.. Copyright 2021 IRT Saint-Exupéry, https://www.irt-saintexupery.com This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA. .. _gen_opt_algos: Optimization algorithms ======================= .. warning:: Some capabilities may require the :ref:`installation ` of |g| with :ref:`all its features ` and some others may depend on :ref:`plugins `. .. note:: All the features of the wrapped libraries may not be exposed through |g|. .. raw:: html

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	✗	✓	✓	✗	✗	✓
mNBI	MNBI	MNBI	gemseo	✓	✓	✓	✓	✓	✗
NELDER-MEAD	SciPy	NELDER-MEAD	gemseo	✗	✗	✓	✗	✗	✗
BFGS	NLopt	NLOPT_BFGS	gemseo	✗	✗	✓	✗	✗	✓
BOBYQA	NLopt	NLOPT_BOBYQA	gemseo	✗	✗	✓	✗	✗	✗
COBYLA	NLopt	NLOPT_COBYLA	gemseo	✓	✓	✓	✗	✗	✗
MMA	NLopt	NLOPT_MMA	gemseo	✗	✓	✓	✗	✗	✓
NEWUOA	NLopt	NLOPT_NEWUOA	gemseo	✗	✗	✓	✗	✗	✗
SLSQP	NLopt	NLOPT_SLSQP	gemseo	✓	✓	✓	✗	✗	✓
BOBYQA	PDFO	PDFO_BOBYQA	gemseo_pdfo	✗	✗	✓	✗	✗	✗
COBYLA	PDFO	PDFO_COBYLA	gemseo_pdfo	✓	✓	✓	✗	✗	✗
NEWUOA	PDFO	PDFO_NEWUOA	gemseo_pdfo	✗	✗	✓	✗	✗	✗
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	✓	✓	✓	✗	✗	✗
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_options: Augmented_Lagrangian_order_0 ---------------------------- Module: :class:`gemseo.algos.opt.augmented_lagrangian.order_0` Augmented Lagrangian algorithm for gradient-less functions. .. raw:: html

Required parameters

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

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. .. raw:: html
**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. .. raw:: html
**gamma** : *float, optional* The increase of the penalty term. By default it is set to 1.5. .. raw:: html
**initial_rho** : *float, optional* The initial value of the penalty. By default it is set to 10.0. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_iter** : *int, optional* The maximum number of iterations, i.e. unique calls to f(x). By default it is set to 999. .. raw:: html
**max_rho** : *float, optional* The max penalty value. By default it is set to 10000. .. raw:: html
**normalize_design_space** : *bool, optional* Whether to scale the variables into ``[0, 1]``. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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 (). .. raw:: html
**sub_problem_options** : *Mapping[str, Any] | None, optional* The options passed to the sub-problem optimization solver. By default it is set to None. .. raw:: html
**tau** : *float, optional* The threshold for the penalty term increase. By default it is set to 0.9. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _Augmented_Lagrangian_order_1_options: Augmented_Lagrangian_order_1 ---------------------------- Module: :class:`gemseo.algos.opt.augmented_lagrangian.order_1` Augmented Lagrangian algorithm using gradient information. .. raw:: html

Required parameters

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

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. .. raw:: html
**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. .. raw:: html
**gamma** : *float, optional* The increase of the penalty term. By default it is set to 1.5. .. raw:: html
**initial_rho** : *float, optional* The initial value of the penalty. By default it is set to 10.0. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_iter** : *int, optional* The maximum number of iterations, i.e. unique calls to f(x). By default it is set to 999. .. raw:: html
**max_rho** : *float, optional* The max penalty value. By default it is set to 10000. .. raw:: html
**normalize_design_space** : *bool, optional* Whether to scale the variables into ``[0, 1]``. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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 (). .. raw:: html
**sub_problem_options** : *Mapping[str, Any] | None, optional* The options passed to the sub-problem optimization solver. By default it is set to None. .. raw:: html
**tau** : *float, optional* The threshold for the penalty term increase. By default it is set to 0.9. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _DIFFERENTIAL_EVOLUTION_options: DIFFERENTIAL_EVOLUTION ---------------------- Module: :class:`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. .. raw:: html

Required parameters

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

Optional parameters

**atol** : *float, optional* The absolute tolerance for convergence. By default it is set to 0.0. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on equality constraints. By default it is set to 1e-06. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on inequality constraints. By default it is set to 1e-06. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, variables are scaled in [0, 1]. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**recombination** : *float, optional* The recombination constant. By default it is set to 0.7. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**strategy** : *str, optional* The differential evolution strategy to use. By default it is set to best1bin. .. raw:: html
**tol** : *float, optional* The relative tolerance for convergence. By default it is set to 0.01. .. raw:: html
**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. .. raw:: html
**workers** : *int, optional* The number of processes for parallel execution. By default it is set to 1. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _DUAL_ANNEALING_options: DUAL_ANNEALING -------------- Module: :class:`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. .. raw:: html

Required parameters

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

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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, variables are scaled in [0, 1]. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _HIGHS_options: HIGHS ----- Module: :class:`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. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations, i.e. unique calls to the objective function. .. raw:: html

Optional parameters

**disp** : *bool, optional* Whether to print convergence messages. By default it is set to False. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, scales variables in [0, 1]. By default it is set to True. .. raw:: html

.. _HIGHS_DUAL_SIMPLEX_options: HIGHS_DUAL_SIMPLEX ------------------ Module: :class:`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. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations, i.e. unique calls to the objective function. .. raw:: html

Optional parameters

**disp** : *bool, optional* Whether to print convergence messages. By default it is set to False. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, scales variables in [0, 1]. By default it is set to True. .. raw:: html

.. _HIGHS_INTERIOR_POINT_options: HIGHS_INTERIOR_POINT -------------------- Module: :class:`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. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations, i.e. unique calls to the objective function. .. raw:: html

Optional parameters

**disp** : *bool, optional* Whether to print convergence messages. By default it is set to False. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, scales variables in [0, 1]. By default it is set to True. .. raw:: html

