HxModel Class¶

class hexaly.optimizer.HxModel¶: 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 optimizer 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 Hexaly Optimizer 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_const_array`	Creates a constant array expression containing the given values.
`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, HxObjectiveDirection.MINIMIZE).
`maximize`	Shortcut for add_objective(expr, HxObjectiveDirection.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.
`interval`	Creates an interval decision included in [minStart, maxEnd).
`optional_interval`	Creates an optional interval decision, which can either be absent (void) or included in [minStart, maxEnd).
`hull`	Creates a hull expression.
`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 an array expression.
`step_array`	Creates a new step 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.
`start`	Creates a start expression.
`end`	Creates an end expression.
`length`	Creates a length expression.
`presence`	Creates a presence expression.
`count`	Creates a count expression.
`index`	Creates an indexOf expression.
`distinct`	Creates a distinct expression.
`intersection`	Creates an intersection expression of intervals.
`union`	Creates an union expression of sets.
`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¶

HxModel.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 HxState.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:	HxExpression

HxModel.create_expression(operator)¶

hexaly.optimizer.create_expression(operator, operands)¶

hexaly.optimizer.create_expression(operator, *operands)

Creates a new expression of the given type with the given operands. Only allowed in state HxState.MODELING. This method cannot be used to create constants: use HxModel.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 HxExpression, a boolean, an integer or a double.

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

HxModel.create_const_array(values)¶

Creates a constant array expression containing the given values. Only allowed in state HxState.MODELING. Note that the constant array created does not have operands.

Parameters:	values – Array of constant values.
Returns:	Created constant array expression.
Since:	13.5

HxModel.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 HxExpressions of type HxOperator.ARGUMENT).
The body of the function. The body is an HxExpression that will be used to evaluate the result of the function. The body can be any HxExpression composed of any operands and operators supported by Hexaly Optimizer. 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 HxExpression of type HxOperator.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 HxExpression will be used as the body of the Hexaly Optimizer function.

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

HxModel.lambda_function(function)¶

Shortcut for create_lambda_function().

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

HxModel.create_int_external_function(function)¶

Creates an integer external function. The provided function must take the external argument values (HxExternalArgumentValues) 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 HxExternalArgumentValues.

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 optimizer is in state HxState.RUNNING. Do not attempt to call any method of the optimizer (to retrieve statistics, values of HxExpressions or whatever) in that state or an exception will be thrown. The only accessible function is HexalyOptimizer.stop().

Note 2: Your functions must be thread-safe. According to the nb_threads parameter, Hexaly Optimizer 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 Hexaly Optimizer to one thread with HxParam.nb_threads.

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

Since:	9.5
Parameters:	function – A python function that accepts a `HxExternalArgumentValues` as first argument and returns an integer value.
Returns:	Expression of type `HxOperator.EXTERNAL_FUNCTION`.
Return type:	HxExpression

HxModel.int_external_function(function)¶

Shortcut for create_int_external_function().

Since:	9.5
Parameters:	function – A python function that accepts a `HxExternalArgumentValues` as first argument and returns an integer value.
Returns:	Expression of type `HxOperator.EXTERNAL_FUNCTION`.
Return type:	HxExpression

HxModel.create_double_external_function(function)¶

Creates a double external function. The provided function must take the external argument values (HxExternalArgumentValues) 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 HxExternalArgumentValues.

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 optimizer is in state HxState.RUNNING. Do not attempt to call any method of the optimizer (to retrieve statistics, values of HxExpressions or whatever) in that state or an exception will be thrown. The only accessible function is HexalyOptimizer.stop().

Note 2: Your functions must be thread-safe. According to the nb_threads parameter, Hexaly Optimizer 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 Hexaly Optimizer to one thread with HxParam.nb_threads.

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

Since:	9.5
Parameters:	function – A python function that accepts a `HxExternalArgumentValues` as first argument and returns a double value.
Returns:	Expression of type `HxOperator.EXTERNAL_FUNCTION`.
Return type:	HxExpression

HxModel.double_external_function(function)¶

Shortcut for create_double_external_function().

