LSModel Class¶

Summary¶

Attributes¶

nb_expressions	Number of expressions in this model.
nb_operands	Number of operands in this model.
nb_objectives	Number of objectives in this model.
nb_constraints	Number of constraints in this model.
nb_decisions	Number of decisions in this model.
expressions	List of the expressions of the model.
decisions	List of the decisions of the model.
objectives	List of the objectives of the model.
objective_directions	List of the objective directions of the model.
constraints	List of the constraints of the model.

Methods¶

create_constant	Creates a constant expression representing the given value.
create_expression	Creates a new expression of the given type with the given operands.
create_lambda_function	Creates a lambda function with arguments.
lambda_function	Shortcut for create_lambda_function().
create_int_external_function	Creates an integer external function.
int_external_function	Shortcut for create_int_external_function().
create_double_external_function	Creates a double external function.
double_external_function	Shortcut for create_double_external_function().
create_double_blackbox_function	Creates a double black-box function.
double_blackbox_function	Shortcut for create_double_blackbox_function().
get_nb_expressions	Returns the number of expressions added to this model.
get_expression	Gets the expression with the given index or the given name in this model.
get_nb_decisions	Gets the number of decisions in the model.
get_decision	Gets the decision with the given index.
add_constraint	Adds the given expression to the list of constraints.
constraint	Shortcut for add_constraint().
remove_constraint	Removes the given expression from the list of constraints.
get_nb_constraints	Gets the number of constraints added to this model.
get_constraint	Gets the constraint with the given index.
add_objective	Adds the given expression to the list of objectives to optimize.
minimize	Shortcut for add_objective(expr, LSObjectiveDirection.MINIMIZE).
maximize	Shortcut for add_objective(expr, LSObjectiveDirection.MAXIMIZE).
remove_objective	Removes the objective at the given position in the list of objectives.
get_nb_objectives	Gets the number of objectives added to this model.
get_objective	Gets the objective with the given index.
get_objective_direction	Gets the direction of the objective with the given index.
get_nb_operands	Gets the number of operands in the model.
close	Closes the model.
open	Reopens the model.
is_closed	Returns true if the model is closed, false otherwise.
bool	Creates a boolean decision.
float	Creates a float decision.
int	Creates an integer decision.
sum	Creates a sum expression.
sub	Creates a substraction expression.
prod	Creates a product expression.
max	Creates a max expression.
min	Creates a min expression.
or_	Creates a boolean or expression.
and_	Creates a boolean and expression.
xor	Creates a boolean xor expression.
not_	Creates a boolean not expression.
eq	Creates an equality expression.
neq	Creates a disequality expression.
geq	Creates an inequality ‘greater than or equal to’.
leq	Creates an inequality ‘lower than or equal to’.
gt	Creates an inequality ‘strictly greater than’.
lt	Creates an inequality ‘strictly lower than’.
iif	Creates a ternary conditional operator.
abs	Creates an absolute value expression.
dist	Creates a distance expression.
div	Creates a division expression.
mod	Creates a modulo expression.
array	Creates a new array.
at	Creates a “at” expression.
scalar	Creates a scalar product between two arrays.
ceil	Creates a ceil expression.
floor	Creates a floor expression.
round	Creates a round expression.
sqrt	Creates a square root expression.
log	Creates a natural log expression.
exp	Creates an exponential expression.
pow	Creates a power expression.
cos	Creates a cosine expression.
sin	Creates a sine expression.
tan	Creates a tangent expression.
piecewise	Creates a piecewise linear expression.
list	Creates a list decision with the given length.
set	Creates a set decision with the given length.
count	Creates a count expression.
index	Creates an indexOf expression.
contains	Creates a contains expression.
partition	Creates a partition expression.
disjoint	Creates a disjoint expression.
call	Creates a call expression.
range	Creates a range expression.

Special methods¶

__str__

Returns a string representation of this model.

Instance methods¶

LSModel.create_constant(value)¶

Creates a constant expression representing the given value. The given value can be a boolean, an integer or a double. Only allowed in state LSState.MODELING. Note that if a constant has been already created with the same value, this method can return the same expression, but it is not guaranteed. The exact behavior is implementation defined.

Parameters:	value – Value of the constant (can be a boolean, integer or double).
Returns:	Created constant expression
Return type:	LSExpression

LSModel.create_expression(operator)¶

localsolver.create_expression(operator, operands)¶

localsolver.create_expression(operator, *operands)

Creates a new expression of the given type with the given operands. Only allowed in state LSState.MODELING. This method cannot be used to create constants: use LSModel.create_constant() instead.

