional*The initial step size \(r\) for derivative-free algorithms. Increasing the initial step size will make the initial DOE of size \(d+1\) take wider steps in the design variables. In details, given a \(d\)-length design vector initialized to \(x_0\), the first value of the design vector will be the initial one \(x^{(1)}=x_0\), the second one will be \(x^{(2)}=x^{(1)}+(r(\max(x_1)-\min(x_1)),0,\ldots,0)\), …, the \(d+1\)-th one will be \(x^{(d+1)}=x^{d}+(0,\ldots,0,r(\max(x_d)-\min(x_d)))\). Note that in a normalized design space, \(\min(x_i)=0\) and \(\max(x_i)=1\).

By default it is set to 0.25.

**kkt_tol_abs**:*float | None, optional*The absolute tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**kkt_tol_rel**:*float | None, optional*The relative tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**max_time**:*float, optional*The maximum runtime in seconds. The value 0 means no runtime limit.

By default it is set to 0.0.

**normalize_design_space**:*bool, optional*If

`True`

, normalize the design variables between 0 and 1.By default it is set to True.

**stop_crit_n_x**:*int | None, optional*The minimum number of design vectors to take into account in the stopping criteria.

By default it is set to None.

**stopval**:*float | None, optional*The objective value at which the optimization will stop. Stop minimizing when an objective value \(\leq\) stopval is found, or stop maximizing when a value \(\geq\) stopval is found. If

`None`

, this termination condition will not be active.By default it is set to None.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## NLOPT_MMA¶

Module: `gemseo.algos.opt.lib_nlopt`

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

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

- Required parameters
**max_iter**:*int*The maximum number of iterations.

- Optional parameters
**ctol_abs**:*float, optional*The absolute tolerance on the constraints.

By default it is set to 1e-06.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**init_step**:*float, optional*By default it is set to 0.25.

**kkt_tol_abs**:*float | None, optional*The absolute tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**kkt_tol_rel**:*float | None, optional*The relative tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**max_time**:*float, optional*The maximum runtime in seconds. The value 0 means no runtime limit.

By default it is set to 0.0.

**normalize_design_space**:*bool, optional*If

`True`

, normalize the design variables between 0 and 1.By default it is set to True.

**stop_crit_n_x**:*int | None, optional*The minimum number of design vectors to take into account in the stopping criteria.

By default it is set to None.

**stopval**:*float | None, optional*`None`

, this termination condition will not be active.By default it is set to None.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## NLOPT_NEWUOA¶

Module: `gemseo.algos.opt.lib_nlopt`

NEWUOA + bound constraints implemented in the NLOPT library

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

- Required parameters
**max_iter**:*int*The maximum number of iterations.

- Optional parameters
**ctol_abs**:*float, optional*The absolute tolerance on the constraints.

By default it is set to 1e-06.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**init_step**:*float, optional*By default it is set to 0.25.

**kkt_tol_abs**:*float | None, optional*The absolute tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**kkt_tol_rel**:*float | None, optional*The relative tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**max_time**:*float, optional*The maximum runtime in seconds. The value 0 means no runtime limit.

By default it is set to 0.0.

**normalize_design_space**:*bool, optional*If

`True`

, normalize the design variables between 0 and 1.By default it is set to True.

**stop_crit_n_x**:*int | None, optional*The minimum number of design vectors to take into account in the stopping criteria.

By default it is set to None.

**stopval**:*float | None, optional*`None`

, this termination condition will not be active.By default it is set to None.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## NLOPT_SLSQP¶

Module: `gemseo.algos.opt.lib_nlopt`

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

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

- Required parameters
**max_iter**:*int*The maximum number of iterations.

- Optional parameters
**ctol_abs**:*float, optional*The absolute tolerance on the constraints.

By default it is set to 1e-06.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**init_step**:*float, optional*By default it is set to 0.25.

**kkt_tol_abs**:*float | None, optional*The absolute tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**kkt_tol_rel**:*float | None, optional*The relative tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**max_time**:*float, optional*The maximum runtime in seconds. The value 0 means no runtime limit.

By default it is set to 0.0.

**normalize_design_space**:*bool, optional*If

`True`

, normalize the design variables between 0 and 1.By default it is set to True.

**stop_crit_n_x**:*int | None, optional*The minimum number of design vectors to take into account in the stopping criteria.

By default it is set to None.

**stopval**:*float | None, optional*`None`

, this termination condition will not be active.By default it is set to None.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*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.lib_pdfo`

Bound Optimization By Quadratic Approximation

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

- Required parameters
**max_iter**:*int*The maximum number of iterations.

- Optional parameters
**chkfunval**:*bool, optional*A flag used when debugging. If both options[‘debug’] and options[‘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**:*bool, optional*The flag indicating whether to call the classical Powell code or not.

By default it is set to False.

**debug**:*bool, optional*The debugging flag.

By default it is set to False.

**ensure_bounds**:*bool, optional*Whether to project the design vector onto the design space before execution.

By default it is set to True.

**ftarget**:*float, optional*The target value of the objective function. If a feasible iterate achieves an objective function value lower or equal to options[‘ftarget’], the algorithm stops immediately.

By default it is set to -inf.

**ftol_abs**:*float, optional*A stop criteria, absolute tolerance on the objective function, if abs(f(xk)-f(xk+1))<= ftol_rel: stop.

By default it is set to 1e-12.

**ftol_rel**:*float, optional*A stop criteria, relative tolerance on the objective function, if abs(f(xk)-f(xk+1))/abs(f(xk))<= ftol_rel: stop.

By default it is set to 1e-12.

**max_time**:*float, optional*The maximum runtime in seconds, disabled if 0.

By default it is set to 0.

**normalize_design_space**:*bool, optional*If True, normalize the design space.

By default it is set to True.

**quiet**:*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.

**rhobeg**:*float, optional*The initial value of the trust region radius.

By default it is set to 0.5.

**rhoend**:*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.

**scale**:*bool, optional*The flag indicating whether to scale the problem according to the bound constraints.

By default it is set to False.

**xtol_abs**:*float, optional*A stop criteria, absolute tolerance on the design variables, if norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-12.

**xtol_rel**:*float, optional*A stop criteria, relative tolerance on the design variables, if norm(xk-xk+1)/norm(xk)<= xtol_rel: stop.

By default it is set to 1e-12.

## PDFO_COBYLA¶

Note

The plugin gemseo_pdfo is required.

Module: `gemseo_pdfo.lib_pdfo`

Constrained Optimization By Linear Approximations

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

- Required parameters
**max_iter**:*int*The maximum number of iterations.

- Optional parameters
**chkfunval**:*bool, optional*A flag used when debugging. If both options[‘debug’] and options[‘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**:*bool, optional*The flag indicating whether to call the classical Powell code or not.

By default it is set to False.

**debug**:*bool, optional*The debugging flag.

By default it is set to False.

**ensure_bounds**:*bool, optional*Whether to project the design vector onto the design space before execution.

By default it is set to True.

**ftarget**:*float, optional*The target value of the objective function. If a feasible iterate achieves an objective function value lower or equal to options[‘ftarget’], the algorithm stops immediately.

By default it is set to -inf.

**ftol_abs**:*float, optional*A stop criteria, absolute tolerance on the objective function, if abs(f(xk)-f(xk+1))<= ftol_rel: stop.

By default it is set to 1e-12.

**ftol_rel**:*float, optional*A stop criteria, relative tolerance on the objective function, if abs(f(xk)-f(xk+1))/abs(f(xk))<= ftol_rel: stop.

By default it is set to 1e-12.

**max_time**:*float, optional*The maximum runtime in seconds, disabled if 0.

By default it is set to 0.

**normalize_design_space**:*bool, optional*If True, normalize the design space.

By default it is set to True.

**quiet**:*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.

**rhobeg**:*float, optional*The initial value of the trust region radius.

By default it is set to 0.5.

**rhoend**:*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.

**scale**:*bool, optional*The flag indicating whether to scale the problem according to the bound constraints.

By default it is set to False.

**xtol_abs**:*float, optional*A stop criteria, absolute tolerance on the design variables, if norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-12.

