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

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_int_array_external_function

Creates an integer array external function.

int_array_external_function

Shortcut for create_int_array_external_function().

create_double_array_external_function

Creates a double array external function.

double_array_external_function

Shortcut for create_double_array_external_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.

cover

Creates a cover expression.

find

Creates a find expression.

sort

Creates a sort 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_int_array_external_function(function)

Creates an integer array external function. The provided function must take a (LSExternalArgumentValues) as single argument and must return an iterable of integer values (such as list, set or tuple of int). 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.

Since

11.0

Parameters

function – A python function that accepts a LSExternalArgumentValues as first argument and returns an integer array value.

Returns

Expression of type LSOperator.EXTERNAL_FUNCTION.

Return type

LSExpression

LSModel.int_array_external_function(function)

Shortcut for create_int_array_external_function().

Since

11.0

Parameters

function – A python function that accepts a LSExternalArgumentValues as first argument and returns an integer array value

Returns

Expression of type LSOperator.EXTERNAL_FUNCTION.

Return type

LSExpression

LSModel.create_double_array_external_function(function)

Creates a double array external function. The provided function must take a (LSExternalArgumentValues) as single argument and must return an iterable of double values (such as list, set or tuple of double). 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.

Since

11.0

Parameters

function – A python function that accepts a LSExternalArgumentValues as first argument and returns a double array value.

Returns

Expression of type LSOperator.EXTERNAL_FUNCTION.

Return type

LSExpression

LSModel.double_array_external_function(function)

Shortcut for create_double_array_external_function().

Since

11.0

Parameters

function – A python function that accepts a LSExternalArgumentValues as first argument and returns a double array value

Returns

Expression of type LSOperator.EXTERNAL_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
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.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

Parameters

operands – Operands to add. An iterable or any number of arguments.

Returns

Expression of type LSOperator.COVER

Return type

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

Parameters
  • op1 – Operand. Accepted type: LSExpression with array value.

  • op2 – Operand. Accepted type: LSExpression or integer.

Returns

Expression of type LSOperator.FIND

Return type

LSExpression

LSModel.sort(op)

Creates a sort expression. This method is a shortcut for create_expression(LSOperator.SORT, op).

The first operand must be an LSExpression representing a one-dimensional array containing integers or doubles.

Since

11.0

Parameters

op – Operand. Accepted type: LSExpression with array value.

Returns

Expression of type LSOperator.SORT

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