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class AbsOp​

A class for representing the absolute value

The AbsOp class is used to represent the absolute value. The number of dimensions of the operand is zero.

Attributes​

  • operand: The operand.

Note​

The AbsOp class does not have a constructor.

class AddOp​

A class for representing addition

The AddOp class is used to represent addition (+) of an arbitrary number of operands. For example a + b + c + d would be one AddOp object. The number of dimensions of each operand is zero.

Attributes​

terms: A sequence of operands to be added.

Note​

The AddOp class does not have a constructor. Its intended instantiation method is by calling the addition operation on other expressions.

class AndOp​

A class for representing logical AND

The AndOp class is used to represent logical AND (&) of an arbitrary number of operands. For example a & b & c & d would be one AndOp object. The number of dimensions of each operand is zero.

Attributes​

  • terms: A sequence of operands to apply the AND operation.

Note​

The AndOp class does not have a constructor.

class ArrayLength​

A class for referring to the length of an array at a given axis.

The ArrayLength class is to refer to the number of elements of an axis in an array.

This class is not intended to be constructed directly. Instead, we recommend using the len_at method of Placeholder, Element or Subscript.

Attributes​

  • array: A variable with ndim >= 1.
  • axis: An axis index. A nn-dimensional variable has nn axes. Axis 0 is the array's outermost axis and n−1n-1 is the innermost.
  • description (str, optional): A description of the ArrayLength instance.

Raises​

ModelingError: Raises if axis >= array.ndim.

Examples​

Create a length of axis 0 in a 2-dimensional placeholder.

>>> import jijmodeling as jm
>>> a = jm.Placeholder("a", ndim=2)
>>> N = a.len_at(0, latex="N")

class BinaryVar​

A class for creating a binary variable

The BinaryVar class is used to create a binary variable.

The index operator ([]) of a binary variable with ndim >= 1 returns a Subscript object.

Attributes​

  • name (str): A name of the binary variable.
  • shape (tuple): A tuple with the size of each dimension of the binary variable. Empty if the variable is not multi-dimensional.
  • description (str): A description of the binary variable.

Args​

  • name (str): A name of the binary variable.
  • shape (list | tuple): A sequence with the size of each dimension of the binary variable. Defaults to an empty tuple (a scalar value).
    • Each item in shape must be a valid expression evaluating to a non-negative scalar.
  • latex (str, optional): A LaTeX-name of the binary variable to be represented in Jupyter notebook.
    • It is set to name by default.
  • description (str, optional): A description of the binary variable.

Examples​

Create a scalar binary variable whose name is "z".

>>> import jijmodeling as jm
>>> z = jm.BinaryVar("z")

Create a 2-dimensional binary variable whose name is "x" and has a 2x2 shape.

>>> import jijmodeling as jm
>>> x = jm.BinaryVar("x", shape=[2, 2])

Create a 1-dimensional binary variable with the index of 123.

>>> import jijmodeling as jm
>>> x = jm.BinaryVar("x", shape=[124])
>>> x[123]
BinaryVar(name='x', shape=[NumberLit(value=124)])[NumberLit(value=123)]

class CeilOp​

A class for representing the ceil operator

The CeilOp class is used to represent the ceil operator. The number of dimensions of the operand is zero.

Attributes​

  • operand: The operand.

Note​

The CeilOp class does not have a constructor.

class Constraint​

A class for creating a constraint

The Constraint class is used to create a constraint.

Attributes​

  • name (str): A name of the constraint.
  • sense: equal sign (=) or inequality sign (>= or <=) included in the expression.
  • expression: The (in)equality equation of the constraint.
  • forall (list): A list that stores forall indices.

Args​

  • name (str): A name of the constraint.
  • expression: The (in)equality equation of the constraint.
  • forall: A list that stores forall indices. Defaults to None.

Raises​

ModelingError: Raises if expression does not contain any decision variable.

Expression​

Create an equality constraint that the sum of NN binary variables is equal to one.