**xtol_rel**:*float, optional*A stop criteria, relative tolerance on the design variables, if norm(xk-xk+1)/norm(xk)<= xtol_rel: stop.

By default it is set to 1e-12.

## PDFO_NEWUOA¶

Note

The plugin gemseo_pdfo is required.

Module: `gemseo_pdfo.lib_pdfo`

NEWUOA

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

- Required parameters
**max_iter**:*int*The maximum number of iterations.

- Optional parameters
**chkfunval**:*bool, optional*A flag used when debugging. If both options[‘debug’] and options[‘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**:*bool, optional*The flag indicating whether to call the classical Powell code or not.

By default it is set to False.

**debug**:*bool, optional*The debugging flag.

By default it is set to False.

**ensure_bounds**:*bool, optional*Whether to project the design vector onto the design space before execution.

By default it is set to True.

**ftarget**:*float, optional*The target value of the objective function. If a feasible iterate achieves an objective function value lower or equal to options[‘ftarget’], the algorithm stops immediately.

By default it is set to -inf.

**ftol_abs**:*float, optional*A stop criteria, absolute tolerance on the objective function, if abs(f(xk)-f(xk+1))<= ftol_rel: stop.

By default it is set to 1e-12.

**ftol_rel**:*float, optional*A stop criteria, relative tolerance on the objective function, if abs(f(xk)-f(xk+1))/abs(f(xk))<= ftol_rel: stop.

By default it is set to 1e-12.

**max_time**:*float, optional*The maximum runtime in seconds, disabled if 0.

By default it is set to 0.

**normalize_design_space**:*bool, optional*If True, normalize the design space.

By default it is set to True.

**quiet**:*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.

**rhobeg**:*float, optional*The initial value of the trust region radius.

By default it is set to 0.5.

**rhoend**:*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.

**scale**:*bool, optional*The flag indicating whether to scale the problem according to the bound constraints.

By default it is set to False.

**xtol_abs**:*float, optional*A stop criteria, absolute tolerance on the design variables, if norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-12.

**xtol_rel**:*float, optional*A stop criteria, relative tolerance on the design variables, if norm(xk-xk+1)/norm(xk)<= xtol_rel: stop.

By default it is set to 1e-12.

## PSEVEN¶

Note

The plugin gemseo_pseven is required.

Module: `gemseo_pseven.lib_pseven`

pSeven’s Generic Tool for Optimization (GTOpt).

More details about the algorithm and its options on https://datadvance.net/product/pseven/manual/.

- Required parameters
**max_iter**:*int*The maximum number of evaluations.

- Optional parameters
**constraints_smoothness**:*str, optional*The assumed smoothness of the constraints functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**detect_nan_clusters**:*bool, optional*Whether to detect and avoid design space areas that yield NaN values (for at least one function). This option has no effect in the absence of “expensive” functions.

By default it is set to True.

**deterministic**:*str | bool, optional*Whether to require optimization process to be reproducible using the passed seed value. Defaults to “Auto”.

By default it is set to Auto.

**diff_scheme**:*str, optional*The order of the differentiation scheme (when the analytic derivatives are unavailable): “FirstOrder”, “SecondOrder”, “Adaptive” or “Auto”.

By default it is set to Auto.

**diff_step**:*float, optional*The numerical differentiation step size.

By default it is set to 1.1920929e-06.

**diff_type**:*str, optional*The strategy for differentiation (when the analytic derivatives are unavailable): “Numerical”, “Framed” or “Auto”.

By default it is set to Auto.

**ensure_feasibility**:*bool, optional*Whether to restrict the evaluations of the objectives to feasible designs only.

By default it is set to False.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**evaluation_cost_type**:*str | Mapping[str, str] | None, optional*The evaluation cost type of each function of the problem: “Cheap” or “Expensive”. If a string, then the same cost type is set for all the functions. If None, the evaluation cost types are set by pSeven.

By default it is set to None.

**expensive_evaluations**:*Mapping[str, int] | None, optional*The maximal number of expensive evaluations for each function of the problem. By default, set automatically by pSeven.

By default it is set to None.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**global_phase_intensity**:*str | float, optional*The configuration of global searching algorithms. This option has different meanings for expensive and non-expensive optimization problems. Refer to the pSeven Core API documentation. Defaults to “Auto”.

By default it is set to Auto.

**globalization_method**:*str | None, optional*The globalization method: “RL” (random linkages), “PM” (plain multistart), or “MS” (surrogate model-based multistart) If None, set automatically by pSeven depending on the problem.

By default it is set to None.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**local_search**:*str, optional*Whether to force the surrogate models to explore the design space locally near the current optimum, or to disable the local search and let the surrogate models explore the whole design space.

By default it is set to Disabled.

**log_level**:*str, optional*The minimum log level: “Debug”, “Info”, “Warn”, “Error” or “Fatal”.

By default it is set to Error.

**log_path**:*str | None, optional*The path where to save the pSeven log. If None, the pSeven log will not be saved.

By default it is set to None.

**max_batch_size**:*int, optional*The maximum number of points in an evaluation batch. Batches of size more than one are evaluated in parallel. The (default) value 0 allows the optimizer to use any batch size. The value 1 implements sequential evaluation.

By default it is set to 0.

**max_expensive_func_iter**:*int, optional*The maximum number of evaluations for each expensive response, excluding the evaluations of initial guesses.

By default it is set to 0.

**max_threads**:*int, optional*The maximum number of parallel threads to use when solving.

By default it is set to 0.

**normalize_design_space**:*bool, optional*If True, normalize the design variables between 0 and 1.

By default it is set to True.

**objectives_smoothness**:*str, optional*The assumed smoothness of the objective functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**responses_scalability**:*int, optional*The maximum number of concurrent response evaluations supported by the problem.

By default it is set to 1.

**restore_analytic_func**:*str | bool, optional*Whether to restore the analytic forms of the linear and quadratic functions. Once the analytic forms are restored the original functions will not be evaluated anymore.

By default it is set to Auto.

**sample_c**:*list[float] | list[ndarray] | None, optional*The constraints values at the design points of the sample.

By default it is set to None.

**sample_f**:*list[float] | list[ndarray] | None, optional*The objectives values at the design points of the sample.

By default it is set to None.

**sample_x**:*list[float] | list[ndarray] | None, optional*A sample of design points (in addition to the problem initial design).

By default it is set to None.

**seed**:*int, optional*The random seed for deterministic mode.

By default it is set to 100.

**stop_crit_n_x**:*int, optional*The number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**surrogate_based**:*bool | None, optional*Whether to use surrogate models. If None, set automatically depending on the problem.

By default it is set to None.

**time_limit**:*int, optional*The maximum allowed time to solve a problem in seconds. Defaults to 0, unlimited.

By default it is set to 0.

**use_gradient**:*bool, optional*Whether to use the functions derivatives.

By default it is set to True.

**use_threading**:*bool, optional*Whether to use threads instead of processes to parallelize the evaluation of the functions.

By default it is set to False.

**verbose_log**:*bool, optional*Whether to enable verbose logging.

By default it is set to False.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## PSEVEN_FD¶

Note

The plugin gemseo_pseven is required.

Module: `gemseo_pseven.lib_pseven`

pSeven’s feasible direction method.

More details about the algorithm and its options on https://datadvance.net/product/pseven/manual/.

- Required parameters
**max_iter**:*int*The maximum number of evaluations.

- Optional parameters
**constraints_smoothness**:*str, optional*The assumed smoothness of the constraints functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**detect_nan_clusters**:*bool, optional*Whether to detect and avoid design space areas that yield NaN values (for at least one function). This option has no effect in the absence of “expensive” functions.

By default it is set to True.

**deterministic**:*str | bool, optional*Whether to require optimization process to be reproducible using the passed seed value. Defaults to “Auto”.

By default it is set to Auto.

**diff_scheme**:*str, optional*The order of the differentiation scheme (when the analytic derivatives are unavailable): “FirstOrder”, “SecondOrder”, “Adaptive” or “Auto”.

By default it is set to Auto.

