knapsack module¶
Knapsack problem.
This module implements the Knapsack problem.
In its simplest form, it states that:
Given a set of items, each with a given weight and value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given weight capacity and the total value is as large as possible.
Multiple variations of the Knapsack problem can be achieved depending on the inputs provided.
Moreover, a multi-objective version of this problem is also available, in which the following new objective function is added to previous formulation:
- class gemseo_pymoo.problems.analytical.knapsack.Knapsack(values, weights, items_ub=None, binary=True, capacity_weight=None, capacity_items=None, initial_guess=None)[source]¶
Bases:
gemseo.algos.opt_problem.OptimizationProblem
Generic knapsack optimization problem.
Different variations can be achieved:
0/1 or Binary Knapsack problem:
Given a set of \(n\) items, each with a weight \(w_i\) and a value \(v_i\), and a knapsack with a maximum weight capacity \(W\). Choose which items to pack in order to maximize the total knapsack value while respecting its weight capacity.
Unbounded Knapsack problem:
With respect to the Binary variant, it removes the restriction that there is only one of each item. This can be achieved by setting the attribute
binary
to False, which will remove the upper bound of the design variables.Bounded Knapsack problem:
With respect to the Binary variant, it specifies an upper bound for each item. This can be achieved by providing an array
items_ub
with the upper bound relative to each item.
Moreover, an additional constraint regarding the total number of items can be added. This is achieved through the attribute
capacity_items
and will limit the number of items that fit into the knapsack.The constructor.
Initialize the Knapsack
OptimizationProblem
by defining theDesignSpace
and the objective and constraint functions.The number of items in the problem is deduced from the
values
array.- Parameters
values (ndarray) – The items’ values.
weights (ndarray) – The items’ weights.
items_ub (ndarray | None) –
The items’ upper bounds. If None, an unlimited number of each item is allowed.
By default it is set to None.
binary (bool) –
If True, the upper bound of design variables is set to 1.
By default it is set to True.
capacity_weight (float | None) –
The knapsack weight capacity. If None, the knapsack will have an unlimited weight capacity.
By default it is set to None.
capacity_items (int | None) –
The knapsack number of items capacity. If None, the knapsack will accept an unlimited total number of items.
By default it is set to None.
initial_guess (ndarray | None) –
The initial guess for the optimal solution. If None, the initial guess will be an empty knapsack (0, 0, …, 0).
By default it is set to None.
- Raises
ValueError – Either if the provided arrays do not have the same length or if no capacity is provided.
- Return type
None
- add_callback(callback_func, each_new_iter=True, each_store=False)¶
Add a callback function after each store operation or new iteration.
- Parameters
callback_func (Callable) – A function to be called after some event.
each_new_iter (bool) –
If True, then callback at every iteration.
By default it is set to True.
each_store (bool) –
If True, then callback at every call to
Database.store()
.By default it is set to False.
- Return type
None
- add_constraint(cstr_func, value=None, cstr_type=None, positive=False)¶
Add a constraint (equality and inequality) to the optimization problem.
- Parameters
cstr_func (MDOFunction) – The constraint.
value (float | None) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
cstr_type (str | None) –
The type of the constraint. Either equality or inequality.
By default it is set to None.
positive (bool) –
If True, then the inequality constraint is positive.
By default it is set to False.
- Raises
TypeError – When the constraint of a linear optimization problem is not an
MDOLinearFunction
.ValueError – When the type of the constraint is missing.
- Return type
None
- add_eq_constraint(cstr_func, value=None)¶
Add an equality constraint to the optimization problem.
- Parameters
cstr_func (MDOFunction) – The constraint.
value (float | None) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
- Return type
None
- add_ineq_constraint(cstr_func, value=None, positive=False)¶
Add an inequality constraint to the optimization problem.
- Parameters
cstr_func (MDOFunction) – The constraint.
value (float | None) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
positive (bool) –
If True, then the inequality constraint is positive.
By default it is set to False.
- Return type
None
- add_observable(obs_func, new_iter=True)¶
Add a function to be observed.
When the
OptimizationProblem
is executed, the observables are called following this sequence:The optimization algorithm calls the objective function with a normalized
x_vect
.The
OptimizationProblem.preprocess_functions()
wraps the function as aNormDBFunction
, which unnormalizes thex_vect
before evaluation.The unnormalized
x_vect
and the result of the evaluation are stored in theOptimizationProblem.database
.The previous step triggers the
OptimizationProblem.new_iter_listeners
, which calls the observables with the unnormalizedx_vect
.The observables themselves are wrapped as a
NormDBFunction
byOptimizationProblem.preprocess_functions()
, but in this case the input is always expected as unnormalized to avoid an additional normalizing-unnormalizing step.Finally, the output is stored in the
OptimizationProblem.database
.
- Parameters
obs_func (gemseo.core.mdofunctions.mdo_function.MDOFunction) – An observable to be observed.
new_iter (bool) –
If True, then the observable will be called at each new iterate.
By default it is set to True.
- Return type
None
- aggregate_constraint(constr_id, method='max', groups=None, **options)¶
Aggregates a constraint to generate a reduced dimension constraint.
- Parameters
constr_id (int) – The index of the constraint in
constraints
.method (str | Callable[[Callable], Callable]) –
The aggregation method, e.g.
"max"
,"KS"
or"IKS"
.By default it is set to max.
groups (tuple[ndarray] | None) –
The groups for which to produce an output. If
None
, a single output constraint is produced.By default it is set to None.