>>> import jijmodeling as jm
>>> N = jm.Placeholder("N")
>>> i = jm.Element("i", belong_to=N)
>>> x = jm.BinaryVar("x", shape=(N,))
>>> repr(jm.Constraint("constraint", jm.sum(i, x[i]) == 1))
'Constraint(name="constraint", expression=sum(i in [0..N), x[i]) == 1)'

Create an inequality constraint with forall.

>>> import jijmodeling as jm
>>> N = jm.Placeholder("N")
>>> i = jm.Element("i", belong_to=N)
>>> j = jm.Element("j", belong_to=N)
>>> x = jm.BinaryVar("x", shape=(N, N))
>>> repr(jm.Constraint("constraint", jm.sum(i, x[i,j]) == 1, forall=j))
'Constraint(name="constraint", expression=sum(i in [0..N), x[i, j]) == 1, forall=[j])'

Create an inequality constraint with conditional forall.

>>> import jijmodeling as jm
>>> N = jm.Placeholder("N")
>>> i = jm.Element("i", belong_to=N)
>>> j = jm.Element("j", belong_to=N)
>>> x = jm.BinaryVar("x", shape=(N, N))
>>> repr(jm.Constraint("constraint", x[i,j] <= 2, forall=[i, (j, j != i)]))
'Constraint(name="constraint", expression=x[i, j] <= 2, forall=[i, (j, j != i)])'

class ConstraintSense​

Equality of a constraint

class ContinuousVar​

A class for creating a continuous variable

The ContinuousVar class is used to create a continuous variable. The lower and upper bounds of the variable can be specified by:

  • an integer value
  • a float value
  • a scalar expression that does not contains any decision variable
  • a Placeholder object whose dimensionality is equal to that of this variable.
  • a subscripted variable whose dimensionality is equal to that of this variable.

The index operator ([]) of a variable with ndim >= 1 returns a Subscript object.

Attributes​

  • name (str): A name of the continuous variable.
  • shape (tuple): A tuple with the size of each dimension of the integer variable. Empty if the variable is not multi-dimensional.
  • lower_bound: The lower bound of the variable.
  • upper_bound: The upper bound of the variable.
  • description (str): A description of the continuous variable.

Args​

  • name (str): A name of the continuous variable.
  • shape (list | tuple): A sequence with the size of each dimension of the continuous variable. Defaults to an empty tuple (a scalar value).
    • Each item in shape must be a valid expression evaluating to a non-negative scalar.
  • lower_bound: The lower bound of the variable.
  • upper_bound: The upper bound of the variable.
  • latex (str, optional): A LaTeX-name of the continuous variable to be represented in Jupyter notebook.
    • It is set to name by default.
  • description (str, optional): A description of the continuous variable.

Raises​

ModelingError: Raises if a bound is a Placeholder or Subscript object whose ndim is neither 0 nor the same value as ndim of the continuous variable.

Examples​

Create a scalar continuous variable whose name is "z" and domain is [-1, 1].

>>> import jijmodeling as jm
>>> z = jm.ContinuousVar("z", lower_bound=-1, upper_bound=1)

Create a 2-dimensional continuous variable...

  • whose name is "x".
  • whose domain is [0, 2].
  • where each dimension has length 2 (making this a 2x2 matrix).
>>> import jijmodeling as jm
>>> x = jm.ContinuousVar("x", shape=[2, 2], lower_bound=0, upper_bound=2)

Create a 1-dimensional continuous variable with the index of 123.

>>> import jijmodeling as jm
>>> x = jm.ContinuousVar("x", shape=[124], lower_bound=0, upper_bound=2)
>>> x[123]
ContinuousVar(name='x', shape=[NumberLit(value=124)], lower_bound=NumberLit(value=0), upper_bound=NumberLit(value=2))[NumberLit(value=123)]

class CustomPenaltyTerm​

A class for creating a custom penalty term

The CustomPenaltyTerm class is used to create a custom penalty term.

Attributes​

  • name (str): A name of the custom penalty term.
  • expression: The expression of the custom penalty term.
  • forall (list): A list that stores forall indices.

Args​

  • name (str): A name of the custom penalty term.
  • expression: The expression of the custom penalty term.
  • forall: A list that stores forall indices. Defaults to None.