.. _L-BFGS-B_options: L-BFGS-B -------- Module: :class:`gemseo.algos.opt.lib_scipy` Limited-memory BFGS algorithm implemented in the SciPy library More details about the algorithm and its options on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-lbfgsb.html. .. raw:: html

Required parameters

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

Optional parameters

**disp** : *bool, optional* The display information flag. By default it is set to False. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_ls_step_nb** : *int, optional* The maximum number of line search steps per iteration. By default it is set to 20. .. raw:: html
**max_time** : *float, optional* The maximum runtime in seconds, disabled if 0. By default it is set to 0. .. raw:: html
**maxcor** : *int, optional* The maximum BFGS updates. By default it is set to 20. .. raw:: html
**normalize_design_space** : *int, optional* If ``True``, scales variables to [0, 1]. By default it is set to True. .. raw:: html
**pg_tol** : *float, optional* A stop criteria on the projected gradient norm. By default it is set to 1e-05. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _LINEAR_INTERIOR_POINT_options: LINEAR_INTERIOR_POINT --------------------- Module: :class:`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. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations, i.e. unique calls to the objective function. .. raw:: html

Optional parameters

**disp** : *bool, optional* Whether to print convergence messages. By default it is set to False. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, scales variables in [0, 1]. By default it is set to True. .. raw:: html

.. _MMA_options: MMA --- .. note:: The plugin `gemseo_mma `_ is required. Module: :class:`gemseo_mma.opt.lib_mma` .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations. .. raw:: html

Optional parameters

**asymptotes_distance_amplification_coefficient** : *float, optional* The amplification factor for successful iterations. By default it is set to 1.2. .. raw:: html
**asymptotes_distance_reduction_coefficient** : *float, optional* The decremental factor for unsuccessful iterations. By default it is set to 0.7. .. raw:: html
**conv_tol** : *float | None, optional* If provided control all other convergence tolerances. By default it is set to None. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.01. .. raw:: html
**initial_asymptotes_distance** : *float, optional* The initial asymptotes distance from the current design variable value. By default it is set to 0.5. .. raw:: html
**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. .. raw:: html
**max_optimization_step** : *float, optional* The maximum optimization step. By default it is set to 0.1. .. raw:: html
**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. .. raw:: html
**normalize_design_space** : *bool, optional* If True, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**tol** : *float, optional* tolerance of convergence used in MMA to be compared with kkt residual. By default it is set to 0.01. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _MNBI_options: MNBI ---- Module: :class:`gemseo.algos.opt.mnbi` Modified Normal Boundary Intersection (mNBI) method .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations. .. raw:: html
**n_sub_optim** : *int* The number of sub optimization in addition to the individual minimums of the objectives. mNBI will generate n_sub_optim points on the Pareto front between the "number of objective" individual minimas. This value must be strictly greater than the number of objectives of the problem. .. raw:: html
**sub_optim_algo** : *str* The optimization algorithm used to solve the generated sub optimization problems. .. raw:: html

Optional parameters

**debug** : *bool, optional* Whether to output a database hdf file containing the sub optimization optimas only. By default it is set to False. .. raw:: html
**debug_file_path** : *str | Path, optional* The path to the debug file if debug mode is active. By default it is set to debug_history.h5. .. raw:: html
**doe_algo** : *str, optional* The design of experiments algorithm for the target points on the Pareto front in problems with more than 2 objectives. A ``fullfactorial`` DOE is used default as these tend to be low dimensions, usually not more than 3 objectives for a given problem. By default it is set to fullfact. .. raw:: html
**doe_algo_options** : *Mapping[str, DOELibraryOptionType], optional* The options for the DOE algorithm. By default it is set to {}. .. raw:: html
**n_processes** : *int, optional* The maximum simultaneous number of processes used to parallelize the sub optimizations. By default it is set to 1. .. raw:: html
**normalize_design_space** : *bool, optional* Whether to normalize the design variables between 0 and 1. By default it is set to False. .. raw:: html
**skip_betas** : *bool, optional* The description is missing. By default it is set to True. .. raw:: html
**sub_optim_algo_options** : *Mapping[str, DriverLibOptionType], optional* The options for the optimization algorithm. By default it is set to {}. .. raw:: html
**sub_optim_max_iter** : *int | None, optional* Maximum number of iterations of the sub optimization algorithms. If ``None``, the ``max_iter`` value is used. By default it is set to None. .. raw:: html

.. _NELDER-MEAD_options: NELDER-MEAD ----------- Module: :class:`gemseo.algos.opt.lib_scipy` Nelder-Mead algorithm implemented in the SciPy library More details about the algorithm and its options on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-neldermead.html. .. raw:: html

Required parameters

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

Optional parameters

**adaptive** : *bool, optional* Whether to adapt the Nelder-Mead algorithm parameters to the dimensionality of the problem. Useful for high-dimensional minimization. By default it is set to False. .. raw:: html
**disp** : *bool, optional* The display information flag. By default it is set to False. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**initial_simplex** : *Sequence[Sequence[float]] | None, optional* If not ``None``, overrides x0 in the Nelder-Mead algorithm. ``initial_simplex[j,:]`` should contain the coordinates of the jth vertex of the N+1 vertices in the simplex, where N is the dimension. By default it is set to None. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_time** : *float, optional* The maximum runtime in seconds, disabled if 0. By default it is set to 0. .. raw:: html
**normalize_design_space** : *int, optional* If ``True``, scales variables to [0, 1]. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _NLOPT_BFGS_options: NLOPT_BFGS ---------- Module: :class:`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. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations. .. raw:: html