The operands parameter accept any object that implements the __iter__ method. Thus, lists, tuples, sets and their comprehensions counterpart are accepted. It is also possible to use this method with a variadic number of arguments.

Each operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	operator (LSOperator) – Type of the expression to create. operands – Operands to add. An iterable or any number of arguments.
Returns:	Created expression
Return type:	LSExpression

LSModel.create_lambda_function(function)¶

Creates a lambda function with arguments. A lambda function is a particular expression composed of two parts:

• The arguments of the function (which are also LSExpressions of type LSOperator.ARGUMENT).
• The body of the function. The body is an LSExpression that will be used to evaluate the result of the function. The body can be any LSExpression composed of any operands and operators supported by LocalSolver. Thus, the body expression can use the arguments of the function but can also capture and refer to expressions declared outside of the function.

The function you provide will not be used directly during the solving process, but will be evaluated once by the API, with a number of LSExpression of type LSOperator.ARGUMENT that corresponds to the number of arguments you want and your function expects. At the end of the evaluation of your function, the returned LSExpression will be used as the body of the LocalSolver function.

Since:	9.5
Parameters:	function – A python function that accepts LSExpression as arguments and returns an LSExpression that will be used as the body of the new LocalSolver function you want to create.
Returns:	Expression of type LSOperator.LAMBDA_FUNCTION
Return type:	LSExpression

LSModel.lambda_function(function)¶

Shortcut for create_lambda_function().

Since:	9.5
Parameters:	function – A python function that accepts LSExpression as arguments and returns an LSExpression that will be used as the body of the new LocalSolver function you want to create.
Returns:	Expression of type LSOperator.LAMBDA_FUNCTION
Return type:	LSExpression

LSModel.create_int_external_function(function)¶

Creates an integer external function. The provided function must take the external argument values (LSExternalArgumentValues) associated with the function as single argument and must return an integer value. When the external function is called, the argument values will be made accessible to your function through the LSExternalArgumentValues.

Once you have instantiated it, you have to use call() to call it in your model.

Note 1: Most of the time your external function will be called when the solver is in state LSState.RUNNING. Do not attempt to call any method of the solver (to retrieve statistics, values of LSExpressions or whatever) in that state or an exception will be thrown. The only accessible function is LocalSolver.stop().

Note 2: Your functions must be thread-safe. According to the “nb_threads” parameter, LocalSolver can be multi-threaded. In that case, your external functions must be thread safe. If you cannot guarantee the thread-safety of your code, we strongly recommend you to limit the search of LocalSolver to one thread with LSParam.nb_threads.

Note 3: You can provide additional data concerning your function (such as lower and upper bounds) with the help of the LSExternalContext associated with your function (see LSExpression.get_external_context().

Since:	9.5
Parameters:	function – A python function that accepts a LSExternalArgumentValues as first argument and returns an integer value.
Returns:	Expression of type LSOperator.EXTERNAL_FUNCTION.
Return type:	LSExpression

LSModel.int_external_function(function)¶

Shortcut for create_int_external_function().

Since:	9.5
Parameters:	function – A python function that accepts a LSExternalArgumentValues as first argument and returns an integer value.
Returns:	Expression of type LSOperator.EXTERNAL_FUNCTION.
Return type:	LSExpression

LSModel.create_double_external_function(function)¶

Creates a double external function. The provided function must take the external argument values (LSExternalArgumentValues) associated with the function as single argument and must return a double value. When the external function is called, the argument values will be made accessible to your function through the LSExternalArgumentValues.

Once you have instantiated it, you have to use call() to call it in your model.

Note 1: Most of the time your external function will be called when the solver is in state LSState.RUNNING. Do not attempt to call any method of the solver (to retrieve statistics, values of LSExpressions or whatever) in that state or an exception will be thrown. The only accessible function is LocalSolver.stop().

Note 2: Your functions must be thread-safe. According to the “nb_threads” parameter, LocalSolver can be multi-threaded. In that case, your external functions must be thread safe. If you cannot guarantee the thread-safety of your code, we strongly recommend you to limit the search of LocalSolver to one thread with LSParam.nb_threads.

Note 3: You can provide additional data concerning your function (such as lower and upper bounds) with the help of the LSExternalContext associated with your function (see LSExpression.get_external_context().