Raises​

ModelingError: Raises if expression does not contain any decision variable.

Expression​

Create a custom penalty term.

>>> import jijmodeling as jm
>>> N = jm.Placeholder("N")
>>> i = jm.Element("i", belong_to=N)
>>> x = jm.BinaryVar("x", shape=(N,))
>>> repr(jm.CustomPenaltyTerm("custom penalty term", (jm.sum(i, x[i]) - 1)**2))  # doctest: +ELLIPSIS
'CustomPenaltyTerm(name="custom penalty term", expression=((sum(i in [0..N), x[i]) - 1) ** 2))'

Create a custom penalty term with forall.

>>> import jijmodeling as jm
>>> N = jm.Placeholder("N")
>>> i = jm.Element("i", belong_to=N)
>>> j = jm.Element("j", belong_to=N)
>>> x = jm.BinaryVar("x", shape=(N, N))
>>> repr(jm.CustomPenaltyTerm("custom penalty term", (jm.sum(i, x[i,j]) - 1)**2, forall=j))  # doctest: +ELLIPSIS
'CustomPenaltyTerm(name="custom penalty term", expression=((sum(i in [0..N), x[i, j]) - 1) ** 2), forall=[j])'

Create a custom penalty term with conditional forall.

>>> import jijmodeling as jm
>>> N = jm.Placeholder("N")
>>> i = jm.Element("i", belong_to=N)
>>> j = jm.Element("j", belong_to=N)
>>> x = jm.BinaryVar("x", shape=(N, N))
>>> repr(jm.CustomPenaltyTerm("custom penalty term", (x[i,j] - 2)**2, forall=[i, (j, j != i)]))  # doctest: +ELLIPSIS
'CustomPenaltyTerm(name="custom penalty term", expression=((x[i, j] - 2) ** 2), forall=[i, (j, j != i)])'

class DummyIndexedVar​

A class for representing a subscripted variable with dummy indices

The DummyIndexedVar class is an intermediate representation to support syntactic sugar of sum/prod with slices.

Note​

The DummyIndexedVar class does not have a constructor.

class Element​

A class for creating an element

The Element class is used to create an element. It is used in the following cases:

  • an index of summation ∑\displaystyle \sum (SumOp)
  • an index of product ∏\displaystyle \prod (ProdOp)
  • a bound variable of the universal quantifier ∀\forall (Forall)

Elements specify a set to which they belong. The set can be:

  1. A half-open range, where the lower bound is included and the upper bound is excluded.
  2. A Placeholder, Element, or Subscript object with ndim >= 1.

Ranges are generally specified with tuples as (start, end). For convenience, passing a single number or scalar object as the argument is interpreted as the end of a range starting from zero.

The index operator ([]) of an element with ndim >= 1 returns a Subscript object.

Attributes​

  • name (str): A name of the element.
  • ndim (int): The number of dimensions of the element. The value is one less than the value of belong_to.ndim.
  • description (str): A description of the element.
  • belong_to: A set the element belongs to.

Args​

  • name (str): A name of the element.
  • belong_to: A set the element belongs to.
  • latex (str, optional): A LaTeX-name of the element to be represented in Jupyter notebook.
    • It is set to name by default.
  • description (str, optional): A description of the element.

Examples​

Note that belong_to is a positional argument, not a keyword argument, and so does not need to be written out. This is done in some of these examples for clarity.

Create an element that belongs to a half-open range.

>>> import jijmodeling as jm
>>> i = jm.Element("i", belong_to=(0,10))

If you pass a scalar as the belong_to argument, the set that the element belongs to is a range starting at 0 going up to that value.

>>> import jijmodeling as jm
>>> i = jm.Element("i", 10)
>>> assert jm.is_same(i, jm.Element("i", belong_to=(0,10)))

The applies not just to numbers, but certain scalars, like Placeholder (with ndim == 0).

>>> import jijmodeling as jm
>>> n = jm.Placeholder("N")
>>> i = jm.Element("i", n)
>>> assert jm.is_same(i, jm.Element("i", belong_to=(0,n)))

Create an element that belongs to a 1-dimensional placeholder.