Optional parameters

**ctol_abs** : *float, optional* The absolute tolerance on the constraints. By default it is set to 1e-06. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**init_step** : *float, optional* The initial step size :math:`r` for derivative-free algorithms. Increasing the initial step size will make the initial DOE of size :math:`d+1` take wider steps in the design variables. In details, given a :math:`d`-length design vector initialized to :math:`x_0`, the first value of the design vector will be the initial one :math:`x^{(1)}=x_0`, the second one will be :math:`x^{(2)}=x^{(1)}+(r(\max(x_1)-\min(x_1)),0,\ldots,0)`, ..., the :math:`d+1`-th one will be :math:`x^{(d+1)}=x^{d}+(0,\ldots,0,r(\max(x_d)-\min(x_d)))`. Note that in a normalized design space, :math:`\min(x_i)=0` and :math:`\max(x_i)=1`. By default it is set to 0.25. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_time** : *float, optional* The maximum runtime in seconds. The value 0 means no runtime limit. By default it is set to 0.0. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**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. .. raw:: html
**stopval** : *float | None, optional* The objective value at which the optimization will stop. Stop minimizing when an objective value :math:`\leq` stopval is found, or stop maximizing when a value :math:`\geq` stopval is found. If ``None``, this termination condition will not be active. By default it is set to None. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _NLOPT_BOBYQA_options: NLOPT_BOBYQA ------------ Module: :class:`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. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations. .. raw:: html

Optional parameters

**ctol_abs** : *float, optional* The absolute tolerance on the constraints. By default it is set to 1e-06. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**init_step** : *float, optional* The initial step size :math:`r` for derivative-free algorithms. Increasing the initial step size will make the initial DOE of size :math:`d+1` take wider steps in the design variables. In details, given a :math:`d`-length design vector initialized to :math:`x_0`, the first value of the design vector will be the initial one :math:`x^{(1)}=x_0`, the second one will be :math:`x^{(2)}=x^{(1)}+(r(\max(x_1)-\min(x_1)),0,\ldots,0)`, ..., the :math:`d+1`-th one will be :math:`x^{(d+1)}=x^{d}+(0,\ldots,0,r(\max(x_d)-\min(x_d)))`. Note that in a normalized design space, :math:`\min(x_i)=0` and :math:`\max(x_i)=1`. By default it is set to 0.25. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_time** : *float, optional* The maximum runtime in seconds. The value 0 means no runtime limit. By default it is set to 0.0. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**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. .. raw:: html
**stopval** : *float | None, optional* The objective value at which the optimization will stop. Stop minimizing when an objective value :math:`\leq` stopval is found, or stop maximizing when a value :math:`\geq` stopval is found. If ``None``, this termination condition will not be active. By default it is set to None. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _NLOPT_COBYLA_options: NLOPT_COBYLA ------------ Module: :class:`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. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations. .. raw:: html

Optional parameters

**ctol_abs** : *float, optional* The absolute tolerance on the constraints. By default it is set to 1e-06. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**init_step** : *float, optional* The initial step size :math:`r` for derivative-free algorithms. Increasing the initial step size will make the initial DOE of size :math:`d+1` take wider steps in the design variables. In details, given a :math:`d`-length design vector initialized to :math:`x_0`, the first value of the design vector will be the initial one :math:`x^{(1)}=x_0`, the second one will be :math:`x^{(2)}=x^{(1)}+(r(\max(x_1)-\min(x_1)),0,\ldots,0)`, ..., the :math:`d+1`-th one will be :math:`x^{(d+1)}=x^{d}+(0,\ldots,0,r(\max(x_d)-\min(x_d)))`. Note that in a normalized design space, :math:`\min(x_i)=0` and :math:`\max(x_i)=1`. By default it is set to 0.25. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_time** : *float, optional* The maximum runtime in seconds. The value 0 means no runtime limit. By default it is set to 0.0. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**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. .. raw:: html
**stopval** : *float | None, optional* The objective value at which the optimization will stop. Stop minimizing when an objective value :math:`\leq` stopval is found, or stop maximizing when a value :math:`\geq` stopval is found. If ``None``, this termination condition will not be active. By default it is set to None. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _NLOPT_MMA_options: NLOPT_MMA --------- Module: :class:`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. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations. .. raw:: html

Optional parameters

**ctol_abs** : *float, optional* The absolute tolerance on the constraints. By default it is set to 1e-06. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**init_step** : *float, optional* The initial step size :math:`r` for derivative-free algorithms. Increasing the initial step size will make the initial DOE of size :math:`d+1` take wider steps in the design variables. In details, given a :math:`d`-length design vector initialized to :math:`x_0`, the first value of the design vector will be the initial one :math:`x^{(1)}=x_0`, the second one will be :math:`x^{(2)}=x^{(1)}+(r(\max(x_1)-\min(x_1)),0,\ldots,0)`, ..., the :math:`d+1`-th one will be :math:`x^{(d+1)}=x^{d}+(0,\ldots,0,r(\max(x_d)-\min(x_d)))`. Note that in a normalized design space, :math:`\min(x_i)=0` and :math:`\max(x_i)=1`. By default it is set to 0.25. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_time** : *float, optional* The maximum runtime in seconds. The value 0 means no runtime limit. By default it is set to 0.0. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**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. .. raw:: html
**stopval** : *float | None, optional* The objective value at which the optimization will stop. Stop minimizing when an objective value :math:`\leq` stopval is found, or stop maximizing when a value :math:`\geq` stopval is found. If ``None``, this termination condition will not be active. By default it is set to None. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _NLOPT_NEWUOA_options: NLOPT_NEWUOA ------------ Module: :class:`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. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations. .. raw:: html