**options (Any) – The options of the aggregation method.
- Raises
ValueError – When the given is index is greater or equal than the number of constraints or when the method is aggregation unknown.
- change_objective_sign()¶
Change the objective function sign in order to minimize its opposite.
The
OptimizationProblem
expresses any optimization problem as a minimization problem. Then, an objective function originally expressed as a performance function to maximize must be converted into a cost function to minimize, by means of this method.- Return type
None
- check()¶
Check if the optimization problem is ready for run.
- Raises
ValueError – If the objective function is missing.
- Return type
None
- static check_format(input_function)¶
Check that a function is an instance of
MDOFunction
.- Parameters
input_function (Any) – The function to be tested.
- Raises
TypeError – If the function is not a
MDOFunction
.- Return type
None
- clear_listeners()¶
Clear all the listeners.
- Return type
None
- static compute_knapsack_items(design_variables)[source]¶
Compute the knapsack number of items.
- Parameters
design_variables (numpy.ndarray) – The design variables vector.
- Returns
The knapsack total number of items.
- Return type
- compute_knapsack_value(design_variables)[source]¶
Compute the knapsack total value.
- Parameters
design_variables (numpy.ndarray) – The design variables vector.
- Returns
The knapsack total value.
- Return type
- compute_knapsack_weight(design_variables)[source]¶
Compute the knapsack total weight.
- Parameters
design_variables (numpy.ndarray) – The design variables vector.
- Returns
The knapsack total weight.
- Return type
- evaluate_functions(x_vect=None, eval_jac=False, eval_obj=True, eval_observables=False, normalize=True, no_db_no_norm=False)¶
Compute the functions of interest, and possibly their derivatives.
These functions of interest are the constraints, and possibly the objective.
Some optimization libraries require the number of constraints as an input parameter which is unknown by the formulation or the scenario. Evaluation of initial point allows to get this mandatory information. This is also used for design of experiments to evaluate samples.
- Parameters
x_vect (ndarray) –
The input vector at which the functions must be evaluated; if None, the initial point x_0 is used.
By default it is set to None.
eval_jac (bool) –
Whether to compute the Jacobian matrices of the functions of interest.
By default it is set to False.
eval_obj (bool) –
Whether to consider the objective function as a function of interest.
By default it is set to True.
normalize (bool) –
Whether to consider the input vector
x_vect
normalized.By default it is set to True.
no_db_no_norm (bool) –
If True, then do not use the pre-processed functions, so we have no database, nor normalization.
By default it is set to False.
eval_observables (bool) –
By default it is set to False.
- Returns
The output values of the functions of interest, as well as their Jacobian matrices if
eval_jac
isTrue
.- Return type
- execute_observables_callback(last_x)¶
The callback function to be passed to the database.
Call all the observables with the last design variables values as argument.
- Parameters
last_x (numpy.ndarray) – The design variables values from the last evaluation.
- Return type
None
- export_hdf(file_path, append=False)¶
Export the optimization problem to an HDF file.
- export_to_dataset(name=None, by_group=True, categorize=True, opt_naming=True, export_gradients=False, input_values=None)¶
Export the database of the optimization problem to a
Dataset
.The variables can be classified into groups:
Dataset.DESIGN_GROUP
orDataset.INPUT_GROUP
for the design variables andDataset.FUNCTION_GROUP
orDataset.OUTPUT_GROUP
for the functions (objective, constraints and observables).- Parameters
name (str | None) –
The name to be given to the dataset. If
None
, use the name of theOptimizationProblem.database
.By default it is set to None.
by_group (bool) –
Whether to store the data by group in
Dataset.data
, in the sense of one unique NumPy array per group. Ifcategorize
isFalse
, there is a unique group:Dataset.PARAMETER_GROUP`
. Ifcategorize
isTrue
, the groups can be eitherDataset.DESIGN_GROUP
andDataset.FUNCTION_GROUP
ifopt_naming
isTrue
, orDataset.INPUT_GROUP
andDataset.OUTPUT_GROUP
. Ifby_group
isFalse
, store the data by variable names.By default it is set to True.
categorize (bool) –
Whether to distinguish between the different groups of variables. Otherwise, group all the variables in
Dataset.PARAMETER_GROUP`
.By default it is set to True.
opt_naming (bool) –
Whether to use
Dataset.DESIGN_GROUP
andDataset.FUNCTION_GROUP
as groups. Otherwise, useDataset.INPUT_GROUP
andDataset.OUTPUT_GROUP
.By default it is set to True.
export_gradients (bool) –
Whether to export the gradients of the functions (objective function, constraints and observables) if the latter are available in the database of the optimization problem.
By default it is set to False.
input_values (Iterable[ndarray] | None) –
The input values to be considered. If
None
, consider all the input values of the database.By default it is set to None.
- Returns
A dataset built from the database of the optimization problem.
- Return type
- get_active_ineq_constraints(x_vect, tol=1e-06)¶
For each constraint, indicate if its different components are active.
- Parameters
x_vect (numpy.ndarray) – The vector of design variables.
tol (float) –
The tolerance for deciding whether a constraint is active.
By default it is set to 1e-06.
- Returns
For each constraint, a boolean indicator of activation of its different components.
- Return type
dict[gemseo.core.mdofunctions.mdo_function.MDOFunction, numpy.ndarray]
- get_all_functions()¶
Retrieve all the functions of the optimization problem.
These functions are the constraints, the objective function and the observables.