**diff_step**:*float, optional*The numerical differentiation step size.

By default it is set to 1.1920929e-06.

**diff_type**:*str, optional*The strategy for differentiation (when the analytic derivatives are unavailable): “Numerical”, “Framed” or “Auto”.

By default it is set to Auto.

**ensure_feasibility**:*bool, optional*Whether to restrict the evaluations of the objectives to feasible designs only.

By default it is set to False.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**evaluation_cost_type**:*str | Mapping[str, str] | None, optional*The evaluation cost type of each function of the problem: “Cheap” or “Expensive”. If a string, then the same cost type is set for all the functions. If None, the evaluation cost types are set by pSeven.

By default it is set to None.

**expensive_evaluations**:*Mapping[str, int] | None, optional*The maximal number of expensive evaluations for each function of the problem. By default, set automatically by pSeven.

By default it is set to None.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**global_phase_intensity**:*str | float, optional*The configuration of global searching algorithms. This option has different meanings for expensive and non-expensive optimization problems. Refer to the pSeven Core API documentation. Defaults to “Auto”.

By default it is set to Auto.

**globalization_method**:*str | None, optional*The globalization method: “RL” (random linkages), “PM” (plain multistart), or “MS” (surrogate model-based multistart) If None, set automatically by pSeven depending on the problem.

By default it is set to None.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**local_search**:*str, optional*Whether to force the surrogate models to explore the design space locally near the current optimum, or to disable the local search and let the surrogate models explore the whole design space.

By default it is set to Disabled.

**log_level**:*str, optional*The minimum log level: “Debug”, “Info”, “Warn”, “Error” or “Fatal”.

By default it is set to Error.

**log_path**:*str | None, optional*The path where to save the pSeven log. If None, the pSeven log will not be saved.

By default it is set to None.

**max_batch_size**:*int, optional*The maximum number of points in an evaluation batch. Batches of size more than one are evaluated in parallel. The (default) value 0 allows the optimizer to use any batch size. The value 1 implements sequential evaluation.

By default it is set to 0.

**max_expensive_func_iter**:*int, optional*The maximum number of evaluations for each expensive response, excluding the evaluations of initial guesses.

By default it is set to 0.

**max_threads**:*int, optional*The maximum number of parallel threads to use when solving.

By default it is set to 0.

**normalize_design_space**:*bool, optional*If True, normalize the design variables between 0 and 1.

By default it is set to True.

**objectives_smoothness**:*str, optional*The assumed smoothness of the objective functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**responses_scalability**:*int, optional*The maximum number of concurrent response evaluations supported by the problem.

By default it is set to 1.

**restore_analytic_func**:*str | bool, optional*Whether to restore the analytic forms of the linear and quadratic functions. Once the analytic forms are restored the original functions will not be evaluated anymore.

By default it is set to Auto.

**sample_c**:*list[float] | list[ndarray] | None, optional*The constraints values at the design points of the sample.

By default it is set to None.

**sample_f**:*list[float] | list[ndarray] | None, optional*The objectives values at the design points of the sample.

By default it is set to None.

**sample_x**:*list[float] | list[ndarray] | None, optional*A sample of design points (in addition to the problem initial design).

By default it is set to None.

**seed**:*int, optional*The random seed for deterministic mode.

By default it is set to 100.

**stop_crit_n_x**:*int, optional*The number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**surrogate_based**:*bool | None, optional*Whether to use surrogate models. If None, set automatically depending on the problem.

By default it is set to None.

**time_limit**:*int, optional*The maximum allowed time to solve a problem in seconds. Defaults to 0, unlimited.

By default it is set to 0.

**use_gradient**:*bool, optional*Whether to use the functions derivatives.

By default it is set to True.

**use_threading**:*bool, optional*Whether to use threads instead of processes to parallelize the evaluation of the functions.

By default it is set to False.

**verbose_log**:*bool, optional*Whether to enable verbose logging.

By default it is set to False.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## PSEVEN_MOM¶

Note

The plugin gemseo_pseven is required.

Module: `gemseo_pseven.lib_pseven`

pSeven’s method of multipliers.

More details about the algorithm and its options on https://datadvance.net/product/pseven/manual/.

- Required parameters
**max_iter**:*int*The maximum number of evaluations.

- Optional parameters
**constraints_smoothness**:*str, optional*The assumed smoothness of the constraints functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**detect_nan_clusters**:*bool, optional*Whether to detect and avoid design space areas that yield NaN values (for at least one function). This option has no effect in the absence of “expensive” functions.

By default it is set to True.

**deterministic**:*str | bool, optional*Whether to require optimization process to be reproducible using the passed seed value. Defaults to “Auto”.

By default it is set to Auto.

**diff_scheme**:*str, optional*The order of the differentiation scheme (when the analytic derivatives are unavailable): “FirstOrder”, “SecondOrder”, “Adaptive” or “Auto”.

By default it is set to Auto.

**diff_step**:*float, optional*The numerical differentiation step size.

By default it is set to 1.1920929e-06.

**diff_type**:*str, optional*The strategy for differentiation (when the analytic derivatives are unavailable): “Numerical”, “Framed” or “Auto”.

By default it is set to Auto.

**ensure_feasibility**:*bool, optional*Whether to restrict the evaluations of the objectives to feasible designs only.

By default it is set to False.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**evaluation_cost_type**:*str | Mapping[str, str] | None, optional*The evaluation cost type of each function of the problem: “Cheap” or “Expensive”. If a string, then the same cost type is set for all the functions. If None, the evaluation cost types are set by pSeven.

By default it is set to None.

**expensive_evaluations**:*Mapping[str, int] | None, optional*The maximal number of expensive evaluations for each function of the problem. By default, set automatically by pSeven.

By default it is set to None.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**global_phase_intensity**:*str | float, optional*The configuration of global searching algorithms. This option has different meanings for expensive and non-expensive optimization problems. Refer to the pSeven Core API documentation. Defaults to “Auto”.

By default it is set to Auto.

**globalization_method**:*str | None, optional*The globalization method: “RL” (random linkages), “PM” (plain multistart), or “MS” (surrogate model-based multistart) If None, set automatically by pSeven depending on the problem.

By default it is set to None.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**local_search**:*str, optional*Whether to force the surrogate models to explore the design space locally near the current optimum, or to disable the local search and let the surrogate models explore the whole design space.

By default it is set to Disabled.

**log_level**:*str, optional*The minimum log level: “Debug”, “Info”, “Warn”, “Error” or “Fatal”.

By default it is set to Error.

**log_path**:*str | None, optional*The path where to save the pSeven log. If None, the pSeven log will not be saved.

By default it is set to None.

**max_batch_size**:*int, optional*The maximum number of points in an evaluation batch. Batches of size more than one are evaluated in parallel. The (default) value 0 allows the optimizer to use any batch size. The value 1 implements sequential evaluation.

By default it is set to 0.

**max_expensive_func_iter**:*int, optional*The maximum number of evaluations for each expensive response, excluding the evaluations of initial guesses.

By default it is set to 0.

**max_threads**:*int, optional*The maximum number of parallel threads to use when solving.

By default it is set to 0.

**normalize_design_space**:*bool, optional*If True, normalize the design variables between 0 and 1.

By default it is set to True.

**objectives_smoothness**:*str, optional*The assumed smoothness of the objective functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**responses_scalability**:*int, optional*The maximum number of concurrent response evaluations supported by the problem.

By default it is set to 1.

**restore_analytic_func**:*str | bool, optional*Whether to restore the analytic forms of the linear and quadratic functions. Once the analytic forms are restored the original functions will not be evaluated anymore.

By default it is set to Auto.

**sample_c**:*list[float] | list[ndarray] | None, optional*The constraints values at the design points of the sample.

By default it is set to None.

**sample_f**:*list[float] | list[ndarray] | None, optional*The objectives values at the design points of the sample.

By default it is set to None.

**sample_x**:*list[float] | list[ndarray] | None, optional*A sample of design points (in addition to the problem initial design).

By default it is set to None.

**seed**:*int, optional*The random seed for deterministic mode.

By default it is set to 100.