Optional parameters

**ctol_abs** : *float, optional* The absolute tolerance on the constraints. By default it is set to 1e-06. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**init_step** : *float, optional* The initial step size :math:`r` for derivative-free algorithms. Increasing the initial step size will make the initial DOE of size :math:`d+1` take wider steps in the design variables. In details, given a :math:`d`-length design vector initialized to :math:`x_0`, the first value of the design vector will be the initial one :math:`x^{(1)}=x_0`, the second one will be :math:`x^{(2)}=x^{(1)}+(r(\max(x_1)-\min(x_1)),0,\ldots,0)`, ..., the :math:`d+1`-th one will be :math:`x^{(d+1)}=x^{d}+(0,\ldots,0,r(\max(x_d)-\min(x_d)))`. Note that in a normalized design space, :math:`\min(x_i)=0` and :math:`\max(x_i)=1`. By default it is set to 0.25. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_time** : *float, optional* The maximum runtime in seconds. The value 0 means no runtime limit. By default it is set to 0.0. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**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. .. raw:: html
**stopval** : *float | None, optional* The objective value at which the optimization will stop. Stop minimizing when an objective value :math:`\leq` stopval is found, or stop maximizing when a value :math:`\geq` stopval is found. If ``None``, this termination condition will not be active. By default it is set to None. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _NLOPT_SLSQP_options: NLOPT_SLSQP ----------- Module: :class:`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. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations. .. raw:: html

Optional parameters

**ctol_abs** : *float, optional* The absolute tolerance on the constraints. By default it is set to 1e-06. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**init_step** : *float, optional* The initial step size :math:`r` for derivative-free algorithms. Increasing the initial step size will make the initial DOE of size :math:`d+1` take wider steps in the design variables. In details, given a :math:`d`-length design vector initialized to :math:`x_0`, the first value of the design vector will be the initial one :math:`x^{(1)}=x_0`, the second one will be :math:`x^{(2)}=x^{(1)}+(r(\max(x_1)-\min(x_1)),0,\ldots,0)`, ..., the :math:`d+1`-th one will be :math:`x^{(d+1)}=x^{d}+(0,\ldots,0,r(\max(x_d)-\min(x_d)))`. Note that in a normalized design space, :math:`\min(x_i)=0` and :math:`\max(x_i)=1`. By default it is set to 0.25. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_time** : *float, optional* The maximum runtime in seconds. The value 0 means no runtime limit. By default it is set to 0.0. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**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. .. raw:: html
**stopval** : *float | None, optional* The objective value at which the optimization will stop. Stop minimizing when an objective value :math:`\leq` stopval is found, or stop maximizing when a value :math:`\geq` stopval is found. If ``None``, this termination condition will not be active. By default it is set to None. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _PDFO_BOBYQA_options: PDFO_BOBYQA ----------- .. note:: The plugin `gemseo_pdfo `_ is required. Module: :class:`gemseo_pdfo.lib_pdfo` Bound Optimization By Quadratic Approximation More details about the algorithm and its options on https://www.pdfo.net/. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations. .. raw:: html

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. .. raw:: html
**classical** : *bool, optional* The flag indicating whether to call the classical Powell code or not. By default it is set to False. .. raw:: html
**debug** : *bool, optional* The debugging flag. By default it is set to False. .. raw:: html
**ensure_bounds** : *bool, optional* Whether to project the design vector onto the design space before execution. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_time** : *float, optional* The maximum runtime in seconds, disabled if 0. By default it is set to 0. .. raw:: html
**normalize_design_space** : *bool, optional* If True, normalize the design space. By default it is set to True. .. raw:: html
**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. .. raw:: html
**rhobeg** : *float, optional* The initial value of the trust region radius. By default it is set to 0.5. .. raw:: html
**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. .. raw:: html
**scale** : *bool, optional* The flag indicating whether to scale the problem according to the bound constraints. By default it is set to False. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _PDFO_COBYLA_options: PDFO_COBYLA ----------- .. note:: The plugin `gemseo_pdfo `_ is required. Module: :class:`gemseo_pdfo.lib_pdfo` Constrained Optimization By Linear Approximations More details about the algorithm and its options on https://www.pdfo.net/. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations. .. raw:: html

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. .. raw:: html
**classical** : *bool, optional* The flag indicating whether to call the classical Powell code or not. By default it is set to False. .. raw:: html
**debug** : *bool, optional* The debugging flag. By default it is set to False. .. raw:: html
**ensure_bounds** : *bool, optional* Whether to project the design vector onto the design space before execution. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_time** : *float, optional* The maximum runtime in seconds, disabled if 0. By default it is set to 0. .. raw:: html
**normalize_design_space** : *bool, optional* If True, normalize the design space. By default it is set to True. .. raw:: html
**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. .. raw:: html
**rhobeg** : *float, optional* The initial value of the trust region radius. By default it is set to 0.5. .. raw:: html
**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. .. raw:: html
**scale** : *bool, optional* The flag indicating whether to scale the problem according to the bound constraints. By default it is set to False. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _PDFO_NEWUOA_options: PDFO_NEWUOA ----------- .. note:: The plugin `gemseo_pdfo `_ is required. Module: :class:`gemseo_pdfo.lib_pdfo` NEWUOA More details about the algorithm and its options on https://www.pdfo.net/. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations. .. raw:: html

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. .. raw:: html
**classical** : *bool, optional* The flag indicating whether to call the classical Powell code or not. By default it is set to False. .. raw:: html
**debug** : *bool, optional* The debugging flag. By default it is set to False. .. raw:: html
**ensure_bounds** : *bool, optional* Whether to project the design vector onto the design space before execution. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_time** : *float, optional* The maximum runtime in seconds, disabled if 0. By default it is set to 0. .. raw:: html
**normalize_design_space** : *bool, optional* If True, normalize the design space. By default it is set to True. .. raw:: html
**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. .. raw:: html
**rhobeg** : *float, optional* The initial value of the trust region radius. By default it is set to 0.5. .. raw:: html
**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. .. raw:: html
**scale** : *bool, optional* The flag indicating whether to scale the problem according to the bound constraints. By default it is set to False. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _PSEVEN_options: PSEVEN ------ .. note:: The plugin `gemseo_pseven `_ is required. Module: :class:`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/. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of evaluations. .. raw:: html