- Returns
All the functions of the optimization problem.
- Return type
- get_all_functions_names()¶
Retrieve the names of all the function of the optimization problem.
These functions are the constraints, the objective function and the observables.
- get_best_infeasible_point()¶
Retrieve the best infeasible point within a given tolerance.
- Returns
The best infeasible point expressed as the design variables values, the objective function value, the feasibility of the point and the functions values.
- Return type
Tuple[Optional[numpy.ndarray], Optional[numpy.ndarray], bool, Dict[str, numpy.ndarray]]
- get_constraints_names()¶
Retrieve the names of the constraints.
- get_constraints_number()¶
Retrieve the number of constraints.
- Returns
The number of constraints.
- Return type
- get_data_by_names(names, as_dict=True, filter_non_feasible=False)¶
Return the data for specific names of variables.
- Parameters
- Returns
The data related to the variables.
- Return type
- get_design_variable_names()¶
Retrieve the names of the design variables.
- get_dimension()¶
Retrieve the total number of design variables.
- Returns
The dimension of the design space.
- Return type
- get_eq_constraints()¶
Retrieve all the equality constraints.
- Returns
The equality constraints.
- Return type
- get_eq_constraints_number()¶
Retrieve the number of equality constraints.
- Returns
The number of equality constraints.
- Return type
- get_eq_cstr_total_dim()¶
Retrieve the total dimension of the equality constraints.
This dimension is the sum of all the outputs dimensions of all the equality constraints.
- Returns
The total dimension of the equality constraints.
- Return type
- get_feasible_points()¶
Retrieve the feasible points within a given tolerance.
This tolerance is defined by
OptimizationProblem.eq_tolerance
for equality constraints andOptimizationProblem.ineq_tolerance
for inequality ones.
- get_function_dimension(name)¶
Return the dimension of a function of the problem (e.g. a constraint).
- Parameters
name (str) – The name of the function.
- Returns
The dimension of the function.
- Raises
ValueError – If the function name is unknown to the problem.
RuntimeError – If the function dimension is not unavailable.
- Return type
- get_function_names(names)¶
Return the names of the functions stored in the database.
- get_functions_dimensions(names=None)¶
Return the dimensions of the outputs of the problem functions.
- Parameters
names (Iterable[str] | None) –
The names of the functions. If None, then the objective and all the constraints are considered.
By default it is set to None.
- Returns
The dimensions of the outputs of the problem functions. The dictionary keys are the functions names and the values are the functions dimensions.
- Return type
- get_ineq_constraints()¶
Retrieve all the inequality constraints.
- Returns
The inequality constraints.
- Return type
- get_ineq_constraints_number()¶
Retrieve the number of inequality constraints.
- Returns
The number of inequality constraints.
- Return type
- get_ineq_cstr_total_dim()¶
Retrieve the total dimension of the inequality constraints.
This dimension is the sum of all the outputs dimensions of all the inequality constraints.
- Returns
The total dimension of the inequality constraints.
- Return type
- get_nonproc_constraints()¶
Retrieve the non-processed constraints.
- Returns
The non-processed constraints.
- Return type
- get_nonproc_objective()¶
Retrieve the non-processed objective function.
- get_number_of_unsatisfied_constraints(design_variables)¶
Return the number of scalar constraints not satisfied by design variables.
- Parameters
design_variables (numpy.ndarray) – The design variables.
- Returns
The number of unsatisfied scalar constraints.
- Return type
- get_objective_name(standardize=True)¶
Retrieve the name of the objective function.
- get_observable(name)¶
Retrieve an observable from its name.
- Parameters
name (str) – The name of the observable.
- Returns
The observable.
- Raises
ValueError – If the observable cannot be found.
- Return type
- get_optimum()¶
Return the optimum solution within a given feasibility tolerances.
- Returns
The optimum result, defined by:
the value of the objective function,
the value of the design variables,
the indicator of feasibility of the optimal solution,
the value of the constraints,
the value of the gradients of the constraints.
- Return type
Tuple[numpy.ndarray, numpy.ndarray, bool, Dict[str, numpy.ndarray], Dict[str, numpy.ndarray]]
- get_scalar_constraints_names()¶
Return the names of the scalar constraints.
- get_violation_criteria(x_vect)¶
Compute a violation measure associated to an iteration.
For each constraint, when it is violated, add the absolute distance to zero, in L2 norm.
If 0, all constraints are satisfied
- Parameters
x_vect (numpy.ndarray) – The vector of the design variables values.
- Returns
The feasibility of the point and the violation measure.
- Return type
- get_x0_normalized(cast_to_real=False)¶
Return the current values of the design variables after normalization.
- Parameters
cast_to_real (bool) –
Whether to cast the return value to real.
By default it is set to False.
- Returns
The current values of the design variables normalized between 0 and 1 from their lower and upper bounds.
- Return type
- has_constraints()¶
Check if the problem has equality or inequality constraints.
- Returns
True if the problem has equality or inequality constraints.
- has_eq_constraints()¶
Check if the problem has equality constraints.
- Returns
True if the problem has equality constraints.
- Return type
- has_ineq_constraints()¶
Check if the problem has inequality constraints.
- Returns
True if the problem has inequality constraints.
- Return type
- has_nonlinear_constraints()¶
Check if the problem has non-linear constraints.
- Returns
True if the problem has equality or inequality constraints.
- Return type
- classmethod import_hdf(file_path, x_tolerance=0.0)¶
Import an optimization history from an HDF file.