**stop_crit_n_x**:*int, optional*The number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**surrogate_based**:*bool | None, optional*Whether to use surrogate models. If None, set automatically depending on the problem.

By default it is set to None.

**time_limit**:*int, optional*The maximum allowed time to solve a problem in seconds. Defaults to 0, unlimited.

By default it is set to 0.

**use_gradient**:*bool, optional*Whether to use the functions derivatives.

By default it is set to True.

**use_threading**:*bool, optional*Whether to use threads instead of processes to parallelize the evaluation of the functions.

By default it is set to False.

**verbose_log**:*bool, optional*Whether to enable verbose logging.

By default it is set to False.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## PSEVEN_NCG¶

Note

The plugin gemseo_pseven is required.

Module: `gemseo_pseven.lib_pseven`

pSeven’s nonlinear conjugate gradient method.

More details about the algorithm and its options on https://datadvance.net/product/pseven/manual/.

- Required parameters
**max_iter**:*int*The maximum number of evaluations.

- Optional parameters
**constraints_smoothness**:*str, optional*The assumed smoothness of the constraints functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**detect_nan_clusters**:*bool, optional*By default it is set to True.

**deterministic**:*str | bool, optional*By default it is set to Auto.

**diff_scheme**:*str, optional*By default it is set to Auto.

**diff_step**:*float, optional*The numerical differentiation step size.

By default it is set to 1.1920929e-06.

**diff_type**:*str, optional*By default it is set to Auto.

**ensure_feasibility**:*bool, optional*Whether to restrict the evaluations of the objectives to feasible designs only.

By default it is set to False.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**evaluation_cost_type**:*str | Mapping[str, str] | None, optional*By default it is set to None.

**expensive_evaluations**:*Mapping[str, int] | None, optional*By default it is set to None.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**global_phase_intensity**:*str | float, optional*By default it is set to Auto.

**globalization_method**:*str | None, optional*By default it is set to None.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**local_search**:*str, optional*By default it is set to Disabled.

**log_level**:*str, optional*The minimum log level: “Debug”, “Info”, “Warn”, “Error” or “Fatal”.

By default it is set to Error.

**log_path**:*str | None, optional*The path where to save the pSeven log. If None, the pSeven log will not be saved.

By default it is set to None.

**max_batch_size**:*int, optional*By default it is set to 0.

**max_expensive_func_iter**:*int, optional*By default it is set to 0.

**max_threads**:*int, optional*The maximum number of parallel threads to use when solving.

By default it is set to 0.

**normalize_design_space**:*bool, optional*If True, normalize the design variables between 0 and 1.

By default it is set to True.

**objectives_smoothness**:*str, optional*The assumed smoothness of the objective functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**responses_scalability**:*int, optional*The maximum number of concurrent response evaluations supported by the problem.

By default it is set to 1.

**restore_analytic_func**:*str | bool, optional*By default it is set to Auto.

**sample_c**:*list[float] | list[ndarray] | None, optional*The constraints values at the design points of the sample.

By default it is set to None.

**sample_f**:*list[float] | list[ndarray] | None, optional*The objectives values at the design points of the sample.

By default it is set to None.

**sample_x**:*list[float] | list[ndarray] | None, optional*A sample of design points (in addition to the problem initial design).

By default it is set to None.

**seed**:*int, optional*The random seed for deterministic mode.

By default it is set to 100.

**stop_crit_n_x**:*int, optional*The number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**surrogate_based**:*bool | None, optional*Whether to use surrogate models. If None, set automatically depending on the problem.

By default it is set to None.

**time_limit**:*int, optional*The maximum allowed time to solve a problem in seconds. Defaults to 0, unlimited.

By default it is set to 0.

**use_gradient**:*bool, optional*Whether to use the functions derivatives.

By default it is set to True.

**use_threading**:*bool, optional*Whether to use threads instead of processes to parallelize the evaluation of the functions.

By default it is set to False.

**verbose_log**:*bool, optional*Whether to enable verbose logging.

By default it is set to False.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## PSEVEN_NLS¶

Note

The plugin gemseo_pseven is required.

Module: `gemseo_pseven.lib_pseven`

pSeven’s nonlinear simplex method.

More details about the algorithm and its options on https://datadvance.net/product/pseven/manual/.

- Required parameters
**max_iter**:*int*The maximum number of evaluations.

- Optional parameters
**constraints_smoothness**:*str, optional*The assumed smoothness of the constraints functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**detect_nan_clusters**:*bool, optional*By default it is set to True.

**deterministic**:*str | bool, optional*By default it is set to Auto.

**diff_scheme**:*str, optional*By default it is set to Auto.

**diff_step**:*float, optional*The numerical differentiation step size.

By default it is set to 1.1920929e-06.

**diff_type**:*str, optional*By default it is set to Auto.

**ensure_feasibility**:*bool, optional*Whether to restrict the evaluations of the objectives to feasible designs only.

By default it is set to False.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**evaluation_cost_type**:*str | Mapping[str, str] | None, optional*By default it is set to None.

**expensive_evaluations**:*Mapping[str, int] | None, optional*By default it is set to None.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**global_phase_intensity**:*str | float, optional*By default it is set to Auto.

**globalization_method**:*str | None, optional*By default it is set to None.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**local_search**:*str, optional*By default it is set to Disabled.

**log_level**:*str, optional*The minimum log level: “Debug”, “Info”, “Warn”, “Error” or “Fatal”.

By default it is set to Error.

**log_path**:*str | None, optional*The path where to save the pSeven log. If None, the pSeven log will not be saved.

By default it is set to None.

**max_batch_size**:*int, optional*By default it is set to 0.

**max_expensive_func_iter**:*int, optional*By default it is set to 0.

**max_threads**:*int, optional*The maximum number of parallel threads to use when solving.

By default it is set to 0.

**normalize_design_space**:*bool, optional*If True, normalize the design variables between 0 and 1.

By default it is set to True.

**objectives_smoothness**:*str, optional*The assumed smoothness of the objective functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**responses_scalability**:*int, optional*The maximum number of concurrent response evaluations supported by the problem.

By default it is set to 1.

**restore_analytic_func**:*str | bool, optional*By default it is set to Auto.

**sample_c**:*list[float] | list[ndarray] | None, optional*The constraints values at the design points of the sample.

By default it is set to None.

**sample_f**:*list[float] | list[ndarray] | None, optional*The objectives values at the design points of the sample.

By default it is set to None.

**sample_x**:*list[float] | list[ndarray] | None, optional*A sample of design points (in addition to the problem initial design).

By default it is set to None.

**seed**:*int, optional*The random seed for deterministic mode.

By default it is set to 100.

**stop_crit_n_x**:*int, optional*The number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**surrogate_based**:*bool | None, optional*Whether to use surrogate models. If None, set automatically depending on the problem.

By default it is set to None.

**time_limit**:*int, optional*The maximum allowed time to solve a problem in seconds. Defaults to 0, unlimited.

By default it is set to 0.

**use_gradient**:*bool, optional*Whether to use the functions derivatives.

By default it is set to True.

**use_threading**:*bool, optional*Whether to use threads instead of processes to parallelize the evaluation of the functions.

By default it is set to False.

**verbose_log**:*bool, optional*Whether to enable verbose logging.

By default it is set to False.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## PSEVEN_POWELL¶

Note

The plugin gemseo_pseven is required.

Module: `gemseo_pseven.lib_pseven`

pSeven’s Powell conjugate direction method.

More details about the algorithm and its options on https://datadvance.net/product/pseven/manual/.

- Required parameters
**max_iter**:*int*The maximum number of evaluations.

- Optional parameters
**constraints_smoothness**:*str, optional*The assumed smoothness of the constraints functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**detect_nan_clusters**:*bool, optional*By default it is set to True.

**deterministic**:*str | bool, optional*By default it is set to Auto.

**diff_scheme**:*str, optional*By default it is set to Auto.

**diff_step**:*float, optional*The numerical differentiation step size.

By default it is set to 1.1920929e-06.