Since:	9.5
Parameters:	function – A python function that accepts a LSExternalArgumentValues as first argument and returns a double value.
Returns:	Expression of type LSOperator.EXTERNAL_FUNCTION.
Return type:	LSExpression

LSModel.double_external_function(function)¶

Shortcut for create_double_external_function().

Since:	9.5
Parameters:	function – A python function that accepts a LSExternalArgumentValues as first argument and returns a double value.
Returns:	Expression of type LSOperator.EXTERNAL_FUNCTION.
Return type:	LSExpression

LSModel.create_double_blackbox_function(function)¶

Creates a double black-box function. The provided function must take a (LSBlackBoxArgumentValues) as single argument and must return a double value. When the black-box function is called, the argument values will be made accessible to your function through the LSBlackBoxArgumentValues.

Once you have instantiated it, you have to use call() to call it in your model.

Note: You can provide additional data and parameters for your function (such as bounds or the maximum number of evaluations) with the help of the LSBlackBoxContext associated with your function (see LSExpression.get_blackbox_context()).

Since:	9.5
Parameters:	function – A python function that accepts a LSBlackBoxArgumentValues as first argument and returns a double value.
Returns:	Expression of type LSOperator.BLACKBOX_FUNCTION.
Return type:	LSExpression

LSModel.double_blackbox_function(function)¶

Shortcut for create_double_blackbox_function().

Since:	9.5
Parameters:	function – A python function that accepts a LSBlackBoxArgumentValues as first argument and returns a double value
Returns:	Expression of type LSOperator.BLACKBOX_FUNCTION.
Return type:	LSExpression

LSModel.get_nb_expressions()¶

Returns the number of expressions added to this model.

You can also use the shortcut member nb_expressions

Returns:	Number of expressions.
Return type:	int

LSModel.get_expression(expr_index)¶

localsolver.get_expression(expr_name)¶

Gets the expression with the given index or the given name in this model. Throws an exception if no expression with the given name or the given index exists.

You can also use the shortcut member expressions

Parameters:	expr_index (int) – Index of the expression expr_name (str) – Name of the expression.
Returns:	Expression with the given index
Return type:	LSExpression

LSModel.get_nb_decisions()¶

Gets the number of decisions in the model. This corresponds to the number of decision variables declared in the model.

You can also use the shortcut member nb_decisions

Returns:	Number of decisions in the model.
Return type:	int

LSModel.get_decision(decision_index)¶

Gets the decision with the given index.

You can also use the shortcut member decisions

Parameters:	decision_index (int) – Index of the decision
Returns:	Decision with the given index
Return type:	LSExpression

LSModel.add_constraint(expr)¶

Adds the given expression to the list of constraints. It means that the value of this expression must be constrained to be equal to 1 in any solution found by the solver. Hence, only boolean expressions (that is, expressions whose value is boolean) can be constrained. Only allowed in state LSState.MODELING. If the expression is already a constraint, this method does nothing and returns immediately.

Parameters:	expr (LSExpression) – Expression

LSModel.constraint(expr)¶

Shortcut for add_constraint().

You can also use the shortcut member constraints

Parameters:	expr (LSExpression) – Expression
Since:	5.5

LSModel.remove_constraint(expr)¶

LSModel.remove_constraint(constraint_index)

Removes the given expression from the list of constraints. If the expression was not constrained, this method does nothing and returns immediately. Only allowed in state LSState.MODELING.

Parameters:	expr (LSExpression) – Expression. constraint_index (int) – Index of the constraint to remove.
Since:	5.0

LSModel.get_nb_constraints()¶

Gets the number of constraints added to this model.

You can also use the shortcut member nb_constraints

Returns:	Number of constraints
Return type:	int

LSModel.get_constraint(index)¶

Gets the constraint with the given index.

Parameters:	index (int) – Index of the constraint
Returns:	Constraint with the given index.
Return type:	LSExpression

LSModel.add_objective(expr, direction)¶

Adds the given expression to the list of objectives to optimize. A same expression can be added more than once. Only allowed in state LSState.MODELING. Note that the objectives will be optimized in the order in which they have been added to the model. It is useful for lexicographic multiobjective optimization, and more particularly for goal programming.

Parameters:	expr (LSExpression) – Expression direction (LSObjectiveDirection) – Optimization direction of this objective

LSModel.minimize(expr)¶

Shortcut for add_objective(expr, LSObjectiveDirection.MINIMIZE).