Since:	9.5
Parameters:	function – A python function that accepts a `HxExternalArgumentValues` as first argument and returns a double value.
Returns:	Expression of type `HxOperator.EXTERNAL_FUNCTION`.
Return type:	HxExpression

HxModel.create_int_array_external_function(function)¶

Creates an integer array external function. The provided function must take a (HxExternalArgumentValues) 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 HxExternalArgumentValues.

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 `HxExternalArgumentValues` as first argument and returns an integer array value.
Returns:	Expression of type `HxOperator.EXTERNAL_FUNCTION`.
Return type:	HxExpression

HxModel.int_array_external_function(function)¶

Shortcut for create_int_array_external_function().

Since:	11.0
Parameters:	function – A python function that accepts a `HxExternalArgumentValues` as first argument and returns an integer array value
Returns:	Expression of type `HxOperator.EXTERNAL_FUNCTION`.
Return type:	HxExpression

HxModel.create_double_array_external_function(function)¶

Creates a double array external function. The provided function must take a (HxExternalArgumentValues) 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 HxExternalArgumentValues.

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 `HxExternalArgumentValues` as first argument and returns a double array value.
Returns:	Expression of type `HxOperator.EXTERNAL_FUNCTION`.
Return type:	HxExpression

HxModel.double_array_external_function(function)¶

Shortcut for create_double_array_external_function().

Since:	11.0
Parameters:	function – A python function that accepts a `HxExternalArgumentValues` as first argument and returns a double array value
Returns:	Expression of type `HxOperator.EXTERNAL_FUNCTION`.
Return type:	HxExpression

HxModel.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`

HxModel.get_expression(expr_index)¶

hexaly.optimizer.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:	HxExpression

HxModel.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`

HxModel.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:	HxExpression

HxModel.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 optimizer. Hence, only boolean expressions (that is, expressions whose value is boolean) can be constrained. Only allowed in state HxState.MODELING. If the expression is already a constraint, this method does nothing and returns immediately.

Parameters:	expr (HxExpression) – Expression

HxModel.constraint(expr)¶

Shortcut for add_constraint().

You can also use the shortcut member constraints

Parameters:	expr (HxExpression) – Expression
Since:	5.5

HxModel.remove_constraint(expr)¶

HxModel.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 HxState.MODELING.

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

HxModel.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`

HxModel.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:	HxExpression

HxModel.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 HxState.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 (HxExpression) – Expression direction (HxObjectiveDirection) – Optimization direction of this objective

HxModel.minimize(expr)¶

Shortcut for add_objective(expr, HxObjectiveDirection.MINIMIZE).

Parameters:	expr (HxExpression) – Expression

HxModel.maximize(expr)¶

Shortcut for add_objective(expr, HxObjectiveDirection.MAXIMIZE).

Parameters:	expr (HxExpression) – Expression

HxModel.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 HxPhase.set_optimized_objective() or to disable it (with HxPhase.enabled). Only allowed in state HxState.MODELING.

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

HxModel.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`

HxModel.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:	HxExpression

HxModel.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:	HxObjectiveDirection

HxModel.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`

HxModel.close()¶

Closes the model. Only allowed in state HxState.MODELING. When this method is called, the optimizer is placed in state HxState.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.

HxModel.open()¶

Reopens the model. Only allowed in state HxState.STOPPED. When this method is called, the optimizer is placed in state HxState.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.

HxModel.is_closed()¶

Returns true if the model is closed, false otherwise.

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

HxModel.bool()¶

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

Since:	5.5
Returns:	Expression of type `HxOperator.BOOL`
Return type:	HxExpression

HxModel.float(min, max)¶

Creates a float decision. Decision variable with domain [min,max]. This method is a shortcut for create_expression(HxOperator.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 `HxOperator.FLOAT`
Return type:	HxExpression

HxModel.int(min, max)¶

Creates an integer decision. Decision variable with domain [min,max]. This method is a shortcut for create_expression(HxOperator.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 `HxOperator.INT`
Return type:	HxExpression

HxModel.interval(minStart, maxEnd)¶

Creates an interval decision included in [minStart, maxEnd). Start is inclusive and end is exclusive. This method is a shortcut for create_expression(HxOperator.INTERVAL, minStart, maxEnd).