**diff_type**:*str, optional*By default it is set to Auto.

**ensure_feasibility**:*bool, optional*Whether to restrict the evaluations of the objectives to feasible designs only.

By default it is set to False.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**evaluation_cost_type**:*str | Mapping[str, str] | None, optional*By default it is set to None.

**expensive_evaluations**:*Mapping[str, int] | None, optional*By default it is set to None.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**global_phase_intensity**:*str | float, optional*By default it is set to Auto.

**globalization_method**:*str | None, optional*By default it is set to None.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**local_search**:*str, optional*By default it is set to Disabled.

**log_level**:*str, optional*The minimum log level: “Debug”, “Info”, “Warn”, “Error” or “Fatal”.

By default it is set to Error.

**log_path**:*str | None, optional*The path where to save the pSeven log. If None, the pSeven log will not be saved.

By default it is set to None.

**max_batch_size**:*int, optional*By default it is set to 0.

**max_expensive_func_iter**:*int, optional*By default it is set to 0.

**max_threads**:*int, optional*The maximum number of parallel threads to use when solving.

By default it is set to 0.

**normalize_design_space**:*bool, optional*If True, normalize the design variables between 0 and 1.

By default it is set to True.

**objectives_smoothness**:*str, optional*The assumed smoothness of the objective functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**responses_scalability**:*int, optional*The maximum number of concurrent response evaluations supported by the problem.

By default it is set to 1.

**restore_analytic_func**:*str | bool, optional*By default it is set to Auto.

**sample_c**:*list[float] | list[ndarray] | None, optional*The constraints values at the design points of the sample.

By default it is set to None.

**sample_f**:*list[float] | list[ndarray] | None, optional*The objectives values at the design points of the sample.

By default it is set to None.

**sample_x**:*list[float] | list[ndarray] | None, optional*A sample of design points (in addition to the problem initial design).

By default it is set to None.

**seed**:*int, optional*The random seed for deterministic mode.

By default it is set to 100.

**stop_crit_n_x**:*int, optional*The number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**surrogate_based**:*bool | None, optional*Whether to use surrogate models. If None, set automatically depending on the problem.

By default it is set to None.

**time_limit**:*int, optional*The maximum allowed time to solve a problem in seconds. Defaults to 0, unlimited.

By default it is set to 0.

**use_gradient**:*bool, optional*Whether to use the functions derivatives.

By default it is set to True.

**use_threading**:*bool, optional*Whether to use threads instead of processes to parallelize the evaluation of the functions.

By default it is set to False.

**verbose_log**:*bool, optional*Whether to enable verbose logging.

By default it is set to False.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## PSEVEN_QP¶

Note

The plugin gemseo_pseven is required.

Module: `gemseo_pseven.lib_pseven`

pSeven’s quadratic programming method.

More details about the algorithm and its options on https://datadvance.net/product/pseven/manual/.

- Required parameters
**max_iter**:*int*The maximum number of evaluations.

- Optional parameters
**constraints_smoothness**:*str, optional*The assumed smoothness of the constraints functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**detect_nan_clusters**:*bool, optional*By default it is set to True.

**deterministic**:*str | bool, optional*By default it is set to Auto.

**diff_scheme**:*str, optional*By default it is set to Auto.

**diff_step**:*float, optional*The numerical differentiation step size.

By default it is set to 1.1920929e-06.

**diff_type**:*str, optional*By default it is set to Auto.

**ensure_feasibility**:*bool, optional*Whether to restrict the evaluations of the objectives to feasible designs only.

By default it is set to False.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**evaluation_cost_type**:*str | Mapping[str, str] | None, optional*By default it is set to None.

**expensive_evaluations**:*Mapping[str, int] | None, optional*By default it is set to None.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**global_phase_intensity**:*str | float, optional*By default it is set to Auto.

**globalization_method**:*str | None, optional*By default it is set to None.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**local_search**:*str, optional*By default it is set to Disabled.

**log_level**:*str, optional*The minimum log level: “Debug”, “Info”, “Warn”, “Error” or “Fatal”.

By default it is set to Error.

**log_path**:*str | None, optional*The path where to save the pSeven log. If None, the pSeven log will not be saved.

By default it is set to None.

**max_batch_size**:*int, optional*By default it is set to 0.

**max_expensive_func_iter**:*int, optional*By default it is set to 0.

**max_threads**:*int, optional*The maximum number of parallel threads to use when solving.

By default it is set to 0.

**normalize_design_space**:*bool, optional*If True, normalize the design variables between 0 and 1.

By default it is set to True.

**objectives_smoothness**:*str, optional*The assumed smoothness of the objective functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**responses_scalability**:*int, optional*The maximum number of concurrent response evaluations supported by the problem.

By default it is set to 1.

**restore_analytic_func**:*str | bool, optional*By default it is set to Auto.

**sample_c**:*list[float] | list[ndarray] | None, optional*The constraints values at the design points of the sample.

By default it is set to None.

**sample_f**:*list[float] | list[ndarray] | None, optional*The objectives values at the design points of the sample.

By default it is set to None.

**sample_x**:*list[float] | list[ndarray] | None, optional*A sample of design points (in addition to the problem initial design).

By default it is set to None.

**seed**:*int, optional*The random seed for deterministic mode.

By default it is set to 100.

**stop_crit_n_x**:*int, optional*The number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**surrogate_based**:*bool | None, optional*Whether to use surrogate models. If None, set automatically depending on the problem.

By default it is set to None.

**time_limit**:*int, optional*The maximum allowed time to solve a problem in seconds. Defaults to 0, unlimited.

By default it is set to 0.

**use_gradient**:*bool, optional*Whether to use the functions derivatives.

By default it is set to True.

**use_threading**:*bool, optional*Whether to use threads instead of processes to parallelize the evaluation of the functions.

By default it is set to False.

**verbose_log**:*bool, optional*Whether to enable verbose logging.

By default it is set to False.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## PSEVEN_SQ2P¶

Note

The plugin gemseo_pseven is required.

Module: `gemseo_pseven.lib_pseven`

pSeven’s sequential quadratic constrained quadratic programming method.

More details about the algorithm and its options on https://datadvance.net/product/pseven/manual/.

- Required parameters
**max_iter**:*int*The maximum number of evaluations.

- Optional parameters
**constraints_smoothness**:*str, optional*The assumed smoothness of the constraints functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**detect_nan_clusters**:*bool, optional*By default it is set to True.

**deterministic**:*str | bool, optional*By default it is set to Auto.

**diff_scheme**:*str, optional*By default it is set to Auto.

**diff_step**:*float, optional*The numerical differentiation step size.

By default it is set to 1.1920929e-06.

**diff_type**:*str, optional*By default it is set to Auto.

**ensure_feasibility**:*bool, optional*Whether to restrict the evaluations of the objectives to feasible designs only.

By default it is set to False.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**evaluation_cost_type**:*str | Mapping[str, str] | None, optional*By default it is set to None.

**expensive_evaluations**:*Mapping[str, int] | None, optional*By default it is set to None.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**global_phase_intensity**:*str | float, optional*By default it is set to Auto.

**globalization_method**:*str | None, optional*By default it is set to None.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**local_search**:*str, optional*By default it is set to Disabled.

**log_level**:*str, optional*The minimum log level: “Debug”, “Info”, “Warn”, “Error” or “Fatal”.

By default it is set to Error.

**log_path**:*str | None, optional*The path where to save the pSeven log. If None, the pSeven log will not be saved.

By default it is set to None.

**max_batch_size**:*int, optional*By default it is set to 0.

**max_expensive_func_iter**:*int, optional*By default it is set to 0.

**max_threads**:*int, optional*The maximum number of parallel threads to use when solving.

By default it is set to 0.

**normalize_design_space**:*bool, optional*If True, normalize the design variables between 0 and 1.

By default it is set to True.

**objectives_smoothness**:*str, optional*The assumed smoothness of the objective functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**responses_scalability**:*int, optional*The maximum number of concurrent response evaluations supported by the problem.

By default it is set to 1.

**restore_analytic_func**:*str | bool, optional*By default it is set to Auto.

**sample_c**:*list[float] | list[ndarray] | None, optional*The constraints values at the design points of the sample.

By default it is set to None.