Optional parameters

**constraints_smoothness** : *str, optional* The assumed smoothness of the constraints functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**diff_step** : *float, optional* The numerical differentiation step size. By default it is set to 1.1920929e-06. .. raw:: html
**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. .. raw:: html
**ensure_feasibility** : *bool, optional* Whether to restrict the evaluations of the objectives to feasible designs only. By default it is set to False. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**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. .. raw:: html
**log_level** : *str, optional* The minimum log level: "Debug", "Info", "Warn", "Error" or "Fatal". By default it is set to Error. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_threads** : *int, optional* The maximum number of parallel threads to use when solving. By default it is set to 0. .. raw:: html
**normalize_design_space** : *bool, optional* If True, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**objectives_smoothness** : *str, optional* The assumed smoothness of the objective functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**responses_scalability** : *int, optional* The maximum number of concurrent response evaluations supported by the problem. By default it is set to 1. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**seed** : *int, optional* The random seed for deterministic mode. By default it is set to 100. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**use_gradient** : *bool, optional* Whether to use the functions derivatives. By default it is set to True. .. raw:: html
**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. .. raw:: html
**verbose_log** : *bool, optional* Whether to enable verbose logging. By default it is set to False. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _PSEVEN_FD_options: PSEVEN_FD --------- .. note:: The plugin `gemseo_pseven `_ is required. Module: :class:`gemseo_pseven.lib_pseven` pSeven's feasible direction method. More details about the algorithm and its options on https://datadvance.net/product/pseven/manual/. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of evaluations. .. raw:: html

Optional parameters

**constraints_smoothness** : *str, optional* The assumed smoothness of the constraints functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**diff_step** : *float, optional* The numerical differentiation step size. By default it is set to 1.1920929e-06. .. raw:: html
**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. .. raw:: html
**ensure_feasibility** : *bool, optional* Whether to restrict the evaluations of the objectives to feasible designs only. By default it is set to False. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**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. .. raw:: html
**log_level** : *str, optional* The minimum log level: "Debug", "Info", "Warn", "Error" or "Fatal". By default it is set to Error. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_threads** : *int, optional* The maximum number of parallel threads to use when solving. By default it is set to 0. .. raw:: html
**normalize_design_space** : *bool, optional* If True, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**objectives_smoothness** : *str, optional* The assumed smoothness of the objective functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**responses_scalability** : *int, optional* The maximum number of concurrent response evaluations supported by the problem. By default it is set to 1. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**seed** : *int, optional* The random seed for deterministic mode. By default it is set to 100. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**use_gradient** : *bool, optional* Whether to use the functions derivatives. By default it is set to True. .. raw:: html
**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. .. raw:: html
**verbose_log** : *bool, optional* Whether to enable verbose logging. By default it is set to False. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _PSEVEN_MOM_options: PSEVEN_MOM ---------- .. note:: The plugin `gemseo_pseven `_ is required. Module: :class:`gemseo_pseven.lib_pseven` pSeven's method of multipliers. More details about the algorithm and its options on https://datadvance.net/product/pseven/manual/. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of evaluations. .. raw:: html

Optional parameters

**constraints_smoothness** : *str, optional* The assumed smoothness of the constraints functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**diff_step** : *float, optional* The numerical differentiation step size. By default it is set to 1.1920929e-06. .. raw:: html
**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. .. raw:: html
**ensure_feasibility** : *bool, optional* Whether to restrict the evaluations of the objectives to feasible designs only. By default it is set to False. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**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. .. raw:: html
**log_level** : *str, optional* The minimum log level: "Debug", "Info", "Warn", "Error" or "Fatal". By default it is set to Error. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_threads** : *int, optional* The maximum number of parallel threads to use when solving. By default it is set to 0. .. raw:: html
**normalize_design_space** : *bool, optional* If True, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**objectives_smoothness** : *str, optional* The assumed smoothness of the objective functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**responses_scalability** : *int, optional* The maximum number of concurrent response evaluations supported by the problem. By default it is set to 1. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**seed** : *int, optional* The random seed for deterministic mode. By default it is set to 100. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**use_gradient** : *bool, optional* Whether to use the functions derivatives. By default it is set to True. .. raw:: html
**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. .. raw:: html
**verbose_log** : *bool, optional* Whether to enable verbose logging. By default it is set to False. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _PSEVEN_NCG_options: PSEVEN_NCG ---------- .. note:: The plugin `gemseo_pseven `_ is required. Module: :class:`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/. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of evaluations. .. raw:: html

Optional parameters

**constraints_smoothness** : *str, optional* The assumed smoothness of the constraints functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**diff_step** : *float, optional* The numerical differentiation step size. By default it is set to 1.1920929e-06. .. raw:: html
**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. .. raw:: html
**ensure_feasibility** : *bool, optional* Whether to restrict the evaluations of the objectives to feasible designs only. By default it is set to False. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**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. .. raw:: html
**log_level** : *str, optional* The minimum log level: "Debug", "Info", "Warn", "Error" or "Fatal". By default it is set to Error. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_threads** : *int, optional* The maximum number of parallel threads to use when solving. By default it is set to 0. .. raw:: html
**normalize_design_space** : *bool, optional* If True, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**objectives_smoothness** : *str, optional* The assumed smoothness of the objective functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**responses_scalability** : *int, optional* The maximum number of concurrent response evaluations supported by the problem. By default it is set to 1. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**seed** : *int, optional* The random seed for deterministic mode. By default it is set to 100. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**use_gradient** : *bool, optional* Whether to use the functions derivatives. By default it is set to True. .. raw:: html
**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. .. raw:: html
**verbose_log** : *bool, optional* Whether to enable verbose logging. By default it is set to False. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _PSEVEN_NLS_options: PSEVEN_NLS ---------- .. note:: The plugin `gemseo_pseven `_ is required. Module: :class:`gemseo_pseven.lib_pseven` pSeven's nonlinear simplex method. More details about the algorithm and its options on https://datadvance.net/product/pseven/manual/. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of evaluations. .. raw:: html