Parameters:	expr (LSExpression) – Expression

LSModel.maximize(expr)¶

Shortcut for add_objective(expr, LSObjectiveDirection.MAXIMIZE).

Parameters:	expr (LSExpression) – Expression

LSModel.remove_objective(obj_index)¶

Removes the objective at the given position in the list of objectives. Note that the objectives created after the removed one have their index decreased by 1. Phases are not modified when an objective is removed. It is the user’s responsibility to change the objective index of each phase to keep it coherent (with LSPhase.set_optimized_objective() or to disable it (with LSPhase.enabled). Only allowed in state LSState.MODELING.

Parameters:	obj_index (int) – Position of the objective to remove.
Since:	5.0

LSModel.get_nb_objectives()¶

Gets the number of objectives added to this model.

You can also use the shortcut member nb_objectives

Returns:	Number of objectives
Return type:	int

LSModel.get_objective(obj_index)¶

Gets the objective with the given index.

You can also use the shortcut member objectives

Parameters:	obj_index (int) – Index of the objective
Returns:	Objective with the given index
Return type:	LSExpression

LSModel.get_objective_direction(obj_index)¶

Gets the direction of the objective with the given index.

You can also use the shortcut member objective_directions

Parameters:	obj_index (int) – Index of the objective
Returns:	Objective direction
Return type:	LSObjectiveDirection

LSModel.get_nb_operands()¶

Gets the number of operands in the model. This corresponds to the number of operands for all expressions declared in the model. It is an analog of the number of non zeros in matrix model encountered in mathematical programming: it gives an hint about the size and the density of your model.

You can also use the shortcut member nb_operands

Returns:	Number of operands.
Return type:	int

LSModel.close()¶

Closes the model. Only allowed in state LSState.MODELING. When this method is called, the solver is placed in state LSState.STOPPED.

Once the model is closed, no expressions, constraints or objectives can be added or removed unless the model is reopened. The model must be closed before starting its resolution.

LSModel.open()¶

Reopens the model. Only allowed in state LSState.STOPPED. When this method is called, the solver is placed in state LSState.MODELING.

In this state, the model can be modified: it is possible to add new expressions, constraints or objectives, modify expression operands, and remove existing constraints and objectives. However, existing expressions cannot be deleted.

LSModel.is_closed()¶

Returns true if the model is closed, false otherwise.

Returns:	True if the model is closed.
Return type:	bool

LSModel.bool()¶

Creates a boolean decision. Binary decision variable with domain [0.1]. This method is a shortcut for create_expression(LSOperator.BOOL).

Since:	5.5
Returns:	Expression of type LSOperator.BOOL
Return type:	LSExpression

LSModel.float(min, max)¶

Creates a float decision. Decision variable with domain [min,max]. This method is a shortcut for create_expression(LSOperator.FLOAT, min, max).

Since:	5.5
Parameters:	min (int or float) – Lower bound of the decision variable. max (int or float) – Upper bound of the decision variable.
Returns:	Expression of type LSOperator.FLOAT
Return type:	LSExpression

LSModel.int(min, max)¶

Creates an integer decision. Decision variable with domain [min,max]. This method is a shortcut for create_expression(LSOperator.INT, min, max).

Since:	5.5
Parameters:	min (int) – Lower bound of the decision variable. max (int) – Upper bound of the decision variable.
Returns:	Expression of type LSOperator.INT
Return type:	LSExpression

LSModel.sum(operands)¶

LSModel.sum(*operands)

Creates a sum expression. This method is a shortcut for create_expression(LSOperator.SUM, operands).

Any object that implements the __iter__ method is accepted. Thus, lists, tuples, sets and their comprehensions counterpart are accepted. It is also possible to use this method with a variadic number of arguments. Each operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	operands – Operands to add. An iterable or any number of arguments.
Returns:	Expression of type LSOperator.SUM
Return type:	LSExpression

LSModel.sub(op1, op2)¶

Creates a substraction expression. This method is a shortcut for create_expression(LSOperator.SUB, op1, op2).

Each operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.SUB
Return type:	LSExpression

LSModel.prod(operands)¶

LSModel.prod(*operands)

Creates a product expression. This method is a shortcut for create_expression(LSOperator.PROD, operands).