- Parameters
- Returns
The read optimization problem.
- Return type
- is_max_iter_reached()¶
Check if the maximum amount of iterations has been reached.
- Returns
Whether the maximum amount of iterations has been reached.
- Return type
- is_point_feasible(out_val, constraints=None)¶
Check if a point is feasible.
Note
If the value of a constraint is absent from this point, then this constraint will be considered satisfied.
- Parameters
out_val (dict[str, ndarray]) – The values of the objective function, and eventually constraints.
constraints (Iterable[MDOFunction] | None) –
The constraints whose values are to be tested. If None, then take all constraints of the problem.
By default it is set to None.
- Returns
The feasibility of the point.
- Return type
- preprocess_functions(is_function_input_normalized=True, use_database=True, round_ints=True, eval_obs_jac=False)¶
Pre-process all the functions and eventually the gradient.
Required to wrap the objective function and constraints with the database and eventually the gradients by complex step or finite differences.
- Parameters
is_function_input_normalized (bool) –
Whether to consider the function input as normalized and unnormalize it before the evaluation takes place.
By default it is set to True.
use_database (bool) –
Whether to wrap the functions in the database.
By default it is set to True.
round_ints (bool) –
Whether to round the integer variables.
By default it is set to True.
eval_obs_jac (bool) –
Whether to evaluate the Jacobian of the observables.
By default it is set to False.
- Return type
None
- static repr_constraint(func, ctype, value=None, positive=False)¶
Express a constraint as a string expression.
- Parameters
func (MDOFunction) – The constraint function.
ctype (str) – The type of the constraint. Either equality or inequality.
value (float | None) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
positive (bool) –
If True, then the inequality constraint is positive.
By default it is set to False.
- Returns
A string representation of the constraint.
- Return type
- reset(database=True, current_iter=True, design_space=True, function_calls=True, preprocessing=True)¶
Partially or fully reset the optimization problem.
- Parameters
database (bool) –
Whether to clear the database.
By default it is set to True.
current_iter (bool) –
Whether to reset the current iteration
OptimizationProblem.current_iter
.By default it is set to True.
design_space (bool) –
Whether to reset the current point of the
OptimizationProblem.design_space
to its initial value (possibly none).By default it is set to True.
function_calls (bool) –
Whether to reset the number of calls of the functions.
By default it is set to True.
preprocessing (bool) –
Whether to turn the pre-processing of functions to False.
By default it is set to True.
- Return type
None
- DIFFERENTIATION_METHODS: ClassVar[str] = ['user', 'complex_step', 'finite_differences', 'no_derivatives']¶
- OPTIM_DESCRIPTION: ClassVar[str] = ['minimize_objective', 'fd_step', 'differentiation_method', 'pb_type', 'ineq_tolerance', 'eq_tolerance']¶
- activate_bound_check: ClassVar[bool] = True¶
Whether to check if a point is in the design space before calling functions.
- constraint_names: dict[str, list[str]]¶
The standardized constraint names bound to the original ones.
- constraints: list[MDOFunction]¶
The constraints.
- design_space: DesignSpace¶
The design space on which the optimization problem is solved.
- new_iter_observables: list[MDOFunction]¶
The observables to be called at each new iterate.
- nonproc_constraints: list[MDOFunction]¶
The non-processed constraints.
- nonproc_new_iter_observables: list[MDOFunction]¶
The non-processed observables to be called at each new iterate.
- nonproc_objective: MDOFunction¶
The non-processed objective function.
- nonproc_observables: list[MDOFunction]¶
The non-processed observables.
- property objective: gemseo.core.mdofunctions.mdo_function.MDOFunction¶
The objective function.
- observables: list[MDOFunction]¶
The observables.
- property parallel_differentiation_options: bool¶
The options to approximate the derivatives in parallel.
- solution: OptimizationResult¶
The solution of the optimization problem.
- use_standardized_objective: bool¶
Whether to use standardized objective for logging and post-processing.
The standardized objective corresponds to the original one expressed as a cost function to minimize. A
DriverLib
works with this standardized objective and theDatabase
stores its values. However, for convenience, it may be more relevant to log the expression and the values of the original objective.
- values: ndarray¶
The knapsack items’ value.
- weights: ndarray¶
The knapsack items’ weight.
- class gemseo_pymoo.problems.analytical.knapsack.MultiObjectiveKnapsack(values, weights, items_ub=None, binary=True, capacity_weight=None, capacity_items=None, initial_guess=None)[source]¶
Bases:
gemseo_pymoo.problems.analytical.knapsack.Knapsack
Multi-objective Knapsack optimization problem.
With respect to the single-objective
Knapsack
, it adds an objective relative to the number of items packed. Therefore, besides maximizing the total knapsack value, one must also minimize the total number of items.All the variations of the
Knapsack
problem can still be achieved.The constructor.
Initialize the MultiObjectiveKnapsack
OptimizationProblem
by defining theDesignSpace
and the objective and constraint functions.The number of items in the problem is deduced from the
values
array.- Parameters
values (ndarray) – The items’ values.
weights (ndarray) – The items’ weights.
items_ub (ndarray | None) –
The items’ upper bounds. If None, an unlimited number of each item is allowed.
By default it is set to None.
binary (bool) –
If True, the upper bound of design variables is set to 1.
By default it is set to True.
capacity_weight (float | None) –
The knapsack weight capacity. If None, the knapsack will have an unlimited weight capacity.