>>> import jijmodeling as jm
>>> E = jm.Placeholder("E", ndim=1)
>>> e = jm.Element("e", E)

Create a 1-dimensional element with the index of 123.

>>> import jijmodeling as jm
>>> a = jm.Placeholder("a", ndim=2)
>>> e = jm.Element("e", a)
>>> e[123]
Element(name='e', belong_to=Placeholder(name='a', ndim=2))[NumberLit(value=123)]

class EqualOp​

A class for representing the equal operator

The EqualOp class is used to represent the equal operator (==). The number of dimensions of each operand is zero.

Attributes​

  • left: The left-hand operand.
  • right: The right-hand operand.

Note​

The EqualOp class does not have a constructor.

class Evaluation​

A class for evaluation.

The Evaluation class is to represent the result of evaluating a model.

Attributes​

  • energy(numpy.ndarray) : The value of energy of each sample.
  • objective(numpy.ndarray) : The value of an objective function of each sample.
  • constraint_violations(dict[str, numpy.ndarray]) : The constraint violation of each sample.
  • constraint_forall(dict[str, numpy.ndarray]) : The constraint forall of each sample.
  • constraint_values(numpy.ndarray) : The constraint value of each sample.
  • penalty(dict[str, numpy.ndarray]) : The penalty of each sample.

class FloorOp​

A class for representing the floor operator

The FloorOp class is used to represent the floor operator. The number of dimensions of the operand is zero.

Attributes​

  • operand: The operand.

Note​

The FloorOp class does not have a constructor.

class GreaterThanEqualOp​

A class for representing the greater than equal operator

The GreaterThanEqualOp class is used to represent the greater than equal operator (>=). The number of dimensions of each operand is zero.

Attributes​

  • left: The left-hand operand.
  • right: The right-hand operand.

Note​

The GreaterThanEqualOp class does not have a constructor.

class GreaterThanOp​

A class for representing the greater than operator

The GreaterThanOp class is used to represent the greater than operator (>). The number of dimensions of each operand is zero.

Attributes​

  • left: The left-hand operand.
  • right: The right-hand operand.

Note​

The GreaterThanOp class does not have a constructor.

class IntegerVar​

A class for creating an integer variable

The IntegerVar class is used to create an integer variable. The lower and upper bounds of the variable can be specified by:

  • an integer value
  • a float value
  • a scalar expression that does not contains any decision variable
  • a Placeholder object whose dimensionality is equal to that of this variable.
  • a subscripted variable whose dimensionality is equal to that of this variable.

The index operator ([]) of a variable with ndim >= 1 returns a Subscript object.

Attributes​

  • name (str): A name of the integer variable.
  • shape (tuple): A tuple with the size of each dimension of the integer variable. Empty if the variable is not multi-dimensional.
  • lower_bound: The lower bound of the variable.
  • upper_bound: The upper bound of the variable.
  • description (str): A description of the integer variable.

Args​

  • name (`str): A name of the integer variable.
  • shape (list | tuple): A sequence with the size of each dimension of the integer variable. Defaults to an empty tuple (a scalar value).
    • Each item in shape must be a valid expression evaluating to a non-negative scalar.
  • lower_bound: The lower bound of the variable.
  • upper_bound: The upper bound of the variable.
  • latex (str, optional): A LaTeX-name of the integer variable to be represented in Jupyter notebook.
    • It is set to name by default.
  • description (str, optional): A description of the integer variable.

Raises​

ModelingError: Raises if a bound is a Placeholder or Subscript object whose ndim is neither 0 nor the same value as ndim of the integer variable.

Examples​

Create a scalar integer variable whose name is "z" and domain is [-1, 1].

>>> import jijmodeling as jm
>>> z = jm.IntegerVar("z", lower_bound=-1, upper_bound=1)

Create a 2-dimensional integer variable...

  • whose name is "x".
  • whose domain is [0, 2].
  • where each dimension has length 2 (making this a 2x2 matrix).
>>> import jijmodeling as jm
>>> x = jm.IntegerVar("x", shape=[2, 2], lower_bound=0, upper_bound=2)

Create a 1-dimensional integer variable with the index of 123.