Any object that implements the __iter__ method is accepted. Thus, lists, tuples, sets and their comprehensions counterpart are accepted. It is also possible to use this method with a variadic number of arguments. Each operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	operands – Operands to add. An iterable or any number of arguments.
Returns:	Expression of type LSOperator.PROD
Return type:	LSExpression

LSModel.max(operands)¶

LSModel.max(*operands)

Creates a max expression. This method is a shortcut for create_expression(LSOperator.MAX, operands).

Any object that implements the __iter__ method is accepted. Thus, lists, tuples, sets and their comprehensions counterpart are accepted. It is also possible to use this method with a variadic number of arguments. Each operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	operands – Operands to add. An iterable or any number of arguments.
Returns:	Expression of type LSOperator.MAX
Return type:	LSExpression

LSModel.min(operands)¶

LSModel.min(*operands)

Creates a min expression. This method is a shortcut for create_expression(LSOperator.MIN, operands).

Any object that implements the __iter__ method is accepted. Thus, lists, tuples, sets and their comprehensions counterpart are accepted. It is also possible to use this method with a variadic number of arguments. Each operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	operands – Operands to add. An iterable or any number of arguments.
Returns:	Expression of type LSOperator.MIN
Return type:	LSExpression

LSModel.or_(operands)¶

LSModel.or_(*operands)

Creates a boolean or expression. This method is a shortcut for create_expression(LSOperator.OR, operands).

Any object that implements the __iter__ method is accepted. Thus, lists, tuples, sets and their comprehensions counterpart are accepted. It is also possible to use this method with a variadic number of arguments. Each operand can be an LSExpression or a boolean.

Since:	5.5
Parameters:	operands – Operands to add. An iterable or any number of arguments.
Returns:	Expression of type LSOperator.OR
Return type:	LSExpression

LSModel.and_(operands)¶

LSModel.and_(*operands)

Creates a boolean and expression. This method is a shortcut for create_expression(LSOperator.AND, operands).

Any object that implements the __iter__ method is accepted. Thus, lists, tuples, sets and their comprehensions counterpart are accepted. It is also possible to use this method with a variadic number of arguments. Each operand can be an LSExpression or a boolean.

Since:	5.5
Parameters:	operands – Operands to add. An iterable or any number of arguments.
Returns:	Expression of type LSOperator.AND
Return type:	LSExpression

LSModel.xor(operands)¶

LSModel.xor(*operands)

Creates a boolean xor expression. This method is a shortcut for create_expression(LSOperator.XOR, operands).

Any object that implements the __iter__ method is accepted. Thus, lists, tuples, sets and their comprehensions counterpart are accepted. It is also possible to use this method with a variadic number of arguments. Each operand can be an LSExpression or a boolean.

Since:	5.5
Parameters:	operands – Operands to add. An iterable or any number of arguments.
Returns:	Expression of type LSOperator.XOR
Return type:	LSExpression

LSModel.not_(op)¶

Creates a boolean not expression. This method is a shortcut for create_expression(LSOperator.NOT, operands).

The operand can be an LSExpression or a boolean.

Since:	5.5
Parameters:	op – Operand. Accepted types: LSExpression or boolean.
Returns:	Expression of type LSOperator.NOT
Return type:	LSExpression

LSModel.eq(op1, op2)¶

Creates an equality expression. This method is a shortcut for create_expression(LSOperator.EQ, op1, op2).

Accepted operands are: LSExpressions, booleans, integers or doubles.

Since:	5.5
Parameters:	op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.EQ
Return type:	LSExpression

LSModel.neq(op1, op2)¶

Creates a disequality expression. This method is a shortcut for create_expression(LSOperator.NEQ, op1, op2).

Accepted operands are: LSExpressions, booleans, integers or doubles.

Since:	5.5
Parameters:	op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.NEQ
Return type:	LSExpression

LSModel.geq(op1, op2)¶

Creates an inequality ‘greater than or equal to’. This method is a shortcut for create_expression(LSOperator.GEQ, op1, op2).

Accepted operands are: LSExpressions, booleans, integers or doubles.

Since:	5.5
Parameters:	op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.GEQ
Return type:	LSExpression

LSModel.leq(op1, op2)¶

Creates an inequality ‘lower than or equal to’. This method is a shortcut for create_expression(LSOperator.LEQ, op1, op2).

Accepted operands are: LSExpressions, booleans, integers or doubles.