Optional parameters

**constraints_smoothness** : *str, optional* The assumed smoothness of the constraints functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**diff_step** : *float, optional* The numerical differentiation step size. By default it is set to 1.1920929e-06. .. raw:: html
**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. .. raw:: html
**ensure_feasibility** : *bool, optional* Whether to restrict the evaluations of the objectives to feasible designs only. By default it is set to False. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**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. .. raw:: html
**log_level** : *str, optional* The minimum log level: "Debug", "Info", "Warn", "Error" or "Fatal". By default it is set to Error. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_threads** : *int, optional* The maximum number of parallel threads to use when solving. By default it is set to 0. .. raw:: html
**normalize_design_space** : *bool, optional* If True, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**objectives_smoothness** : *str, optional* The assumed smoothness of the objective functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**responses_scalability** : *int, optional* The maximum number of concurrent response evaluations supported by the problem. By default it is set to 1. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**seed** : *int, optional* The random seed for deterministic mode. By default it is set to 100. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**use_gradient** : *bool, optional* Whether to use the functions derivatives. By default it is set to True. .. raw:: html
**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. .. raw:: html
**verbose_log** : *bool, optional* Whether to enable verbose logging. By default it is set to False. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _PSEVEN_POWELL_options: PSEVEN_POWELL ------------- .. note:: The plugin `gemseo_pseven `_ is required. Module: :class:`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/. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of evaluations. .. raw:: html

Optional parameters

**constraints_smoothness** : *str, optional* The assumed smoothness of the constraints functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**diff_step** : *float, optional* The numerical differentiation step size. By default it is set to 1.1920929e-06. .. raw:: html
**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. .. raw:: html
**ensure_feasibility** : *bool, optional* Whether to restrict the evaluations of the objectives to feasible designs only. By default it is set to False. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**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. .. raw:: html
**log_level** : *str, optional* The minimum log level: "Debug", "Info", "Warn", "Error" or "Fatal". By default it is set to Error. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_threads** : *int, optional* The maximum number of parallel threads to use when solving. By default it is set to 0. .. raw:: html
**normalize_design_space** : *bool, optional* If True, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**objectives_smoothness** : *str, optional* The assumed smoothness of the objective functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**responses_scalability** : *int, optional* The maximum number of concurrent response evaluations supported by the problem. By default it is set to 1. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**seed** : *int, optional* The random seed for deterministic mode. By default it is set to 100. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**use_gradient** : *bool, optional* Whether to use the functions derivatives. By default it is set to True. .. raw:: html
**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. .. raw:: html
**verbose_log** : *bool, optional* Whether to enable verbose logging. By default it is set to False. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _PSEVEN_QP_options: PSEVEN_QP --------- .. note:: The plugin `gemseo_pseven `_ is required. Module: :class:`gemseo_pseven.lib_pseven` pSeven's quadratic programming method. More details about the algorithm and its options on https://datadvance.net/product/pseven/manual/. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of evaluations. .. raw:: html

Optional parameters

**constraints_smoothness** : *str, optional* The assumed smoothness of the constraints functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**diff_step** : *float, optional* The numerical differentiation step size. By default it is set to 1.1920929e-06. .. raw:: html
**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. .. raw:: html
**ensure_feasibility** : *bool, optional* Whether to restrict the evaluations of the objectives to feasible designs only. By default it is set to False. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**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. .. raw:: html
**log_level** : *str, optional* The minimum log level: "Debug", "Info", "Warn", "Error" or "Fatal". By default it is set to Error. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_threads** : *int, optional* The maximum number of parallel threads to use when solving. By default it is set to 0. .. raw:: html
**normalize_design_space** : *bool, optional* If True, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**objectives_smoothness** : *str, optional* The assumed smoothness of the objective functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**responses_scalability** : *int, optional* The maximum number of concurrent response evaluations supported by the problem. By default it is set to 1. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**seed** : *int, optional* The random seed for deterministic mode. By default it is set to 100. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**use_gradient** : *bool, optional* Whether to use the functions derivatives. By default it is set to True. .. raw:: html
**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. .. raw:: html
**verbose_log** : *bool, optional* Whether to enable verbose logging. By default it is set to False. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _PSEVEN_SQ2P_options: PSEVEN_SQ2P ----------- .. note:: The plugin `gemseo_pseven `_ is required. Module: :class:`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/. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of evaluations. .. raw:: html

Optional parameters

**constraints_smoothness** : *str, optional* The assumed smoothness of the constraints functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**diff_step** : *float, optional* The numerical differentiation step size. By default it is set to 1.1920929e-06. .. raw:: html
**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. .. raw:: html
**ensure_feasibility** : *bool, optional* Whether to restrict the evaluations of the objectives to feasible designs only. By default it is set to False. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**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. .. raw:: html
**log_level** : *str, optional* The minimum log level: "Debug", "Info", "Warn", "Error" or "Fatal". By default it is set to Error. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_threads** : *int, optional* The maximum number of parallel threads to use when solving. By default it is set to 0. .. raw:: html
**normalize_design_space** : *bool, optional* If True, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**objectives_smoothness** : *str, optional* The assumed smoothness of the objective functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**responses_scalability** : *int, optional* The maximum number of concurrent response evaluations supported by the problem. By default it is set to 1. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**seed** : *int, optional* The random seed for deterministic mode. By default it is set to 100. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**use_gradient** : *bool, optional* Whether to use the functions derivatives. By default it is set to True. .. raw:: html
**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. .. raw:: html
**verbose_log** : *bool, optional* Whether to enable verbose logging. By default it is set to False. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _PSEVEN_SQP_options: PSEVEN_SQP ---------- .. note:: The plugin `gemseo_pseven `_ is required. Module: :class:`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/. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of evaluations. .. raw:: html

