# LSModel Class¶

class localsolver.LSModel

Mathematical optimization model. A model is composed of expressions (some of which are decisions), organized as a Directed Acyclic Graph (DAG). Then, some expressions of the model can be constrained or optimized. Once your optimization model is created and closed, the solver can be launched to solve it. Note that you cannot modify a model which has been closed: you must reopen it (with open()) or instantiate another LocalSolver environment to optimize another model.

## Summary¶

 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.
 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_int_blackbox_function Creates an integer black-box function. int_blackbox_function Shortcut for create_int_blackbox_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 \u2018greater than or equal to\u2019. leq Creates an inequality \u2018lower than or equal to\u2019. gt Creates an inequality \u2018strictly greater than\u2019. lt Creates an inequality \u2018strictly lower than\u2019. 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 \u201cat\u201d 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. cover Creates a cover expression. find Creates a find expression. call Creates a call expression. range Creates a range expression.
 __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). Created constant expression 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 operator (LSOperator) – Type of the expression to create. operands – Operands to add. An iterable or any number of arguments. Created expression 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 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. Expression of type LSOperator.LAMBDA_FUNCTION LSExpression
LSModel.lambda_function(function)

Shortcut for create_lambda_function().

Since: 9.5 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. Expression of type LSOperator.LAMBDA_FUNCTION 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 function – A python function that accepts a LSExternalArgumentValues as first argument and returns an integer value. Expression of type LSOperator.EXTERNAL_FUNCTION. LSExpression
LSModel.int_external_function(function)

Shortcut for create_int_external_function().

Since: 9.5 function – A python function that accepts a LSExternalArgumentValues as first argument and returns an integer value. Expression of type LSOperator.EXTERNAL_FUNCTION. 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 function – A python function that accepts a LSExternalArgumentValues as first argument and returns a double value. Expression of type LSOperator.EXTERNAL_FUNCTION. LSExpression
LSModel.double_external_function(function)

Shortcut for create_double_external_function().

Since: 9.5 function – A python function that accepts a LSExternalArgumentValues as first argument and returns a double value. Expression of type LSOperator.EXTERNAL_FUNCTION. LSExpression
LSModel.create_int_blackbox_function(function)

Creates an integer black-box function. The provided function must take a (LSBlackBoxArgumentValues) as single argument and must return an integer 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: 10.0 function – A python function that accepts a LSBlackBoxArgumentValues as first argument and returns an integer value. Expression of type LSOperator.BLACKBOX_FUNCTION. LSExpression
LSModel.int_blackbox_function(function)

Shortcut for create_int_blackbox_function().

Since: 10.0 function – A python function that accepts a LSBlackBoxArgumentValues as first argument and returns an integer value Expression of type LSOperator.BLACKBOX_FUNCTION. 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 function – A python function that accepts a LSBlackBoxArgumentValues as first argument and returns a double value. Expression of type LSOperator.BLACKBOX_FUNCTION. LSExpression
LSModel.double_blackbox_function(function)

Shortcut for create_double_blackbox_function().

Since: 9.5 function – A python function that accepts a LSBlackBoxArgumentValues as first argument and returns a double value Expression of type LSOperator.BLACKBOX_FUNCTION. 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. 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. Expression with the given index 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. 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 Decision with the given index 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 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. 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 int
LSModel.get_constraint(index)

Gets the constraint with the given index.

Parameters: index (int) – Index of the constraint Constraint with the given index. 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. 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 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 Objective with the given index 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 Objective direction 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. 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. 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 Expression of type LSOperator.BOOL 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 min (int or float) – Lower bound of the decision variable. max (int or float) – Upper bound of the decision variable. Expression of type LSOperator.FLOAT 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 min (int) – Lower bound of the decision variable. max (int) – Upper bound of the decision variable. Expression of type LSOperator.INT 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 operands – Operands to add. An iterable or any number of arguments. Expression of type LSOperator.SUM 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 op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.SUB 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 operands – Operands to add. An iterable or any number of arguments. Expression of type LSOperator.PROD 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 operands – Operands to add. An iterable or any number of arguments. Expression of type LSOperator.MAX 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 operands – Operands to add. An iterable or any number of arguments. Expression of type LSOperator.MIN 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 operands – Operands to add. An iterable or any number of arguments. Expression of type LSOperator.OR 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 operands – Operands to add. An iterable or any number of arguments. Expression of type LSOperator.AND 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 operands – Operands to add. An iterable or any number of arguments. Expression of type LSOperator.XOR 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 op – Operand. Accepted types: LSExpression or boolean. Expression of type LSOperator.NOT 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 op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.EQ 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 op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.NEQ 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 op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.GEQ 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 op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.LEQ 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 op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.GT 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 op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.LT 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 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. Expression of type LSOperator.IF 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 op – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.ABS 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 op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.DIST 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 op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.DIV 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 op1 – Operand. Accepted types: LSExpression with integer value, boolean or integer. op2 – Operand. Accepted types: LSExpression with integer value, boolean or integer. Expression of type LSOperator.MOD 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 operands – Operands to add. An iterable or any number of arguments. Expression of type LSOperator.ARRAY 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 array_expr – Operand. Accepted types: LSExpression with array or collection value. indices_expr – Operands for the indices. An iterable or any number of arguments. Expression of type LSOperator.AT 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 op1 – Operand. Accepted types: LSExpression with array value. op2 – Operand. Accepted types: LSExpression with array value. Expression of type LSOperator.SCALAR 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 op – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.CEIL 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 op – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.FLOOR 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 op – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.ROUND 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 op – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.SQRT 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 op – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.LOG 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 op – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.EXP 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 op1 – Operand. Accepted types: LSExpression, boolean, integer or double. op2 – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.POW 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 op – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.COS 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 op – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.SIN 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 op – Operand. Accepted types: LSExpression, boolean, integer or double. Expression of type LSOperator.TAN 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 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. Expression of type LSOperator.PIECEWISE 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 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 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 op – Operand. Accepted type: LSExpression with collection value. Expression of type LSOperator.COUNT 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 op1 – Operand. Accepted type: LSExpression with list value. op2 – Operand. Accepted type: LSExpression or integer. Expression of type LSOperator.INDEXOF 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 op1 – Operand. Accepted type: LSExpression with collection value. op2 – Operand. Accepted type: LSExpression or integer. Expression of type LSOperator.CONTAINS 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 operands – Operands to add. An iterable or any number of arguments. Expression of type LSOperator.PARTITION 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 operands – Operands to add. An iterable or any number of arguments. Expression of type LSOperator.DISJOINT LSExpression
LSModel.cover(operands)
LSModel.cover(*operands)

Creates a cover expression. This method is a shortcut for create_expression(LSOperator.COVER, 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: 10.5 operands – Operands to add. An iterable or any number of arguments. Expression of type LSOperator.COVER LSExpression
LSModel.find(op1, op2)

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

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

Since: 10.5 op1 – Operand. Accepted type: LSExpression with array value. op2 – Operand. Accepted type: LSExpression or integer. Expression of type LSOperator.FIND 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 operands – Operands to add. An iterable or any number of arguments. Expression of type LSOperator.CALL 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 op1 – Operand. Accepted types: LSExpression with integer value, boolean or integer. op2 – Operand. Accepted types: LSExpression with integer value, boolean or integer. Expression of type LSOperator.RANGE 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. str