>>> import jijmodeling as jm
>>> x = jm.IntegerVar("x", shape=[124], lower_bound=0, upper_bound=2)
>>> x[123]
IntegerVar(name='x', shape=[NumberLit(value=124)], lower_bound=NumberLit(value=0), upper_bound=NumberLit(value=2))[NumberLit(value=123)]

class LessThanEqualOp​

A class for representing the less than equal operator

The LessThanEqualOp class is used to represent the less than equal operator (<=). The number of dimensions of each operand is zero.

Attributes​

  • left: The left-hand operand.
  • right: The right-hand operand.

Note​

The LessThanEqualOp class does not have a constructor.

class LessThanOp​

A class for representing the less than operator

The LessThanOp class is used to represent the less than operator (<). The number of dimensions of each operand is zero.

Attributes​

  • left: The left-hand operand.
  • right: The right-hand operand.

Note​

The LessThanOp class does not have a constructor.

class LnOp​

A class for representing the natural logarithm

The LnOp class is used to represent the natural logarithm. The number of dimensions of the operand is zero.

Attributes​

operand: The operand.

Note​

The LnOp class does not have a constructor.

class Log10Op​

A class for representing the base 10 logarithm

The Log10Op class is used to represent the base 10 logarithm. The number of dimensions of the operand is zero.

Attributes​

  • operand: The operand.

Note​

The Log10Op class does not have a constructor.

class Log2Op​

A class for representing the base 2 logarithm

The Log2Op class is used to represent the base 2 logarithm. The number of dimensions of the operand is zero.

Attributes​

operand: The operand.

Note​

The Log2Op class does not have a constructor.

class MaxOp​

A class for representing the maximum value.

The MaxOp class is used to represent the minimum value of operands. The number of dimensions of each operand is zero.

Attributes​

  • terms: A sequence of operands.

Note​

The MaxOp class does not have a constructor. Its intended instantiation method is by calling the max function.

class MeasuringTime​

A class for storing time to be measured.

Attributes​

  • solve (SolvingTime): Time to solve the problem.
  • system (SystemTime): Time to measure system time.
  • total (float, optional): Total time to solve the problem. Defaults to None.

class MinOp​

A class for representing the minimum value.

The MinOp class is used to represent the minimum value of operands. The number of dimensions of each operand is zero.

Attributes​

  • terms: A sequence of operands.

Note​

The MinOp class does not have a constructor. Its intended instantiation method is by calling the min function.

class ModOp​

A class for representing modulo

The ModOp class is used to represent modulo (or remainder) (%). The number of dimensions of each operand is zero.

Attributes​

  • left: The left-hand operand.
  • right: The right-hand operand.

Note​

The ModOp class does not have a constructor.

class MulOp​

A class for representing multiplication

The MulOp class is used to represent multiplication (*) of an arbitrary number of operands. For example a * b * c * d would be one AddOp object. The number of dimensions of each operand is zero.

Attributes​

terms: A sequence of operands to be multiplied.

Note​

The MulOp class does not have a constructor. Its intended instantiation method is by calling the multiplication operation on other expressions.

class NotEqualOp​

A class for representing the not equal operator

The NotEqualOp class is used to represent the not equal operator (!=). The number of dimensions of each operand is zero.

Attributes​

  • left: The left-hand operand.
  • right: The right-hand operand.

Note​

The NotEqualOp class does not have a constructor.

class NumberLit​

A class for creating a number literal

The NumberLit class is used to create a number literal. Its instance is automatically generated by the return value of arithmetic or mathematical functions taking a number literal and an object defined by jijmodeling as arguments.

Attributes​

  • value (int | float): A numeric value.
  • dtype (DataType): A type of the value.
    • dtype is DataType.INTEGER if the type of the value is integer else dtype is DataType.FLOAT.

Args​

  • value (int | float): A numeric value.

Examples​

Create a number literal with a integer value 123.

>>> import jijmodeling as jm
>>> v = jm.NumberLit(123)
>>> assert v.value == 123
>>> assert v.dtype == jm.DataType.INTEGER

Create a number literal with a float value 1.23.