Optional parameters

**constraints_smoothness** : *str, optional* The assumed smoothness of the constraints functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**diff_step** : *float, optional* The numerical differentiation step size. By default it is set to 1.1920929e-06. .. raw:: html
**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. .. raw:: html
**ensure_feasibility** : *bool, optional* Whether to restrict the evaluations of the objectives to feasible designs only. By default it is set to False. .. raw:: html
**eq_tolerance** : *float, optional* The tolerance on the equality constraints. By default it is set to 0.01. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ftol_abs** : *float, optional* The absolute tolerance on the objective function. By default it is set to 1e-14. .. raw:: html
**ftol_rel** : *float, optional* The relative tolerance on the objective function. By default it is set to 1e-08. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on the inequality constraints. By default it is set to 0.0001. .. raw:: html
**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. .. raw:: html
**log_level** : *str, optional* The minimum log level: "Debug", "Info", "Warn", "Error" or "Fatal". By default it is set to Error. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_threads** : *int, optional* The maximum number of parallel threads to use when solving. By default it is set to 0. .. raw:: html
**normalize_design_space** : *bool, optional* If True, normalize the design variables between 0 and 1. By default it is set to True. .. raw:: html
**objectives_smoothness** : *str, optional* The assumed smoothness of the objective functions: "Smooth", "Noisy" or "Auto". By default it is set to Auto. .. raw:: html
**responses_scalability** : *int, optional* The maximum number of concurrent response evaluations supported by the problem. By default it is set to 1. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**seed** : *int, optional* The random seed for deterministic mode. By default it is set to 100. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**use_gradient** : *bool, optional* Whether to use the functions derivatives. By default it is set to True. .. raw:: html
**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. .. raw:: html
**verbose_log** : *bool, optional* Whether to enable verbose logging. By default it is set to False. .. raw:: html
**xtol_abs** : *float, optional* The absolute tolerance on the design parameters. By default it is set to 1e-14. .. raw:: html
**xtol_rel** : *float, optional* The relative tolerance on the design parameters. By default it is set to 1e-08. .. raw:: html

.. _PYMOO_GA_options: PYMOO_GA -------- .. note:: The plugin `gemseo_pymoo `_ is required. Module: :class:`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. .. raw:: html

Required parameters

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

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. .. raw:: html
**eliminate_duplicates** : *bool, optional* If True, eliminate duplicates after merging the parent and the offspring population. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_gen** : *int, optional* The maximum number of generations. By default it is set to 10000000. .. raw:: html
**mutation** : *Mutation | None, optional* The mutation operator. If None, the algorithm's default is used. By default it is set to None. .. raw:: html
**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. .. raw:: html
**normalize_design_space** : *bool, optional* If True, scale the variables to the range [0, 1]. By default it is set to True. .. raw:: html
**pop_size** : *int, optional* The population size. By default it is set to 100. .. raw:: html
**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. .. raw:: html
**seed** : *int, optional* The random seed to be used. By default it is set to 1. .. raw:: html
**selection** : *Selection | None, optional* The mating selection operator. If None, the algorithm's default is used. By default it is set to None. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _PYMOO_NSGA2_options: PYMOO_NSGA2 ----------- .. note:: The plugin `gemseo_pymoo `_ is required. Module: :class:`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. .. raw:: html

Required parameters

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

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. .. raw:: html
**eliminate_duplicates** : *bool, optional* If True, eliminate duplicates after merging the parent and the offspring population. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_gen** : *int, optional* The maximum number of generations. By default it is set to 10000000. .. raw:: html
**mutation** : *Mutation | None, optional* The mutation operator. If None, the algorithm's default is used. By default it is set to None. .. raw:: html
**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. .. raw:: html
**normalize_design_space** : *bool, optional* If True, scale the variables to the range [0, 1]. By default it is set to True. .. raw:: html
**pop_size** : *int, optional* The population size. By default it is set to 100. .. raw:: html
**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. .. raw:: html
**seed** : *int, optional* The random seed to be used. By default it is set to 1. .. raw:: html
**selection** : *Selection | None, optional* The mating selection operator. If None, the algorithm's default is used. By default it is set to None. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _PYMOO_NSGA3_options: PYMOO_NSGA3 ----------- .. note:: The plugin `gemseo_pymoo `_ is required. Module: :class:`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. .. raw:: html

Required parameters

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

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. .. raw:: html
**eliminate_duplicates** : *bool, optional* If True, eliminate duplicates after merging the parent and the offspring population. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_gen** : *int, optional* The maximum number of generations. By default it is set to 10000000. .. raw:: html
**mutation** : *Mutation | None, optional* The mutation operator. If None, the algorithm's default is used. By default it is set to None. .. raw:: html
**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. .. raw:: html
**n_partitions** : *int, optional* The number of gaps between two consecutive points along an objective axis. By default it is set to 20. .. raw:: html
**n_points** : *int | None, optional* The number of points on the unit simplex. By default it is set to None. .. raw:: html
**normalize_design_space** : *bool, optional* If True, scale the variables to the range [0, 1]. By default it is set to True. .. raw:: html
**partitions** : *ndarray | None, optional* The custom partitions. By default it is set to None. .. raw:: html
**pop_size** : *int, optional* The population size. By default it is set to 100. .. raw:: html
**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. .. raw:: html
**scaling_1** : *float | None, optional* The scaling of the first simplex. By default it is set to None. .. raw:: html
**scaling_2** : *float | None, optional* The scaling of the second simplex. By default it is set to None. .. raw:: html
**seed** : *int, optional* The random seed to be used. By default it is set to 1. .. raw:: html
**selection** : *Selection | None, optional* The mating selection operator. If None, the algorithm's default is used. By default it is set to None. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _PYMOO_RNSGA3_options: PYMOO_RNSGA3 ------------ .. note:: The plugin `gemseo_pymoo `_ is required. Module: :class:`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. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations, i.e. unique calls to f(x). .. raw:: html
**ref_points** : *ndarray | None* The reference points (Aspiration Points) as a NumPy array where each row represents a point and each column a variable. .. raw:: html