Since:	5.5
Parameters:	op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.LEQ
Return type:	LSExpression

LSModel.gt(op1, op2)¶

Creates an inequality ‘strictly greater than’. This method is a shortcut for create_expression(LSOperator.GT, op1, op2).

Accepted operands are: LSExpressions, booleans, integers or doubles.

Since:	5.5
Parameters:	op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.GT
Return type:	LSExpression

LSModel.lt(op1, op2)¶

Creates an inequality ‘strictly lower than’. This method is a shortcut for create_expression(LSOperator.LT, op1, op2).

Accepted operands are: LSExpressions, booleans, integers or doubles.

Since:	5.5
Parameters:	op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.LT
Return type:	LSExpression

LSModel.iif(op1, op2, op3)¶

Creates a ternary conditional operator. This method is a shortcut for create_expression(LSOperator.IF, op1, op2, op3).

The first operand must be an LSExpression with a boolean value or a boolean. The other operands can be LSExpressions, booleans, integers or doubles.

Since:	5.5
Parameters:	op1 – Operand. Accepted types: LSExpression with boolean value or boolean. op2 – Operand. Accepted types: LSExpression, boolean, integer or double. op3 – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.IF
Return type:	LSExpression

LSModel.abs(op)¶

Creates an absolute value expression. This method is a shortcut for create_expression(LSOperator.ABS, op).

The operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	op – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.ABS
Return type:	LSExpression

LSModel.dist(op1, op2)¶

Creates a distance expression. This method is a shortcut for create_expression(LSOperator.DIST, op1, op2).

Accepted operands are: LSExpressions, booleans, integers or doubles.

Since:	5.5
Parameters:	op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.DIST
Return type:	LSExpression

LSModel.div(op1, op2)¶

Creates a division expression. This method is a shortcut for create_expression(LSOperator.DIV, op1, op2).

Accepted operands are: LSExpressions, booleans, integers or doubles.

Since:	5.5
Parameters:	op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.DIV
Return type:	LSExpression

LSModel.mod(op1, op2)¶

Creates a modulo expression. This method is a shortcut for create_expression(LSOperator.MOD, op1, op2).

Accepted operands are: LSExpressions with integer values, booleans, integers.

Since:	5.5
Parameters:	op1 – Operand. Accepted types: LSExpression with integer value, boolean or integer. op2 – Operand. Accepted types: LSExpression with integer value, boolean or integer.
Returns:	Expression of type LSOperator.MOD
Return type:	LSExpression

LSModel.array(operands)¶

LSModel.array(*operands)

Creates a new array. This method behaves as a shortcut for create_expression(LSOperator.ARRAY, operands), but attempts to create an N-dimensional array in a recursive way: if an operand is iterable, it will be turned into an array too, and so on.

Any object that implements the __iter__ method is accepted. Thus, lists, tuples, sets and their comprehensions counterpart are accepted. It is also possible to use this method with a variadic number of arguments. Each operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	operands – Operands to add. An iterable or any number of arguments.
Returns:	Expression of type LSOperator.ARRAY
Return type:	LSExpression

LSModel.at(array_expr, indices_expr)¶

LSModel.at(array_expr, *indices_expr)

Creates a “at” expression. This method is a shortcut for create_expression(LSOperator.AT, array_expr, indices_expr).

The first operand must be an LSExpression with array or collection value. The second operand accepts any object that implements the __iter__ method. Thus, lists, tuples, sets and their comprehensions counterpart are accepted. It is also possible to use this method with a variadic number of arguments. These operands must be LSExpressions with integer value, booleans or integers.

Since:	5.5
Parameters:	array_expr – Operand. Accepted types: LSExpression with array or collection value. indices_expr – Operands for the indices. An iterable or any number of arguments.
Returns:	Expression of type LSOperator.AT
Return type:	LSExpression

LSModel.scalar(op1, op2)¶

Creates a scalar product between two arrays. This method is a shortcut for create_expression(LSOperator.SCALAR, op1, op2).

The operands must be LSExpressions of type LSOperator.ARRAY.

Since:	5.5
Parameters:	op1 – Operand. Accepted types: LSExpression with array value. op2 – Operand. Accepted types: LSExpression with array value.
Returns:	Expression of type LSOperator.SCALAR
Return type:	LSExpression

LSModel.ceil(op)¶

Creates a ceil expression. This method is a shortcut for create_expression(LSOperator.CEIL, op).

The operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	op – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.CEIL
Return type:	LSExpression

LSModel.floor(op)¶

Creates a floor expression. This method is a shortcut for create_expression(LSOperator.FLOOR, op).

The operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	op – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.FLOOR
Return type:	LSExpression

LSModel.round(op)¶

Creates a round expression. This method is a shortcut for create_expression(LSOperator.ROUND, op).

The operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	op – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.ROUND
Return type:	LSExpression

LSModel.sqrt(op)¶

Creates a square root expression. This method is a shortcut for create_expression(LSOperator.SQRT, op).

The operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	op – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.SQRT
Return type:	LSExpression

LSModel.log(op)¶

Creates a natural log expression. This method is a shortcut for create_expression(LSOperator.LOG, op).

The operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	op – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.LOG
Return type:	LSExpression

LSModel.exp(op)¶

Creates an exponential expression. This method is a shortcut for create_expression(LSOperator.EXP, op).

The operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	op – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.EXP
Return type:	LSExpression

LSModel.pow(op1, op2)¶

Creates a power expression. This method is a shortcut for create_expression(LSOperator.POW, op1, op2).

Accepted operands are: LSExpressions, booleans, integers or doubles.

Since:	5.5
Parameters:	op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.POW
Return type:	LSExpression

LSModel.cos(op)¶

Creates a cosine expression. This method is a shortcut for create_expression(LSOperator.COS, op).

The operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	op – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.COS
Return type:	LSExpression

LSModel.sin(op)¶

Creates a sine expression. This method is a shortcut for create_expression(LSOperator.SIN, op).

The operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	op – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.SIN
Return type:	LSExpression

LSModel.tan(op)¶

Creates a tangent expression. This method is a shortcut for create_expression(LSOperator.TAN, op).

The operand can be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	op – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.TAN
Return type:	LSExpression

LSModel.piecewise(op1, op2, op3)¶

Creates a piecewise linear expression. This method is a shortcut for create_expression(LSOperator.PIECEWISE, op1, op2, op3).

The first and the second operands must be LSExpressions of type LSOperator.ARRAY. The third argument must be an LSExpression, a boolean, an integer or a double.

Since:	5.5
Parameters:	op1 – Operand. Accepted types: LSExpression of type LSOperator.ARRAY op2 – Operand. Accepted types: LSExpression of type LSOperator.ARRAY op3 – Operand. Accepted types: LSExpression, boolean, integer or double.
Returns:	Expression of type LSOperator.PIECEWISE
Return type:	LSExpression

LSModel.list(n)¶

Creates a list decision with the given length. A list is an ordered collection of integers within a domain [0, n-1]. This method is a shortcut for create_expression(LSOperator.LIST, n).

Since:	5.5
Parameters:	n – Collection size. Accepted types: bool or int.

LSModel.set(n)¶

Creates a set decision with the given length. A set is an unordered collection of integers within a domain [0, n-1]. This method is a shortcut for create_expression(LSOperator.SET, n).

Since:	8.0
Parameters:	n – Collection size. Accepted types: bool or int.

LSModel.count(op)¶

Creates a count expression. This method is a shortcut for create_expression(LSOperator.COUNT, op).

The operand must be an LSExpression with collection value.

Since:	5.5
Parameters:	op – Operand. Accepted type: LSExpression with collection value.
Returns:	Expression of type LSOperator.COUNT
Return type:	LSExpression

LSModel.index(op1, op2)¶

Creates an indexOf expression. This method is a shortcut for create_expression(LSOperator.INDEXOF, op1, op2).

The first operand must be an LSExpression with list value. The second operand must be an LSExpression with integer value, an integer or a boolean.

Since:	5.5
Parameters:	op1 – Operand. Accepted type: LSExpression with list value. op2 – Operand. Accepted type: LSExpression or integer.
Returns:	Expression of type LSOperator.INDEXOF
Return type:	LSExpression

LSModel.contains(op1, op2)¶

Creates a contains expression. This method is a shortcut for create_expression(LSOperator.CONTAINS, op1, op2).

The first operand must be an LSExpression with collection value. The second operand must be an LSExpression with integer value, an integer or a boolean.

Since:	7.5
Parameters:	op1 – Operand. Accepted type: LSExpression with collection value. op2 – Operand. Accepted type: LSExpression or integer.
Returns:	Expression of type LSOperator.CONTAINS
Return type:	LSExpression

LSModel.partition(operands)¶

LSModel.partition(*operands)

Creates a partition expression. This method is a shortcut for create_expression(LSOperator.PARTITION, operands).