Since:	12.0
Parameters:	minStart (`int`) – Min start of the decision variable. maxEnd (`int`) – Max end of the decision variable.
Returns:	Expression of type `HxOperator.INTERVAL`
Return type:	HxExpression

HxModel.optional_interval(minStart, maxEnd)¶

Creates an optional interval decision, which can either be absent (void) or included in [minStart, maxEnd). When present, start is inclusive and end is exclusive. When absent, start and end are undefined. This method is a shortcut for create_expression(HxOperator.OPTIONAL_INTERVAL, minStart, maxEnd).

Since:	14.0
Parameters:	minStart (`int`) – Min start of the decision variable. maxEnd (`int`) – Max end of the decision variable.
Returns:	Expression of type `HxOperator.OPTIONAL_INTERVAL`
Return type:	HxExpression

HxModel.hull(operands)¶

HxModel.hull(*operands)

Creates a hull expression. This method is a shortcut for create_expression(HxOperator.HULL, 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 HxExpression with interval value.

When defining a variadic hull (with an iterable as the first operand and a lambda function as the second operand), the operator calls the function on each element of the iterable and returns the smallest interval including all intervals returned by the function.

Since:	13.0
Parameters:	operands – Operands to add. An iterable or any number of arguments.
Returns:	Expression of type `HxOperator.INTERVAL`
Return type:	HxExpression

HxModel.sum(operands)¶

HxModel.sum(*operands)

Creates a sum expression. This method is a shortcut for create_expression(HxOperator.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 HxExpression, 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 `HxOperator.SUM`
Return type:	HxExpression

HxModel.sub(op1, op2)¶

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

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

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

HxModel.prod(operands)¶

HxModel.prod(*operands)

Creates a product expression. This method is a shortcut for create_expression(HxOperator.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 HxExpression, 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 `HxOperator.PROD`
Return type:	HxExpression

HxModel.max(operands)¶

HxModel.max(*operands)

Creates a max expression. This method is a shortcut for create_expression(HxOperator.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 HxExpression, 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 `HxOperator.MAX`
Return type:	HxExpression

HxModel.min(operands)¶

HxModel.min(*operands)

Creates a min expression. This method is a shortcut for create_expression(HxOperator.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 HxExpression, 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 `HxOperator.MIN`
Return type:	HxExpression

HxModel.or_(operands)¶

HxModel.or_(*operands)

Creates a boolean or expression. This method is a shortcut for create_expression(HxOperator.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 HxExpression or a boolean.

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

HxModel.and_(operands)¶

HxModel.and_(*operands)

Creates a boolean and expression. This method is a shortcut for create_expression(HxOperator.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 HxExpression or a boolean.

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

HxModel.xor(operands)¶

HxModel.xor(*operands)

Creates a boolean xor expression. This method is a shortcut for create_expression(HxOperator.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 HxExpression or a boolean.

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

HxModel.not_(op)¶

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

The operand can be an HxExpression or a boolean.

Since:	5.5
Parameters:	op – Operand. Accepted types: HxExpression or boolean.
Returns:	Expression of type `HxOperator.NOT`
Return type:	HxExpression

HxModel.eq(op1, op2)¶

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

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

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

HxModel.neq(op1, op2)¶

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

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

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

HxModel.geq(op1, op2)¶

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

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

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

HxModel.leq(op1, op2)¶

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

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

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

HxModel.gt(op1, op2)¶

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

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

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

HxModel.lt(op1, op2)¶

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

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

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

HxModel.iif(op1, op2, op3)¶

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

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

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

HxModel.abs(op)¶

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

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

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

HxModel.dist(op1, op2)¶

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

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

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

HxModel.div(op1, op2)¶

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

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

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

HxModel.mod(op1, op2)¶

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

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

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

HxModel.array(operands)¶

HxModel.array(*operands)

Creates an array expression. This method behaves as a shortcut for create_expression(HxOperator.ARRAY, 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 HxExpression, a boolean, an integer or a double.