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. .. raw:: html
**eliminate_duplicates** : *bool, optional* If True, eliminate duplicates after merging the parent and the offspring population. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_gen** : *int, optional* The maximum number of generations. By default it is set to 10000000. .. raw:: html
**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. .. raw:: html
**mutation** : *Mutation | None, optional* The mutation operator. If None, the algorithm's default is used. By default it is set to None. .. raw:: html
**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. .. raw:: html
**normalize_design_space** : *bool, optional* If True, scale the variables to the range [0, 1]. By default it is set to True. .. raw:: html
**pop_per_ref_point** : *int, optional* The size of the population used for each reference point. By default it is set to 1. .. raw:: html
**pop_size** : *int, optional* The population size. By default it is set to 100. .. raw:: html
**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. .. raw:: html
**seed** : *int, optional* The random seed to be used. By default it is set to 1. .. raw:: html
**selection** : *Selection | None, optional* The mating selection operator. If None, the algorithm's default is used. By default it is set to None. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _PYMOO_UNSGA3_options: PYMOO_UNSGA3 ------------ .. note:: The plugin `gemseo_pymoo `_ is required. Module: :class:`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. .. raw:: html

Required parameters

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

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. .. raw:: html
**eliminate_duplicates** : *bool, optional* If True, eliminate duplicates after merging the parent and the offspring population. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_gen** : *int, optional* The maximum number of generations. By default it is set to 10000000. .. raw:: html
**mutation** : *Mutation | None, optional* The mutation operator. If None, the algorithm's default is used. By default it is set to None. .. raw:: html
**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. .. raw:: html
**n_partitions** : *int, optional* The number of gaps between two consecutive points along an objective axis. By default it is set to 20. .. raw:: html
**n_points** : *int | None, optional* The number of points on the unit simplex. By default it is set to None. .. raw:: html
**normalize_design_space** : *bool, optional* If True, scale the variables to the range [0, 1]. By default it is set to True. .. raw:: html
**partitions** : *ndarray | None, optional* The custom partitions. By default it is set to None. .. raw:: html
**pop_size** : *int, optional* The population size. By default it is set to 100. .. raw:: html
**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. .. raw:: html
**scaling_1** : *float | None, optional* The scaling of the first simplex. By default it is set to None. .. raw:: html
**scaling_2** : *float | None, optional* The scaling of the second simplex. By default it is set to None. .. raw:: html
**seed** : *int, optional* The random seed to be used. By default it is set to 1. .. raw:: html
**selection** : *Selection | None, optional* The mating selection operator. If None, the algorithm's default is used. By default it is set to None. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _REVISED_SIMPLEX_options: REVISED_SIMPLEX --------------- Module: :class:`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. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations, i.e. unique calls to the objective function. .. raw:: html

Optional parameters

**disp** : *bool, optional* Whether to print convergence messages. By default it is set to False. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, scales variables in [0, 1]. By default it is set to True. .. raw:: html

.. _SHGO_options: SHGO ---- Module: :class:`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. .. raw:: html

Required parameters

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

Optional parameters

**eq_tolerance** : *float, optional* The tolerance on equality constraints. By default it is set to 1e-06. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ineq_tolerance** : *float, optional* The tolerance on inequality constraints. By default it is set to 1e-06. .. raw:: html
**iters** : *int, optional* The number of iterations used in the construction of the simplicial complex. By default it is set to 1. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**n** : *int, optional* The number of sampling points used in the construction of the simplicial complex. By default it is set to 100. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, variables are scaled in [0, 1]. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _SIMPLEX_options: SIMPLEX ------- Module: :class:`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. .. raw:: html

Required parameters

**max_iter** : *int* The maximum number of iterations, i.e. unique calls to the objective function. .. raw:: html

Optional parameters

**disp** : *bool, optional* Whether to print convergence messages. By default it is set to False. .. raw:: html
**normalize_design_space** : *bool, optional* If ``True``, scales variables in [0, 1]. By default it is set to True. .. raw:: html

.. _SLSQP_options: SLSQP ----- Module: :class:`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. .. raw:: html

Required parameters

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

Optional parameters

**disp** : *bool, optional* The display information flag. By default it is set to False. .. raw:: html
**eq_tolerance** : *float, optional* The equality tolerance. By default it is set to 0.01. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ineq_tolerance** : *float, optional* The inequality tolerance. By default it is set to 0.0001. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_time** : *float, optional* The maximum runtime in seconds, disabled if 0. By default it is set to 0. .. raw:: html
**normalize_design_space** : *int, optional* If ``True``, scales variables to [0, 1]. By default it is set to True. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _Scipy_MILP_options: Scipy_MILP ---------- Module: :class:`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. .. raw:: 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. .. raw:: html
**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. .. raw:: html
**node_limit** : *int, optional* The maximum number of nodes (linear program relaxations) to solve before stopping. By default it is set to 1000. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html

.. _TNC_options: TNC --- Module: :class:`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. .. raw:: html

Required parameters

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

Optional parameters

**disp** : *bool, optional* The display information flag. By default it is set to False. .. raw:: html
**eq_tolerance** : *float, optional* The equality tolerance. By default it is set to 0.01. .. raw:: html
**eta** : *float, optional* The severity of the line search, specific to the TNC algorithm. By default it is set to -1.0. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**ineq_tolerance** : *float, optional* The inequality tolerance. By default it is set to 0.0001. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html
**max_time** : *float, optional* The maximum runtime in seconds, disabled if 0. By default it is set to 0. .. raw:: html
**maxCGit** : *int, optional* The maximum Conjugate Gradient internal solver iterations. By default it is set to -1. .. raw:: html
**minfev** : *float, optional* The minimum function value estimate. By default it is set to 0.0. .. raw:: html
**normalize_design_space** : *int, optional* If ``True``, scales variables to [0, 1]. By default it is set to True. .. raw:: html
**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. .. raw:: html
**pg_tol** : *float, optional* A stop criteria on the projected gradient norm. By default it is set to 1e-05. .. raw:: html
**rescale** : *float, optional* The scaling factor (in log10) used to trigger f value rescaling. By default it is set to -1. .. raw:: html
**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. .. raw:: html
**stepmx** : *float, optional* The maximum step for the line search. By default it is set to 0.0. .. raw:: html
**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. .. raw:: html
**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. .. raw:: html