**sample_f**:*list[float] | list[ndarray] | None, optional*The objectives values at the design points of the sample.

By default it is set to None.

**sample_x**:*list[float] | list[ndarray] | None, optional*A sample of design points (in addition to the problem initial design).

By default it is set to None.

**seed**:*int, optional*The random seed for deterministic mode.

By default it is set to 100.

**stop_crit_n_x**:*int, optional*The number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**surrogate_based**:*bool | None, optional*Whether to use surrogate models. If None, set automatically depending on the problem.

By default it is set to None.

**time_limit**:*int, optional*The maximum allowed time to solve a problem in seconds. Defaults to 0, unlimited.

By default it is set to 0.

**use_gradient**:*bool, optional*Whether to use the functions derivatives.

By default it is set to True.

**use_threading**:*bool, optional*Whether to use threads instead of processes to parallelize the evaluation of the functions.

By default it is set to False.

**verbose_log**:*bool, optional*Whether to enable verbose logging.

By default it is set to False.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## PSEVEN_SQP¶

Note

The plugin gemseo_pseven is required.

Module: `gemseo_pseven.lib_pseven`

pSeven’s sequential quadratic programming method.

More details about the algorithm and its options on https://datadvance.net/product/pseven/manual/.

- Required parameters
**max_iter**:*int*The maximum number of evaluations.

- Optional parameters
**constraints_smoothness**:*str, optional*The assumed smoothness of the constraints functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**detect_nan_clusters**:*bool, optional*By default it is set to True.

**deterministic**:*str | bool, optional*By default it is set to Auto.

**diff_scheme**:*str, optional*By default it is set to Auto.

**diff_step**:*float, optional*The numerical differentiation step size.

By default it is set to 1.1920929e-06.

**diff_type**:*str, optional*By default it is set to Auto.

**ensure_feasibility**:*bool, optional*Whether to restrict the evaluations of the objectives to feasible designs only.

By default it is set to False.

**eq_tolerance**:*float, optional*The tolerance on the equality constraints.

By default it is set to 0.01.

**evaluation_cost_type**:*str | Mapping[str, str] | None, optional*By default it is set to None.

**expensive_evaluations**:*Mapping[str, int] | None, optional*By default it is set to None.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**global_phase_intensity**:*str | float, optional*By default it is set to Auto.

**globalization_method**:*str | None, optional*By default it is set to None.

**ineq_tolerance**:*float, optional*The tolerance on the inequality constraints.

By default it is set to 0.0001.

**local_search**:*str, optional*By default it is set to Disabled.

**log_level**:*str, optional*The minimum log level: “Debug”, “Info”, “Warn”, “Error” or “Fatal”.

By default it is set to Error.

**log_path**:*str | None, optional*The path where to save the pSeven log. If None, the pSeven log will not be saved.

By default it is set to None.

**max_batch_size**:*int, optional*By default it is set to 0.

**max_expensive_func_iter**:*int, optional*By default it is set to 0.

**max_threads**:*int, optional*The maximum number of parallel threads to use when solving.

By default it is set to 0.

**normalize_design_space**:*bool, optional*If True, normalize the design variables between 0 and 1.

By default it is set to True.

**objectives_smoothness**:*str, optional*The assumed smoothness of the objective functions: “Smooth”, “Noisy” or “Auto”.

By default it is set to Auto.

**responses_scalability**:*int, optional*The maximum number of concurrent response evaluations supported by the problem.

By default it is set to 1.

**restore_analytic_func**:*str | bool, optional*By default it is set to Auto.

**sample_c**:*list[float] | list[ndarray] | None, optional*The constraints values at the design points of the sample.

By default it is set to None.

**sample_f**:*list[float] | list[ndarray] | None, optional*The objectives values at the design points of the sample.

By default it is set to None.

**sample_x**:*list[float] | list[ndarray] | None, optional*A sample of design points (in addition to the problem initial design).

By default it is set to None.

**seed**:*int, optional*The random seed for deterministic mode.

By default it is set to 100.

**stop_crit_n_x**:*int, optional*The number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**surrogate_based**:*bool | None, optional*Whether to use surrogate models. If None, set automatically depending on the problem.

By default it is set to None.

**time_limit**:*int, optional*The maximum allowed time to solve a problem in seconds. Defaults to 0, unlimited.

By default it is set to 0.

**use_gradient**:*bool, optional*Whether to use the functions derivatives.

By default it is set to True.

**use_threading**:*bool, optional*Whether to use threads instead of processes to parallelize the evaluation of the functions.

By default it is set to False.

**verbose_log**:*bool, optional*Whether to enable verbose logging.

By default it is set to False.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## PYMOO_GA¶

Note

The plugin gemseo_pymoo is required.

Module: `gemseo_pymoo.algos.opt.lib_pymoo`

Genetic Algorithm

More details about the algorithm and its options on https://www.pymoo.org/algorithms/soo/ga.html#GA:-Genetic-Algorithm.

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to f(x).

- Optional parameters
**crossover**:*Crossover | None, 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**:*bool, optional*If True, eliminate duplicates after merging the parent and the offspring population.

By default it is set to True.

**ftol_abs**:*float, optional*A stop criterion, the absolute tolerance on the objective function. If abs(f(xk)-f(xk+1))<= ftol_rel: stop.

By default it is set to 1e-09.

**ftol_rel**:*float, optional*A stop criterion, the relative tolerance on the objective function. If abs(f(xk)-f(xk+1))/abs(f(xk))<= ftol_rel: stop.

By default it is set to 1e-09.

**hv_tol_abs**:*float, optional*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**:*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.

**max_gen**:*int, optional*The maximum number of generations.

By default it is set to 10000000.

**mutation**:*Mutation | None, optional*The mutation operator. If None, the algorithm’s default is used.

By default it is set to None.

**n_offsprings**:*int | None, 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.

**normalize_design_space**:*bool, optional*If True, scale the variables to the range [0, 1].

By default it is set to True.

**pop_size**:*int, optional*The population size.

By default it is set to 100.

**sampling**:*Sampling | Population | 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.

**seed**:*int, optional*The random seed to be used.

By default it is set to 1.

**selection**:*Selection | None, optional*The mating selection operator. If None, the algorithm’s default is used.

By default it is set to None.

**stop_crit_n_hv**:*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**:*int, optional*The number of design vectors to account for during the criteria check.

By default it is set to 3.

**xtol_abs**:*float, optional*A stop criterion, absolute tolerance on the design variables. If norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-09.

**xtol_rel**:*float, optional*A stop criterion, the relative tolerance on the design variables. If norm(xk-xk+1)/norm(xk)<= xtol_rel: stop.

By default it is set to 1e-09.

## PYMOO_NSGA2¶

Note

The plugin gemseo_pymoo is required.

Module: `gemseo_pymoo.algos.opt.lib_pymoo`

Non-dominated Sorting Genetic Algorithm II

More details about the algorithm and its options on https://www.pymoo.org/algorithms/moo/nsga2.html#nb-nsga2.

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to f(x).

- Optional parameters
**crossover**:*Crossover | None, 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**:*bool, optional*If True, eliminate duplicates after merging the parent and the offspring population.

By default it is set to True.

**ftol_abs**:*float, optional*A stop criterion, the absolute tolerance on the objective function. If abs(f(xk)-f(xk+1))<= ftol_rel: stop.

By default it is set to 1e-09.

**ftol_rel**:*float, optional*A stop criterion, the relative tolerance on the objective function. If abs(f(xk)-f(xk+1))/abs(f(xk))<= ftol_rel: stop.

By default it is set to 1e-09.

**hv_tol_abs**:*float, optional*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**:*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.

**max_gen**:*int, optional*The maximum number of generations.

By default it is set to 10000000.

**mutation**:*Mutation | None, optional*The mutation operator. If None, the algorithm’s default is used.

By default it is set to None.

**n_offsprings**:*int | None, 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.

**normalize_design_space**:*bool, optional*If True, scale the variables to the range [0, 1].

By default it is set to True.

**pop_size**:*int, optional*The population size.

By default it is set to 100.