By default it is set to None.
capacity_items (int | None) –
The knapsack number of items capacity. If None, the knapsack will accept an unlimited total number of items.
By default it is set to None.
initial_guess (ndarray | None) –
The initial guess for the optimal solution. If None, the initial guess will be an empty knapsack (0, 0, …, 0).
By default it is set to None.
- Return type
None
- add_callback(callback_func, each_new_iter=True, each_store=False)¶
Add a callback function after each store operation or new iteration.
- Parameters
callback_func (Callable) – A function to be called after some event.
each_new_iter (bool) –
If True, then callback at every iteration.
By default it is set to True.
each_store (bool) –
If True, then callback at every call to
Database.store()
.By default it is set to False.
- Return type
None
- add_constraint(cstr_func, value=None, cstr_type=None, positive=False)¶
Add a constraint (equality and inequality) to the optimization problem.
- Parameters
cstr_func (MDOFunction) – The constraint.
value (float | None) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
cstr_type (str | None) –
The type of the constraint. Either equality or inequality.
By default it is set to None.
positive (bool) –
If True, then the inequality constraint is positive.
By default it is set to False.
- Raises
TypeError – When the constraint of a linear optimization problem is not an
MDOLinearFunction
.ValueError – When the type of the constraint is missing.
- Return type
None
- add_eq_constraint(cstr_func, value=None)¶
Add an equality constraint to the optimization problem.
- Parameters
cstr_func (MDOFunction) – The constraint.
value (float | None) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
- Return type
None
- add_ineq_constraint(cstr_func, value=None, positive=False)¶
Add an inequality constraint to the optimization problem.
- Parameters
cstr_func (MDOFunction) – The constraint.
value (float | None) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
positive (bool) –
If True, then the inequality constraint is positive.
By default it is set to False.
- Return type
None
- add_observable(obs_func, new_iter=True)¶
Add a function to be observed.
When the
OptimizationProblem
is executed, the observables are called following this sequence:The optimization algorithm calls the objective function with a normalized
x_vect
.The
OptimizationProblem.preprocess_functions()
wraps the function as aNormDBFunction
, which unnormalizes thex_vect
before evaluation.The unnormalized
x_vect
and the result of the evaluation are stored in theOptimizationProblem.database
.The previous step triggers the
OptimizationProblem.new_iter_listeners
, which calls the observables with the unnormalizedx_vect
.The observables themselves are wrapped as a
NormDBFunction
byOptimizationProblem.preprocess_functions()
, but in this case the input is always expected as unnormalized to avoid an additional normalizing-unnormalizing step.Finally, the output is stored in the
OptimizationProblem.database
.
- Parameters
obs_func (gemseo.core.mdofunctions.mdo_function.MDOFunction) – An observable to be observed.
new_iter (bool) –
If True, then the observable will be called at each new iterate.
By default it is set to True.
- Return type
None
- aggregate_constraint(constr_id, method='max', groups=None, **options)¶
Aggregates a constraint to generate a reduced dimension constraint.
- Parameters
constr_id (int) – The index of the constraint in
constraints
.method (str | Callable[[Callable], Callable]) –
The aggregation method, e.g.
"max"
,"KS"
or"IKS"
.By default it is set to max.
groups (tuple[ndarray] | None) –
The groups for which to produce an output. If
None
, a single output constraint is produced.By default it is set to None.
**options (Any) – The options of the aggregation method.
- Raises
ValueError – When the given is index is greater or equal than the number of constraints or when the method is aggregation unknown.
- change_objective_sign()¶
Change the objective function sign in order to minimize its opposite.
The
OptimizationProblem
expresses any optimization problem as a minimization problem. Then, an objective function originally expressed as a performance function to maximize must be converted into a cost function to minimize, by means of this method.- Return type
None
- check()¶
Check if the optimization problem is ready for run.
- Raises
ValueError – If the objective function is missing.
- Return type
None
- static check_format(input_function)¶
Check that a function is an instance of
MDOFunction
.- Parameters
input_function (Any) – The function to be tested.
- Raises
TypeError – If the function is not a
MDOFunction
.- Return type
None
- clear_listeners()¶
Clear all the listeners.
- Return type
None
- static compute_knapsack_items(design_variables)¶
Compute the knapsack number of items.
- Parameters
design_variables (numpy.ndarray) – The design variables vector.
- Returns
The knapsack total number of items.
- Return type
- compute_knapsack_value(design_variables)¶
Compute the knapsack total value.
- Parameters
design_variables (numpy.ndarray) – The design variables vector.
- Returns
The knapsack total value.
- Return type
- compute_knapsack_weight(design_variables)¶
Compute the knapsack total weight.
- Parameters
design_variables (numpy.ndarray) – The design variables vector.
- Returns
The knapsack total weight.
- Return type
- evaluate_functions(x_vect=None, eval_jac=False, eval_obj=True, eval_observables=False, normalize=True, no_db_no_norm=False)¶
Compute the functions of interest, and possibly their derivatives.
These functions of interest are the constraints, and possibly the objective.
Some optimization libraries require the number of constraints as an input parameter which is unknown by the formulation or the scenario. Evaluation of initial point allows to get this mandatory information. This is also used for design of experiments to evaluate samples.
- Parameters
x_vect (ndarray) –
The input vector at which the functions must be evaluated; if None, the initial point x_0 is used.
By default it is set to None.
eval_jac (bool) –
Whether to compute the Jacobian matrices of the functions of interest.