>>> import jijmodeling as jm
>>> v = jm.NumberLit(1.23)
>>> assert v.value == 1.23
>>> assert v.dtype == jm.DataType.FLOAT

class OrOp​

A class for representing logical OR

The OrOp class is used to represent logical OR (|) of an arbitrary number of operands. For example a | b | c | d would be one OrOp object. The number of dimensions of each operand is zero.

Attributes​

  • terms: A sequence of operands to apply the OR operation.

Note​

The OrOp class does not have a constructor.

class Placeholder​

A class for creating a placeholder

The Placeholder class is used to create a placeholder. It is a symbol to be replaced by a numerical value when you solve an optimization problem.

The index operator ([]) of a placeholder with ndim >= 1 returns a Subscript object.

Attributes​

  • name (str): A name of the placeholder.
  • ndim (int): The number of dimensions of the placeholder.
  • description (str, optional): A description of the placeholder.

Args​

  • name (str): A name of the placeholder.
  • ndim (int): The number of dimensions of the placeholder. Defaults to 0. The ndim must be set to a non-negative value.
  • latex (str, optional): A LaTeX-name of the placeholder to be represented in Jupyter notebook. It is set to name by default.
  • description (str, optional): A description of the placeholder.

Raises​

  • TypeError: Raises if set a float value to ndim.
  • OverflowError: Raises if set a negative value to ndim.

Examples​

Create a scalar (or ndim is 0) placeholder whose name is "a".

>>> import jijmodeling as jm
>>> a = jm.Placeholder("a")

Create a 2-dimensional placeholder whose name is "m".

>>> import jijmodeling as jm
>>> m = jm.Placeholder("m", ndim=2)

Create a 1-dimensional placeholder with the index of 123.

>>> import jijmodeling as jm
>>> a = jm.Placeholder("a", ndim=2)
>>> a[123]
Placeholder(name='a', ndim=2)[NumberLit(value=123)]

class PowOp​

A class for representing the power operator

The ModOp class is used to represent the power operator(**). The number of dimensions of each operand is zero.

Attributes​

  • base: The base operand.
  • exponent: The exponent operand.

Note​

The PowOp class does not have a constructor.

class Problem​

A class for creating an optimization problem

The Problem class is used to create an optimization problem.

Attributes​

  • name (str): A name of the optimization problem.
  • sense: Sense of the optimization problem.
  • objective: The objective function of the optimization problem.
  • constraints (dict): A dictionary that stores constraints.
    • A key is the name of a constraint and the value is the constraint object.
  • custom_penalty_terms (dict): A dictionary that stores custom penalty terms.
    • A key is the name of a custom penalty and the value is the custom penalty object.

Args​

  • name (str): A name of the optimization problem.
  • sense (optional): Sense of the optimization problem. Defaults to ProblemSense.MINIMIZE.

class ProblemSense​

An optimization sense

class ProdOp​

A class for representing product

The ProdOp class is used to represent product. The number of dimensions of the opreand is zero.

Attributes​

  • index: The index of product.
  • condition: The condition for the product index.
  • operand: The opreand.

Note​

The ProdOp class does not have a constructor.

class Range​

A class representing a half-open interval.

The Range class is used to represent a half-open interval [start, end). This class does not have a constructor because it should be created by the Element class.

Attributes​

  • start: The lower bound of the range (inclusive).
  • end: The upper bound of the range (exclusive).

Note​

This class does not contain any decision variable.

class Record​

A class for representing a record.

There are two types of solutions that can be given; dense solutions and sparse solutions. A dense solution is a dict whose key is a variable name and the value is a list of numpy.ndarray. A sparse solution is a dict whose key is a variable name and the value is a list of tuples with three elements, where the first element is a list of indices, the second element is a list of non-zero values, and the third element is a shape of the array. The length of the list of solutions must be the same as the length of the list of num_occurrences. Each index of the list of solutions corresponds to the same index of the list of non-zero values.