**sampling**:*Sampling | Population | 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.

**seed**:*int, optional*The random seed to be used.

By default it is set to 1.

**selection**:*Selection | None, optional*The mating selection operator. If None, the algorithm’s default is used.

By default it is set to None.

**stop_crit_n_hv**:*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**:*int, optional*The number of design vectors to account for during the criteria check.

By default it is set to 3.

**xtol_abs**:*float, optional*A stop criterion, absolute tolerance on the design variables. If norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-09.

**xtol_rel**:*float, optional*A stop criterion, the relative tolerance on the design variables. If norm(xk-xk+1)/norm(xk)<= xtol_rel: stop.

By default it is set to 1e-09.

## PYMOO_NSGA3¶

Note

The plugin gemseo_pymoo is required.

Module: `gemseo_pymoo.algos.opt.lib_pymoo`

Non-dominated Sorting Genetic Algorithm III

More details about the algorithm and its options on https://www.pymoo.org/algorithms/moo/nsga3.html#nb-nsga3.

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to f(x).

**ref_dirs_name**: **

- Optional parameters
**crossover**:*Crossover | None, 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**:*bool, optional*If True, eliminate duplicates after merging the parent and the offspring population.

By default it is set to True.

**ftol_abs**:*float, optional*A stop criterion, the absolute tolerance on the objective function. If abs(f(xk)-f(xk+1))<= ftol_rel: stop.

By default it is set to 1e-09.

**ftol_rel**:*float, optional*A stop criterion, the relative tolerance on the objective function. If abs(f(xk)-f(xk+1))/abs(f(xk))<= ftol_rel: stop.

By default it is set to 1e-09.

**hv_tol_abs**:*float, optional*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**:*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.

**max_gen**:*int, optional*The maximum number of generations.

By default it is set to 10000000.

**mutation**:*Mutation | None, optional*The mutation operator. If None, the algorithm’s default is used.

By default it is set to None.

**n_offsprings**:*int | None, 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**:*int, optional*The number of gaps between two consecutive points along an objective axis.

By default it is set to 20.

**n_points**:*int | None, optional*The number of points on the unit simplex.

By default it is set to None.

**normalize_design_space**:*bool, optional*If True, scale the variables to the range [0, 1].

By default it is set to True.

**partitions**:*ndarray | None, optional*The custom partitions.

By default it is set to None.

**pop_size**:*int, optional*The population size.

By default it is set to 100.

**sampling**:*Sampling | Population | 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.

**seed**:*int, optional*The random seed to be used.

By default it is set to 1.

**selection**:*Selection | None, optional*The mating selection operator. If None, the algorithm’s default is used.

By default it is set to None.

**stop_crit_n_hv**:*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**:*int, optional*The number of design vectors to account for during the criteria check.

By default it is set to 3.

**xtol_abs**:*float, optional*A stop criterion, absolute tolerance on the design variables. If norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-09.

**xtol_rel**:*float, optional*A stop criterion, the relative tolerance on the design variables. If norm(xk-xk+1)/norm(xk)<= xtol_rel: stop.

By default it is set to 1e-09.

## PYMOO_RNSGA3¶

Note

The plugin gemseo_pymoo is required.

Module: `gemseo_pymoo.algos.opt.lib_pymoo`

Reference Point Based NSGA3

More details about the algorithm and its options on https://www.pymoo.org/algorithms/moo/rnsga3.html#nb-rnsga3.

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to f(x).

**ref_points**:*ndarray | None*The reference points (Aspiration Points) as a NumPy array where each row represents a point and each column a variable.

- Optional parameters
**crossover**:*Crossover | None, 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**:*bool, optional*If True, eliminate duplicates after merging the parent and the offspring population.

By default it is set to True.

**ftol_abs**:*float, optional*By default it is set to 1e-09.

**ftol_rel**:*float, optional*By default it is set to 1e-09.

**hv_tol_abs**:*float, optional*By default it is set to 1e-09.

**hv_tol_rel**:*float, optional*By default it is set to 1e-09.

**max_gen**:*int, optional*The maximum number of generations.

By default it is set to 10000000.

**mu**:*float, optional*The scaling of the reference lines used during survival selection. Increasing mu will generate solutions with a larger spread.

By default it is set to 0.1.

**mutation**:*Mutation | None, optional*The mutation operator. If None, the algorithm’s default is used.

By default it is set to None.

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

**normalize_design_space**:*bool, optional*If True, scale the variables to the range [0, 1].

By default it is set to True.

**pop_per_ref_point**:*int, optional*The size of the population used for each reference point.

By default it is set to 1.

**pop_size**:*int, optional*The population size.

By default it is set to 100.

**sampling**:*Sampling | Population | None, optional*By default it is set to None.

**seed**:*int, optional*The random seed to be used.

By default it is set to 1.

**selection**:*Selection | None, optional*The mating selection operator. If None, the algorithm’s default is used.

By default it is set to None.

**stop_crit_n_hv**:*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**:*int, optional*The number of design vectors to account for during the criteria check.

By default it is set to 3.

**xtol_abs**:*float, optional*A stop criterion, absolute tolerance on the design variables. If norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-09.

**xtol_rel**:*float, optional*By default it is set to 1e-09.

## PYMOO_UNSGA3¶

Note

The plugin gemseo_pymoo is required.

Module: `gemseo_pymoo.algos.opt.lib_pymoo`

Unified NSGA3

More details about the algorithm and its options on https://www.pymoo.org/algorithms/moo/unsga3.html#nb-unsga3.

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to f(x).

**ref_dirs_name**: **

- Optional parameters
**crossover**:*Crossover | None, 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**:*bool, optional*If True, eliminate duplicates after merging the parent and the offspring population.

By default it is set to True.

**ftol_abs**:*float, optional*By default it is set to 1e-09.

**ftol_rel**:*float, optional*By default it is set to 1e-09.

**hv_tol_abs**:*float, optional*By default it is set to 1e-09.

**hv_tol_rel**:*float, optional*By default it is set to 1e-09.

**max_gen**:*int, optional*The maximum number of generations.

By default it is set to 10000000.

**mutation**:*Mutation | None, optional*The mutation operator. If None, the algorithm’s default is used.

By default it is set to None.

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

**n_partitions**:*int, optional*The number of gaps between two consecutive points along an objective axis.

By default it is set to 20.

**n_points**:*int | None, optional*The number of points on the unit simplex.

By default it is set to None.

**normalize_design_space**:*bool, optional*If True, scale the variables to the range [0, 1].

By default it is set to True.

**partitions**:*ndarray | None, optional*The custom partitions.

By default it is set to None.

**pop_size**:*int, optional*The population size.

By default it is set to 100.

**sampling**:*Sampling | Population | None, optional*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.

**seed**:*int, optional*The random seed to be used.

By default it is set to 1.

**selection**:*Selection | None, optional*The mating selection operator. If None, the algorithm’s default is used.

By default it is set to None.

**stop_crit_n_hv**:*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**:*int, optional*The number of design vectors to account for during the criteria check.

By default it is set to 3.

**xtol_abs**:*float, optional*A stop criterion, absolute tolerance on the design variables. If norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-09.

**xtol_rel**:*float, optional*By default it is set to 1e-09.

## REVISED_SIMPLEX¶

Module: `gemseo.algos.opt.lib_scipy_linprog`

Linear programming by a two-phase revised simplex algorithm implemented in the SciPy library

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

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to the objective function.

- Optional parameters
**disp**:*bool, optional*Whether to print convergence messages.

By default it is set to False.

**normalize_design_space**:*bool, optional*If

`True`

, scales variables in [0, 1].By default it is set to True.

## SBO¶

Note

The plugin gemseo_mlearning is required.

Module: `gemseo_mlearning.algos.opt.lib_surrogate_based`

GEMSEO in-house surrogate-based optimizer.

- Required parameters
**max_iter**:*int*The maximum number of evaluations.

**regression_file_path**:*str | Path*The path to the file to save the regression model. If empty, do not save the regression model.

- Optional parameters
**acquisition_algorithm**:*str, optional*The name of the algorithm to optimize the data acquisition criterion.