By default it is set to False.
eval_obj (bool) –
Whether to consider the objective function as a function of interest.
By default it is set to True.
normalize (bool) –
Whether to consider the input vector
x_vect
normalized.By default it is set to True.
no_db_no_norm (bool) –
If True, then do not use the pre-processed functions, so we have no database, nor normalization.
By default it is set to False.
eval_observables (bool) –
By default it is set to False.
- Returns
The output values of the functions of interest, as well as their Jacobian matrices if
eval_jac
isTrue
.- Return type
- execute_observables_callback(last_x)¶
The callback function to be passed to the database.
Call all the observables with the last design variables values as argument.
- Parameters
last_x (numpy.ndarray) – The design variables values from the last evaluation.
- Return type
None
- export_hdf(file_path, append=False)¶
Export the optimization problem to an HDF file.
- export_to_dataset(name=None, by_group=True, categorize=True, opt_naming=True, export_gradients=False, input_values=None)¶
Export the database of the optimization problem to a
Dataset
.The variables can be classified into groups:
Dataset.DESIGN_GROUP
orDataset.INPUT_GROUP
for the design variables andDataset.FUNCTION_GROUP
orDataset.OUTPUT_GROUP
for the functions (objective, constraints and observables).- Parameters
name (str | None) –
The name to be given to the dataset. If
None
, use the name of theOptimizationProblem.database
.By default it is set to None.
by_group (bool) –
Whether to store the data by group in
Dataset.data
, in the sense of one unique NumPy array per group. Ifcategorize
isFalse
, there is a unique group:Dataset.PARAMETER_GROUP`
. Ifcategorize
isTrue
, the groups can be eitherDataset.DESIGN_GROUP
andDataset.FUNCTION_GROUP
ifopt_naming
isTrue
, orDataset.INPUT_GROUP
andDataset.OUTPUT_GROUP
. Ifby_group
isFalse
, store the data by variable names.By default it is set to True.
categorize (bool) –
Whether to distinguish between the different groups of variables. Otherwise, group all the variables in
Dataset.PARAMETER_GROUP`
.By default it is set to True.
opt_naming (bool) –
Whether to use
Dataset.DESIGN_GROUP
andDataset.FUNCTION_GROUP
as groups. Otherwise, useDataset.INPUT_GROUP
andDataset.OUTPUT_GROUP
.By default it is set to True.
export_gradients (bool) –
Whether to export the gradients of the functions (objective function, constraints and observables) if the latter are available in the database of the optimization problem.
By default it is set to False.
input_values (Iterable[ndarray] | None) –
The input values to be considered. If
None
, consider all the input values of the database.By default it is set to None.
- Returns
A dataset built from the database of the optimization problem.
- Return type
- get_active_ineq_constraints(x_vect, tol=1e-06)¶
For each constraint, indicate if its different components are active.
- Parameters
x_vect (numpy.ndarray) – The vector of design variables.
tol (float) –
The tolerance for deciding whether a constraint is active.
By default it is set to 1e-06.
- Returns
For each constraint, a boolean indicator of activation of its different components.
- Return type
dict[gemseo.core.mdofunctions.mdo_function.MDOFunction, numpy.ndarray]
- get_all_functions()¶
Retrieve all the functions of the optimization problem.
These functions are the constraints, the objective function and the observables.
- Returns
All the functions of the optimization problem.
- Return type
- get_all_functions_names()¶
Retrieve the names of all the function of the optimization problem.
These functions are the constraints, the objective function and the observables.
- get_best_infeasible_point()¶
Retrieve the best infeasible point within a given tolerance.
- Returns
The best infeasible point expressed as the design variables values, the objective function value, the feasibility of the point and the functions values.
- Return type
Tuple[Optional[numpy.ndarray], Optional[numpy.ndarray], bool, Dict[str, numpy.ndarray]]
- get_constraints_names()¶
Retrieve the names of the constraints.
- get_constraints_number()¶
Retrieve the number of constraints.
- Returns
The number of constraints.
- Return type
- get_data_by_names(names, as_dict=True, filter_non_feasible=False)¶
Return the data for specific names of variables.
- Parameters
- Returns
The data related to the variables.
- Return type
- get_design_variable_names()¶
Retrieve the names of the design variables.
- get_dimension()¶
Retrieve the total number of design variables.
- Returns
The dimension of the design space.
- Return type
- get_eq_constraints()¶
Retrieve all the equality constraints.
- Returns
The equality constraints.
- Return type
- get_eq_constraints_number()¶
Retrieve the number of equality constraints.
- Returns
The number of equality constraints.
- Return type
- get_eq_cstr_total_dim()¶
Retrieve the total dimension of the equality constraints.
This dimension is the sum of all the outputs dimensions of all the equality constraints.
- Returns
The total dimension of the equality constraints.
- Return type
- get_feasible_points()¶
Retrieve the feasible points within a given tolerance.
This tolerance is defined by
OptimizationProblem.eq_tolerance
for equality constraints andOptimizationProblem.ineq_tolerance
for inequality ones.
- get_function_dimension(name)¶
Return the dimension of a function of the problem (e.g. a constraint).
- Parameters
name (str) – The name of the function.
- Returns
The dimension of the function.
- Raises
ValueError – If the function name is unknown to the problem.
RuntimeError – If the function dimension is not unavailable.
- Return type
- get_function_names(names)¶
Return the names of the functions stored in the database.
- get_functions_dimensions(names=None)¶
Return the dimensions of the outputs of the problem functions.