As an example, consider the following solutions:

{
    "x": [
        np.array([[0.0, 1.0, 0.0], [2.0, 0.0, 3.0]]),
        np.array([[1.0, 0.0, 0.0], [2.0, 3.0, 4.0]])
    ],
    "y": [
        np.array([0.0, 0.0, 1.0]),
        np.array([0.0, 1.0, 0.0])
    ]
}

This is a dense solution. The corresponding sparse solution is as follows:

{
    "x": [
        (([0, 1, 1], [1, 0, 2]), [1.0, 2.0, 3.0], (2, 3)),
        (([0, 1, 1, 1], [0, 0, 1, 2]), [1.0, 2.0, 3.0, 4.0], (2, 3))
    ],
    "y": [
        (([2],), [1.0], (3,)),
        (([1],), [1.0], (3,))
    ]
}

Attributes​

  • solution (Union[Dict[str, List[numpy.ndarray]], Dict[str, List[Tuple[List[int], List[float], Tuple[int, ...]]]]]): A solution.
  • num_occurrences (List[int]): A list of the number of occurrences in which the solution is observed.

class SampleSet​

A class for storing time of jijzept running.

Attributes​

  • post_problem_and_instance_data (float, optional): Time to upload problem and instance_data to blob. Defaults to None.
  • request_queue (float, optional): Time to send request to queue. Defaults to None.
  • fetch_problem_and_instance_data (float, optional): Time to fetch problem and instance_data from blob. Defaults to None.
  • fetch_result (float, optional): Time to fetch result. Defaults to None.
  • deserialize_solution (float, optional): Time to deserialize json object. Defaults to None.

class SemiContinuousVar​

A class for creating a semi-continuous variable

The SemiContinuousVar class is used to create a semi-continuous variable. Either the lower bound or the upper bound is set by the following object:

  • an integer value
  • a float value
  • a scalar expression that does not contains any decision variable
  • a Placeholder object whose dimensionality is equal to that of this variable.
  • a subscripted variable whose dimensionality is equal to that of this variable.

The index operator ([]) of a semi-continuous variable with ndim >= 1 returns a Subscript object.

Attributes​

  • name (str): A name of the semi-continuous variable.
  • shape (tuple): A tuple with the size of each dimension of the semi-continuous variable. Empty if the variable is not multi-dimensional.
  • lower_bound: The lower bound of the variable.
  • upper_bound: The upper bound of the variable.
  • description (str): A description of the semi-continuous variable.

Args​

  • name (str): A name of the semi-continuous variable.
  • shape (list | tuple): A sequence with the size of each dimension of the binary variable. Defaults to an empty tuple (a scalar value).
    • Each item in shape must be a valid expression evaluating to a non-negative scalar.
  • lower_bound: The lower bound of the variable.
  • upper_bound: The upper bound of the variable.
  • latex (str, optional): A LaTeX-name of the semi-continuous variable to be represented in Jupyter notebook.
    • It is set to name by default.
  • description (str, optional): A description of the semi-continuous variable.

Raises​

ModelingError: Raises if a bound is a Placeholder or Subscript object whose ndim is neither 0 nor the same value as ndim of the semi-continuous variable.

Examples​

Create a scalar semi-continuous variable whose name is "z" and domain is [-1, 1].

>>> import jijmodeling as jm
>>> z = jm.SemiContinuousVar("z", lower_bound=-1, upper_bound=1)

Create a 2-dimensional semi-continuous variable...

  • whose name is "x".
  • whose domain is [0, 2].
  • where each dimension has length 2 (making this a 2x2 matrix).
>>> import jijmodeling as jm
>>> x = jm.SemiContinuousVar("x", shape=[2, 2], lower_bound=0, upper_bound=2)

Create a 1-dimensional semi-continuous variable with the index of 123.

>>> import jijmodeling as jm
>>> x = jm.SemiContinuousVar("x", shape=[124], lower_bound=0, upper_bound=2)
>>> x[123]
SemiContinuousVar(name='x', shape=[NumberLit(value=124)], lower_bound=NumberLit(value=0), upper_bound=NumberLit(value=2))[NumberLit(value=123)]

class SemiIntegerVar​

A class for creating a semi-integer variable

The SemiIntegerVar class is used to create a semi-integer variable. The lower and upper bounds of the variable can be specified by:

  • an integer value
  • a float value
  • a scalar expression that does not contains any decision variable
  • a Placeholder object whose dimensionality is equal to that of this variable.
  • a subscripted variable whose dimensionality is equal to that of this variable.