When defining a variadic array (with a range or a list decision as the first operand and a lambda function as the second operand), we allow a recursive definition of the elements in this array by using a second argument in the function, containing the evaluation of the function on the previous element of the range. In this case, a third operand can be added, representing the value of the element before the first element in the array.

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

HxModel.step_array(op1, op2)¶

Creates a new step array. This method is a shortcut for create_expression(HxOperator.STEP_ARRAY, op1, op2).

The first operand must be an HxExpression with constant array value. The second operand must be an HxExpression with constant array value.

Since:	13.0
Parameters:	op1 – Operand. Accepted type: `HxExpression` with array value. op2 – Operand. Accepted type: `HxExpression` with array value.
Returns:	Expression of type `HxOperator.STEPARRAY`
Return type:	HxExpression

HxModel.at(array_expr, indices_expr)¶

HxModel.at(array_expr, *indices_expr)

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

The first operand must be an HxExpression 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 HxExpressions with integer value, booleans or integers.

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

HxModel.scalar(op1, op2)¶

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

The operands must be HxExpressions of type HxOperator.ARRAY.

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

HxModel.ceil(op)¶

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

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

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

HxModel.floor(op)¶

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

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

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

HxModel.round(op)¶

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

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

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

HxModel.sqrt(op)¶

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

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

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

HxModel.log(op)¶

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

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

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

HxModel.exp(op)¶

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

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

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

HxModel.pow(op1, op2)¶

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

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

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

HxModel.cos(op)¶

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

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

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

HxModel.sin(op)¶

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

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

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

HxModel.tan(op)¶

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

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

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

HxModel.piecewise(op1, op2, op3)¶

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

The first and the second operands must be HxExpressions of type HxOperator.ARRAY. The third argument must be an HxExpression, a boolean, an integer or a double.

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

HxModel.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(HxOperator.LIST, n).

Since:	5.5
Parameters:	n (`bool` or `int`) – Collection size.

HxModel.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(HxOperator.SET, n).

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

HxModel.start(op)¶

Creates a start expression. This method is a shortcut for create_expression(HxOperator.START, op).

The operand must be an HxExpression with interval value.

Since:	12.0
Parameters:	op – Operand. Accepted type: `HxExpression` with interval value.
Returns:	Expression of type `HxOperator.START`
Return type:	HxExpression

HxModel.end(op)¶

Creates an end expression. This method is a shortcut for create_expression(HxOperator.END, op).

The operand must be an HxExpression with interval value.

Since:	12.0
Parameters:	op – Operand. Accepted type: `HxExpression` with interval value.
Returns:	Expression of type `HxOperator.END`
Return type:	HxExpression

HxModel.length(op)¶

Creates a length expression. This method is a shortcut for create_expression(HxOperator.LENGTH, op).

The operand must be an HxExpression with interval value.

Since:	12.0
Parameters:	op – Operand. Accepted type: `HxExpression` with interval value.
Returns:	Expression of type `HxOperator.LENGTH`
Return type:	HxExpression

HxModel.presence(op)¶

Creates a presence expression. This method is a shortcut for create_expression(HxOperator.PRESENCE, op).

The operand must be an HxExpression with interval value.

Since:	14.0
Parameters:	op – Operand. Accepted type: `HxExpression` with interval value.
Returns:	Expression of type `HxOperator.PRESENCE`
Return type:	HxExpression

HxModel.count(op)¶

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

The operand must be an HxExpression with array, collection or interval value.

Since:	5.5
Parameters:	op – Operand. Accepted type: `HxExpression` with array, collection or interval value.
Returns:	Expression of type `HxOperator.COUNT`
Return type:	HxExpression

HxModel.index(op1, op2)¶

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

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

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

HxModel.distinct(operands)¶

Creates a distinct expression. This method is a shortcut for create_expression(HxOperator.DISTINCT, operands).