Any object that implements the __iter__ method is accepted. Thus, lists, tuples, sets and their comprehensions counterpart are accepted. It is also possible to use this method with a variadic number of arguments. Each operand must be an LSExpression with collection value.

Since:	5.5
Parameters:	operands – Operands to add. An iterable or any number of arguments.
Returns:	Expression of type LSOperator.PARTITION
Return type:	LSExpression

LSModel.disjoint(operands)¶

LSModel.disjoint(*operands)

Creates a disjoint expression. This method is a shortcut for create_expression(LSOperator.DISJOINT, operands).

Any object that implements the __iter__ method is accepted. Thus, lists, tuples, sets and their comprehensions counterpart are accepted. It is also possible to use this method with a variadic number of arguments. Each operand must be an LSExpression with collection value.

Since:	5.5
Parameters:	operands – Operands to add. An iterable or any number of arguments.
Returns:	Expression of type LSOperator.DISJOINT
Return type:	LSExpression

LSModel.call(operands)¶

LSModel.call(*operands)

Creates a call expression. This method is a shortcut for create_expression(LSOperator.CALL, operands).

The first operand must be an LSExpression of type LSOperator.FUNCTION or LSOperator.EXTERNAL_FUNCTION. The second operand accepts any object that implements the __iter__ method. Thus, lists, tuples, sets and their comprehensions counterpart are accepted. It is also possible to use this method with a variadic number of arguments. These operands may be LSExpressions, booleans, integers, and doubles. They are passed to the function as arguments.

Since:	6.0
Parameters:	operands – Operands to add. An iterable or any number of arguments.
Returns:	Expression of type LSOperator.CALL
Return type:	LSExpression

LSModel.range([op1, ]op2)¶

Creates a range expression. op1 is the lower bound (inclusive) and op2 is the upper bound (exclusive). When only one operand is used, the lower bound is 0. This method is a shortcut for create_expression(LSOperator.RANGE, op1, op2).

Since:	7.0
Parameters:	op1 – Operand. Accepted types: LSExpression with integer value, boolean or integer. op2 – Operand. Accepted types: LSExpression with integer value, boolean or integer.
Returns:	Expression of type LSOperator.RANGE
Return type:	LSExpression

Instance attributes¶

All get/set methods have their attribute counterpart. You can use them as shortcuts to improve the readability or your models and codes.

LSModel.nb_expressions¶

Number of expressions in this model. This attribute is read-only. It is a shortcut for get_nb_expressions().

LSModel.nb_operands¶

Number of operands in this model. This attribute is read-only. It is a shortcut for get_nb_operands().

LSModel.nb_objectives¶

Number of objectives in this model. This attribute is read-only. It is a shortcut for get_nb_objectives().

LSModel.nb_constraints¶

Number of constraints in this model. This attribute is read-only. It is a shortcut for get_nb_constraints().

LSModel.nb_decisions¶

Number of decisions in this model. This attribute is read-only. It is a shortcut for get_nb_decisions().

LSModel.expressions¶

List of the expressions of the model. This attribute is read-only. The returned object is iterable, supports the len function and can be indexed with integers. It is a shortcut for get_expression() and get_nb_expressions() methods.

LSModel.decisions¶

List of the decisions of the model. This attribute is read-only. The returned object is iterable, supports the len function and can be indexed with integers. It is a shortcut for get_decision() and get_nb_decisions() methods.

LSModel.objectives¶

List of the objectives of the model. This attribute is read-only. The returned object is iterable, supports the len function and can be indexed with integers. It is a shortcut for get_objective() and get_nb_objectives() methods.

LSModel.objective_directions¶

List of the objective directions of the model. This attribute is read-only. The returned object is iterable, supports the len function and can be indexed with integers. It is a shortcut for get_objective_direction() and get_nb_objectives() methods.

LSModel.constraints¶

List of the constraints of the model. This attribute is read-only. The returned object is iterable, supports the len function and can be indexed with integers. It is a shortcut for get_constraint() and get_nb_constraints() methods.

Special operators and methods¶

LSModel.__str__()¶

Returns a string representation of this model. This representation provides:

• The number of expressions, decisions, constraints, and objectives.
• The density of the model.

Useful for debugging or logging purposes.

Returns:	String representation of this model.
Return type:	str