By default it is set to DIFFERENTIAL_EVOLUTION.

**acquisition_options**:*Mapping[str, OptimizationLibraryOptionType], optional*The options of the algorithm to optimize the data acquisition criterion.

By default it is set to {}.

**doe_algorithm**:*str, optional*The name of the algorithm for the initial sampling. This argument is ignored when

`regression_algorithm`

is an`MLRegressionAlgo`

.By default it is set to OT_OPT_LHS.

**doe_options**:*Mapping[str, DOELibraryOptionType], optional*The options of the algorithm for the initial sampling. This argument is ignored when

`regression_algorithm`

is an`MLRegressionAlgo`

.By default it is set to {}.

**doe_size**:*int, optional*Either the size of the initial DOE or

`0`

if the size is inferred from`doe_options`

. This argument is ignored when`regression_algorithm`

is an`MLRegressionAlgo`

.By default it is set to 10.

**ftol_abs**:*float, optional*The absolute tolerance on the objective function.

By default it is set to 1e-14.

**ftol_rel**:*float, optional*The relative tolerance on the objective function.

By default it is set to 1e-08.

**max_time**:*float, optional*The maximum runtime in seconds. The value 0 disables the cap on the runtime.

By default it is set to 0.0.

**regression_algorithm**:*str | MLRegressionAlgo, optional*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 GaussianProcessRegressor.

**regression_options**:*Mapping[str, MLAlgoParameterType], optional*The options of the regression algorithm. This argument is ignored when

`regression_algorithm`

is an`MLRegressionAlgo`

.By default it is set to {}.

**stop_crit_n_x**:*int, optional*The number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**xtol_abs**:*float, optional*The absolute tolerance on the design parameters.

By default it is set to 1e-14.

**xtol_rel**:*float, optional*The relative tolerance on the design parameters.

By default it is set to 1e-08.

## SHGO¶

Module: `gemseo.algos.opt.lib_scipy_global`

Simplicial homology global optimization

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

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to f(x).

- Optional parameters
**eq_tolerance**:*float, optional*The tolerance on equality constraints.

By default it is set to 1e-06.

**ftol_abs**:*float, optional*By default it is set to 1e-09.

**ftol_rel**:*float, optional*By default it is set to 1e-09.

**ineq_tolerance**:*float, optional*The tolerance on inequality constraints.

By default it is set to 1e-06.

**iters**:*int, optional*The number of iterations used in the construction of the simplicial complex.

By default it is set to 1.

**local_options**:*Mapping[str, Any] | None, optional*The options for the local optimization algorithm, only for shgo, see scipy.optimize doc.

By default it is set to None.

**max_time**:*float, optional*The maximum runtime in seconds. The value 0 disables the cap on the runtime.

By default it is set to 0.0.

**n**:*int, optional*The number of sampling points used in the construction of the simplicial complex.

By default it is set to 100.

**normalize_design_space**:*bool, optional*If

`True`

, variables are scaled in [0, 1].By default it is set to True.

**sampling_method**:*str, optional*The method to compute the initial points. Current built in sampling method options are

`halton`

,`sobol`

and`simplicial`

.By default it is set to simplicial.

**seed**:*int, optional*The seed to be used for repeatable minimizations. If

`None`

, the`numpy.random.RandomState`

singleton is used.By default it is set to 0.

**stop_crit_n_x**:*int, optional*The number of design vectors to take into account in the stopping criteria.

By default it is set to 3.

**xtol_abs**:*float, optional*A stop criteria, the absolute tolerance on the design variables. If norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-09.

**xtol_rel**:*float, optional*By default it is set to 1e-09.

## SIMPLEX¶

Module: `gemseo.algos.opt.lib_scipy_linprog`

Linear programming by the two-phase simplex algorithm implemented in the SciPy library

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

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to the objective function.

- Optional parameters
**disp**:*bool, optional*Whether to print convergence messages.

By default it is set to False.

**normalize_design_space**:*bool, optional*If

`True`

, scales variables in [0, 1].By default it is set to True.

## SLSQP¶

Module: `gemseo.algos.opt.lib_scipy`

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

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

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to f(x).

- Optional parameters
**disp**:*int, optional*The display information flag.

By default it is set to 0.

**eq_tolerance**:*float, optional*The equality tolerance.

By default it is set to 0.01.

**ftol_abs**:*float, optional*By default it is set to 1e-09.

**ftol_rel**:*float, optional*By default it is set to 1e-09.

**ineq_tolerance**:*float, optional*The inequality tolerance.

By default it is set to 0.0001.

**kkt_tol_abs**:*float | None, optional*The absolute tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**kkt_tol_rel**:*float | None, optional*The relative tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**max_time**:*float, optional*The maximum runtime in seconds, disabled if 0.

By default it is set to 0.

**normalize_design_space**:*int, optional*If

`True`

, scales variables to [0, 1].By default it is set to True.

**xtol_abs**:*float, optional*A stop criteria, absolute tolerance on the design variables. If norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-09.

**xtol_rel**:*float, optional*By default it is set to 1e-09.

## Scipy_MILP¶

Module: `gemseo.algos.opt.lib_scipy_milp`

Mixed-integer linear programming

More details about the algorithm and its options on https://docs.scipy.org/doc/scipy/reference/scipy.optimize.milp.html.

- Optional parameters
**disp**:*bool, optional*Whether indicators of optimization status are to be printed to the console during optimization.

By default it is set to False.

**mip_rel_gap**:*float, optional*The termination criterion for MIP solver: 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**:*int, optional*The maximum number of nodes (linear program relaxations) to solve before stopping.

By default it is set to 1000.

**presolve**:*bool, optional*Whether to attempt to detect infeasibility, unboundedness or problem simplifications before solving. Refer to the SciPy documentation for more details.

By default it is set to True.

**time_limit**:*int | None, optional*The maximum number of seconds allotted to solve the problem. If

`None`

, there is no time limit.By default it is set to None.

## TNC¶

Module: `gemseo.algos.opt.lib_scipy`

Truncated Newton (TNC) algorithm implemented in SciPy library

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

- Required parameters
**max_iter**:*int*The maximum number of iterations, i.e. unique calls to f(x).

- Optional parameters
**disp**:*int, optional*The display information flag.

By default it is set to 0.

**eq_tolerance**:*float, optional*The equality tolerance.

By default it is set to 0.01.

**eta**:*float, optional*The severity of the line search, specific to the TNC algorithm.

By default it is set to -1.0.

**ftol_abs**:*float, optional*By default it is set to 1e-09.

**ftol_rel**:*float, optional*By default it is set to 1e-09.

**ineq_tolerance**:*float, optional*The inequality tolerance.

By default it is set to 0.0001.

**kkt_tol_abs**:*float | None, optional*The absolute tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**kkt_tol_rel**:*float | None, optional*The relative tolerance on the KKT residual norm. If

`None`

this criterion is not activated.By default it is set to None.

**max_time**:*float, optional*The maximum runtime in seconds, disabled if 0.

By default it is set to 0.

**maxCGit**:*int, optional*The maximum Conjugate Gradient internal solver iterations.

By default it is set to -1.

**minfev**:*float, optional*The minimum function value estimate.

By default it is set to 0.0.

**normalize_design_space**:*int, optional*If

`True`

, scales variables to [0, 1].By default it is set to True.

**offset**:*float | None, optional*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.

**pg_tol**:*float, optional*A stop criteria on the projected gradient norm.

By default it is set to 1e-05.

**rescale**:*float, optional*The scaling factor (in log10) used to trigger f value rescaling.

By default it is set to -1.

**scale**:*float | None, optional*The scaling factor to apply to each variable. If

`None`

, the factors are up-low for interval bounded variables and 1+|x| for the others.By default it is set to None.

**stepmx**:*float, optional*The maximum step for the line search.

By default it is set to 0.0.

**xtol_abs**:*float, optional*A stop criteria, absolute tolerance on the design variables. If norm(xk-xk+1)<= xtol_abs: stop.

By default it is set to 1e-09.

**xtol_rel**:*float, optional*By default it is set to 1e-09.