The index operator ([]) of a semi-integer variable with ndim >= 1 returns a Subscript object.

Attributes​

  • name (str): A name of the semi-integer variable.
  • shape (tuple): A tuple with the size of each dimension of the integer variable. Empty if the variable is not multi-dimensional.
  • lower_bound: The lower bound of the variable.
  • upper_bound: The upper bound of the variable.
  • description (str): A description of the semi-integer variable.

Args​

  • name (str): A name of the semi-integer variable.
  • shape (list | tuple): A sequence with the size of each dimension of the integer variable. Defaults to an empty tuple (a scalar value).
    • Each item in shape must be a valid expression evaluating to a non-negative scalar.
  • lower_bound: The lower bound of the variable.
  • upper_bound: The upper bound of the variable.
  • latex (str, optional): A LaTeX-name of the semi-integer variable to be represented in Jupyter notebook.
    • It is set to name by default.
  • description (str, optional): A description of the semi-integer variable.

Raises​

ModelingError: Raises if a bound is a Placeholder or Subscript object whose ndim is neither 0 nor the same value as ndim of the semi-integer variable.

Examples​

Create a scalar semi-integer variable whose name is "z" and domain is [-1, 1].

>>> import jijmodeling as jm
>>> z = jm.SemiIntegerVar("z", lower_bound=-1, upper_bound=1)

Create a 2-dimensional semi-integer variable...

  • whose name is "x".
  • whose domain is [0, 2].
  • where each dimension has length 2 (making this a 2x2 matrix).
>>> import jijmodeling as jm
>>> x = jm.SemiIntegerVar("x", shape=[2, 2], lower_bound=0, upper_bound=2)

Create a 1-dimensional semi-integer variable with the index of 123.

>>> import jijmodeling as jm
>>> x = jm.SemiIntegerVar("x", shape=[124], lower_bound=0, upper_bound=2)
>>> x[123]
SemiIntegerVar(name='x', shape=[NumberLit(value=124)], lower_bound=NumberLit(value=0), upper_bound=NumberLit(value=2))[NumberLit(value=123)]

class SolvingTime​

A class for storing time to solve a problem.

Attributes​

  • preprocess (float, optional): Time to preprocess the problem. Defaults to None.
  • solve (float, optional): Time to solve the problem. Defaults to None.
  • postprocess (float, optional): Time to postprocess the problem. Defaults to None.

class Subscript​

A class for representing a subscripted variable

The Subscript class is used to represent a variable with subscriptions.

Attributes​

  • variable: A variable that has subscripts.
  • subscripts (list): A list of subscripts.
  • ndim (int): The number of dimensions of the subscripted variable.

Note​

The Subscript class does not have a constructor.

class SumOp​

A class for representing summation

The SumOp class is used to represent summation. The number of dimensions of the opreand is zero.

Attributes​

  • index: The index of summation.
  • condition: The condition for the summation index.
  • operand: The opreand.

Note​

The SumOp class does not have a constructor.

class SystemTime​

A class for storing time of jijzept running.

Attributes​

  • post_problem_and_instance_data (float, optional): Time to upload problem and instance_data to blob. Defaults to None.
  • request_queue (float, optional): Time to send request to queue. Defaults to None.
  • fetch_problem_and_instance_data (float, optional): Time to fetch problme and instance_data from blob. Defaults to None.
  • fetch_result (float, optional): Time to fetch result. Defaults to None.
  • deserialize_solution (float, optional): Time to deserialize json object. Defaults to None.

class XorOp​

A class for representing logical XOR

The XorOp class is used to represent logical XOR (^) of an arbitrary number of operands. For example a ^ b ^ c ^ d would be one XorOp object. The number of dimensions of each operand is zero.

Attributes​

  • terms- : A sequence of operands to apply the XOR operation.

Note​

The XorOp class does not have a constructor.