- Parameters
names (Iterable[str] | None) –
The names of the functions. If None, then the objective and all the constraints are considered.
By default it is set to None.
- Returns
The dimensions of the outputs of the problem functions. The dictionary keys are the functions names and the values are the functions dimensions.
- Return type
- get_ineq_constraints()¶
Retrieve all the inequality constraints.
- Returns
The inequality constraints.
- Return type
- get_ineq_constraints_number()¶
Retrieve the number of inequality constraints.
- Returns
The number of inequality constraints.
- Return type
- get_ineq_cstr_total_dim()¶
Retrieve the total dimension of the inequality constraints.
This dimension is the sum of all the outputs dimensions of all the inequality constraints.
- Returns
The total dimension of the inequality constraints.
- Return type
- get_nonproc_constraints()¶
Retrieve the non-processed constraints.
- Returns
The non-processed constraints.
- Return type
- get_nonproc_objective()¶
Retrieve the non-processed objective function.
- get_number_of_unsatisfied_constraints(design_variables)¶
Return the number of scalar constraints not satisfied by design variables.
- Parameters
design_variables (numpy.ndarray) – The design variables.
- Returns
The number of unsatisfied scalar constraints.
- Return type
- get_objective_name(standardize=True)¶
Retrieve the name of the objective function.
- get_observable(name)¶
Retrieve an observable from its name.
- Parameters
name (str) – The name of the observable.
- Returns
The observable.
- Raises
ValueError – If the observable cannot be found.
- Return type
- get_optimum()¶
Return the optimum solution within a given feasibility tolerances.
- Returns
The optimum result, defined by:
the value of the objective function,
the value of the design variables,
the indicator of feasibility of the optimal solution,
the value of the constraints,
the value of the gradients of the constraints.
- Return type
Tuple[numpy.ndarray, numpy.ndarray, bool, Dict[str, numpy.ndarray], Dict[str, numpy.ndarray]]
- get_scalar_constraints_names()¶
Return the names of the scalar constraints.
- get_violation_criteria(x_vect)¶
Compute a violation measure associated to an iteration.
For each constraint, when it is violated, add the absolute distance to zero, in L2 norm.
If 0, all constraints are satisfied
- Parameters
x_vect (numpy.ndarray) – The vector of the design variables values.
- Returns
The feasibility of the point and the violation measure.
- Return type
- get_x0_normalized(cast_to_real=False)¶
Return the current values of the design variables after normalization.
- Parameters
cast_to_real (bool) –
Whether to cast the return value to real.
By default it is set to False.
- Returns
The current values of the design variables normalized between 0 and 1 from their lower and upper bounds.
- Return type
- has_constraints()¶
Check if the problem has equality or inequality constraints.
- Returns
True if the problem has equality or inequality constraints.
- has_eq_constraints()¶
Check if the problem has equality constraints.
- Returns
True if the problem has equality constraints.
- Return type
- has_ineq_constraints()¶
Check if the problem has inequality constraints.
- Returns
True if the problem has inequality constraints.
- Return type
- has_nonlinear_constraints()¶
Check if the problem has non-linear constraints.
- Returns
True if the problem has equality or inequality constraints.
- Return type
- classmethod import_hdf(file_path, x_tolerance=0.0)¶
Import an optimization history from an HDF file.
- Parameters
- Returns
The read optimization problem.
- Return type
- is_max_iter_reached()¶
Check if the maximum amount of iterations has been reached.
- Returns
Whether the maximum amount of iterations has been reached.
- Return type
- is_point_feasible(out_val, constraints=None)¶
Check if a point is feasible.
Note
If the value of a constraint is absent from this point, then this constraint will be considered satisfied.
- Parameters
out_val (dict[str, ndarray]) – The values of the objective function, and eventually constraints.
constraints (Iterable[MDOFunction] | None) –
The constraints whose values are to be tested. If None, then take all constraints of the problem.
By default it is set to None.
- Returns
The feasibility of the point.
- Return type
- preprocess_functions(is_function_input_normalized=True, use_database=True, round_ints=True, eval_obs_jac=False)¶
Pre-process all the functions and eventually the gradient.
Required to wrap the objective function and constraints with the database and eventually the gradients by complex step or finite differences.
- Parameters
is_function_input_normalized (bool) –
Whether to consider the function input as normalized and unnormalize it before the evaluation takes place.
By default it is set to True.
use_database (bool) –
Whether to wrap the functions in the database.
By default it is set to True.
round_ints (bool) –
Whether to round the integer variables.
By default it is set to True.
eval_obs_jac (bool) –
Whether to evaluate the Jacobian of the observables.
By default it is set to False.
- Return type
None
- static repr_constraint(func, ctype, value=None, positive=False)¶
Express a constraint as a string expression.
- Parameters
func (MDOFunction) – The constraint function.
ctype (str) – The type of the constraint. Either equality or inequality.
value (float | None) –
The value for which the constraint is active. If None, this value is 0.
By default it is set to None.
positive (bool) –
If True, then the inequality constraint is positive.
By default it is set to False.
- Returns
A string representation of the constraint.
- Return type
- reset(database=True, current_iter=True, design_space=True, function_calls=True, preprocessing=True)¶
Partially or fully reset the optimization problem.
- Parameters
database (bool) –
Whether to clear the database.