This operator accepts one or two operands. If one operand is passed, the operand must be an HxExpression with one-dimensional array value. If two operands are passed, the first one must be an HxExpression with collection (list or set), interval or range value, and the second must be an HxExpression with lambda function value.

Since:	12.5
Parameters:	operands – Operands (1 or 2). Accepted type: `HxExpression`.
Returns:	Expression of type `HxOperator.DISTINCT`
Return type:	HxExpression

HxModel.intersection(operands)¶

Creates an intersection expression of intervals. This method is a shortcut for create_expression(HxOperator.INTERSECTION, operands).

Operands must be interval. There must be at least one operand.

since: 13.5

param operands: Operands to add. An iterable or any number of interval arguments.

return: Expression of type HxOperator.INTERVAL

rtype: HxExpression

HxModel.intersection(op1, op2)

Creates an intersection expression. This method is a shortcut for create_expression(HxOperator.INTERSECTION, op1, op2).

Since:	12.5
Parameters:	op1 – Operand. Accepted type: `HxExpression` with collection or array value. op2 – Operand. Accepted type: `HxExpression` with collection or array value.
Returns:	Expression of type `HxOperator.INTERSECTION`
Return type:	HxExpression

HxModel.union(operands)¶

Creates an union expression of sets. This method is a shortcut for create_expression(HxOperator.UNION, operands).

Operands must be collections. There must be at least one operand.

since: 13.5

param operands: Operands to add. Any number of collection arguments.

return: Expression of type HxOperator.UNION

rtype: HxExpression

HxModel.contains(op1, op2)¶

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

The first operand must be an HxExpression with collection, interval or array value. The second operand must be an HxExpression with either an integer or interval value.

Since:	7.5
Parameters:	op1 – Operand. Accepted type: `HxExpression` with collection, interval or array value. op2 – Operand. Accepted type: `HxExpression`, integer or interval.
Returns:	Expression of type `HxOperator.CONTAINS`
Return type:	HxExpression

HxModel.partition(operands)¶

HxModel.partition(*operands)

Creates a partition expression. This method is a shortcut for create_expression(HxOperator.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 HxExpression with collection value.

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

HxModel.disjoint(operands)¶

HxModel.disjoint(*operands)

Creates a disjoint expression. This method is a shortcut for create_expression(HxOperator.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 HxExpression with collection value.

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

HxModel.cover(operands)¶

HxModel.cover(*operands)

Creates a cover expression. This method is a shortcut for create_expression(HxOperator.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 HxExpression with collection value.

Since:	10.5
Parameters:	operands – Operands to add. An iterable or any number of arguments.
Returns:	Expression of type `HxOperator.COVER`
Return type:	HxExpression

HxModel.find(op1, op2)¶

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

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

Since:	10.5
Parameters:	op1 – Operand. Accepted type: `HxExpression` with array value. op2 – Operand. Accepted type: `HxExpression` or integer.
Returns:	Expression of type `HxOperator.FIND`
Return type:	HxExpression

HxModel.sort(op1[, op2])¶

Creates a sort expression. This method is a shortcut for create_expression(HxOperator.SORT, op1 [, op2]).

The first operand must be an HxExpression representing either a collection or a one-dimensional array containing integers or doubles. The second argument is optional and, if specified, must be an HxExpression with lambda function value.

Since:	11.0
Parameters:	op1 – Operand. Accepted type: `HxExpression` with array or collection value. op2 – Operand. Accepted type: `HxExpression` with lambda function value.
Returns:	Expression of type `HxOperator.SORT`
Return type:	HxExpression

HxModel.call(operands)¶

HxModel.call(*operands)

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

The first operand must be an HxExpression of type HxOperator.LAMBDA_FUNCTION or HxOperator.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 HxExpressions, 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 `HxOperator.CALL`
Return type:	HxExpression

HxModel.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(HxOperator.RANGE, op1, op2).

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

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.

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

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

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

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

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

HxModel.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.

HxModel.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.

HxModel.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.

HxModel.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.

HxModel.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¶

HxModel.__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`