By default it is set to True.
current_iter (bool) –
Whether to reset the current iteration
OptimizationProblem.current_iter
.By default it is set to True.
design_space (bool) –
Whether to reset the current point of the
OptimizationProblem.design_space
to its initial value (possibly none).By default it is set to True.
function_calls (bool) –
Whether to reset the number of calls of the functions.
By default it is set to True.
preprocessing (bool) –
Whether to turn the pre-processing of functions to False.
By default it is set to True.
- Return type
None
- DIFFERENTIATION_METHODS: ClassVar[str] = ['user', 'complex_step', 'finite_differences', 'no_derivatives']¶
- OPTIM_DESCRIPTION: ClassVar[str] = ['minimize_objective', 'fd_step', 'differentiation_method', 'pb_type', 'ineq_tolerance', 'eq_tolerance']¶
- activate_bound_check: ClassVar[bool] = True¶
Whether to check if a point is in the design space before calling functions.
- constraint_names: dict[str, list[str]]¶
The standardized constraint names bound to the original ones.
- constraints: list[MDOFunction]¶
The constraints.
- design_space: DesignSpace¶
The design space on which the optimization problem is solved.
- new_iter_observables: list[MDOFunction]¶
The observables to be called at each new iterate.
- nonproc_constraints: list[MDOFunction]¶
The non-processed constraints.
- nonproc_new_iter_observables: list[MDOFunction]¶
The non-processed observables to be called at each new iterate.
- nonproc_objective: MDOFunction¶
The non-processed objective function.
- nonproc_observables: list[MDOFunction]¶
The non-processed observables.
- property objective: gemseo.core.mdofunctions.mdo_function.MDOFunction¶
The objective function.
- observables: list[MDOFunction]¶
The observables.
- property parallel_differentiation_options: bool¶
The options to approximate the derivatives in parallel.
- solution: OptimizationResult¶
The solution of the optimization problem.
- use_standardized_objective: bool¶
Whether to use standardized objective for logging and post-processing.
The standardized objective corresponds to the original one expressed as a cost function to minimize. A
DriverLib
works with this standardized objective and theDatabase
stores its values. However, for convenience, it may be more relevant to log the expression and the values of the original objective.
- values: ndarray¶
The knapsack items’ value.
- weights: ndarray¶
The knapsack items’ weight.
- gemseo_pymoo.problems.analytical.knapsack.create_random_knapsack_problem(n_items, capacity_level=0.1, binary=True, obj_variant='single')[source]¶
Create a random
Knapsack
problem.One can also create a
MultiObjectiveKnapsack
problem by providingobj_variant
= ‘multi’.The value and the weight of the items are integers randomly generated between 1 and 100.
- Parameters
n_items (int) – The size of the set of items.
capacity_level (float) –
The percentage of the set of items total weight corresponding to the knapsack capacity.
By default it is set to 0.1.
binary (bool) –
If True, only one unit of each item is allowed.
By default it is set to True.
obj_variant (str) –
Single-objective (‘single’) or multi-objective (‘multi’) problem.
By default it is set to single.
- Returns
- An instance of
Knapsack
orMultiObjectiveKnapsack
depending on the
obj_variant
provided.
- An instance of
- Raises
ValueError – Either if the number of items is not a positive integer or if the capacity_level is outside the range (0, 1).
- Return type
- gemseo_pymoo.problems.analytical.knapsack.randint(low, high=None, size=None, dtype=int)¶
Return random integers from low (inclusive) to high (exclusive).
Return random integers from the “discrete uniform” distribution of the specified dtype in the “half-open” interval [low, high). If high is None (the default), then results are from [0, low).
Note
New code should use the
integers
method of adefault_rng()
instance instead; please see the Quick Start.- Parameters
low (int or array-like of ints) – Lowest (signed) integers to be drawn from the distribution (unless
high=None
, in which case this parameter is one above the highest such integer).high (int or array-like of ints, optional) – If provided, one above the largest (signed) integer to be drawn from the distribution (see above for behavior if
high=None
). If array-like, must contain integer valuessize (int or tuple of ints, optional) – Output shape. If the given shape is, e.g.,
(m, n, k)
, thenm * n * k
samples are drawn. Default is None, in which case a single value is returned.dtype (dtype, optional) –
Desired dtype of the result. Byteorder must be native. The default value is int.
New in version 1.11.0.
- Returns
out – size-shaped array of random integers from the appropriate distribution, or a single such random int if size not provided.
- Return type
int or ndarray of ints
See also
random_integers
similar to randint, only for the closed interval [low, high], and 1 is the lowest value if high is omitted.
Generator.integers
which should be used for new code.
Examples
>>> np.random.randint(2, size=10) array([1, 0, 0, 0, 1, 1, 0, 0, 1, 0]) # random >>> np.random.randint(1, size=10) array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
Generate a 2 x 4 array of ints between 0 and 4, inclusive:
>>> np.random.randint(5, size=(2, 4)) array([[4, 0, 2, 1], # random [3, 2, 2, 0]])
Generate a 1 x 3 array with 3 different upper bounds
>>> np.random.randint(1, [3, 5, 10]) array([2, 2, 9]) # random
Generate a 1 by 3 array with 3 different lower bounds
>>> np.random.randint([1, 5, 7], 10) array([9, 8, 7]) # random
Generate a 2 by 4 array using broadcasting with dtype of uint8
>>> np.random.randint([1, 3, 5, 7], [[10], [20]], dtype=np.uint8) array([[ 8, 6, 9, 7], # random [ 1, 16, 9, 12]], dtype=uint8)