relationalai.experimental.solvers.zero_one()

Signature

zero_one(arg: dsl.Instance) -> SolverExpression

Returns a solver expression that constrains the solver variables for entities produced by arg to binary values (0 or 1). Equivalent to setting type="zero_one" in the SolverModel.variable() method. Must be called in a Model.rule() or solvers.operators() context.

Parameters

Name	Type	Description
arg	dsl.Instance	An instance of an entity type corresponding to a solver variable.

Returns

A SolverExpression object.

Example

Use zero_one() with the SolverModel.constraint() method to constrain solver variables to binary values:

import relationalai as rai
from relationalai.experimental import solvers


# Create a RAI model.
model = rai.Model("WeeklyShiftAssignment")

# Declare entity types and properties.

# Entity types.
Employee = model.Type("Employee")
Shift = model.Type("Shift")
Day = model.Type("Day")
Available = model.Type("Available")
Scenario = model.Type("Scenario")  # All possible employee–shift–day combinations.
Assignment = model.Type("Assignment")  # A Scenario that is assigned.

# Properties.
Employee.name.declare()
Shift.name.declare()
Shift.capacity.declare()
Available.employee.declare()
Available.day.declare()
Scenario.employee.declare()
Scenario.shift.declare()
Scenario.day.declare()

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# Define sample data.

# Employees.
with model.rule(dynamic=True):
    for name in ["Alice", "Bob", "Carol", "Dave", "Eve"]:
        Employee.add(name=name)

# Shifts.
with model.rule():
    Shift.add(name="Morning").set(capacity=2)
    Shift.add(name="Evening").set(capacity=3)

# Days of the week.
with model.rule(dynamic=True):
    for name in ["Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"]:
        Day.add(name=name)

# Employee-day availability.
with model.rule(dynamic=True):
    # Alice works weekdays only
    for name in ["Mon", "Tue", "Wed", "Thu", "Fri"]:
        Available.add(employee=Employee(name="Alice"), day=Day(name=name))
    # Bob works all days
    Available.add(employee=Employee(name="Bob"), day=Day())
    # Carol works weekends only
    for name in ["Sat", "Sun"]:
        Available.add(employee=Employee(name="Carol"), day=Day(name=name))
    # Dave works Mon/Wed/Fri
    for name in ["Mon", "Wed", "Fri"]:
        Available.add(employee=Employee(name="Dave"), day=Day(name=name))
    # Eve works Tue/Thu/Sat
    for name in ["Tue", "Thu", "Sat"]:
        Available.add(employee=Employee(name="Eve"), day=Day(name=name))

# All possible employee–shift–day combinations
with model.rule():
    Scenario.add(employee=Employee(), shift=Shift(), day=Day())

# Create a SolverModel instance from the model.
solver_model = solvers.SolverModel(model)

# Define solver variables.

# Scenario assignment: binary variable for each employee–shift–day combination.
with model.rule():
    scenario = Scenario()
    solver_model.variable(
        scenario,
        name_args=["assigned", scenario.employee.name, scenario.day.name, scenario.shift.name],
    )

with solvers.operators():
    assignment = Assignment()
    solver_model.constraint(solvers.zero_one(assignment))

Alternatively, you may set type="zero_one" in the SolverModel.variable() method to achieve the same effect:

import relationalai as rai
from relationalai.experimental import solvers

67 collapsed lines

# Create a RAI model.
model = rai.Model("WeeklyShiftAssignment")

# Declare entity types and properties.

# Entity types.
Employee = model.Type("Employee")
Shift = model.Type("Shift")
Day = model.Type("Day")
Available = model.Type("Available")
Scenario = model.Type("Scenario")  # All possible employee–shift–day combinations.
Assignment = model.Type("Assignment")  # A Scenario that is assigned.

# Properties.
Employee.name.declare()
Shift.name.declare()
Shift.capacity.declare()
Available.employee.declare()
Available.day.declare()
Scenario.employee.declare()
Scenario.shift.declare()
Scenario.day.declare()


# Define sample data.

# Employees.
with model.rule(dynamic=True):
    for name in ["Alice", "Bob", "Carol", "Dave", "Eve"]:
        Employee.add(name=name)

# Shifts.
with model.rule():
    Shift.add(name="Morning").set(capacity=2)
    Shift.add(name="Evening").set(capacity=3)

# Days of the week.
with model.rule(dynamic=True):
    for name in ["Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"]:
        Day.add(name=name)

# Employee-day availability.
with model.rule(dynamic=True):
    # Alice works weekdays only
    for name in ["Mon", "Tue", "Wed", "Thu", "Fri"]:
        Available.add(employee=Employee(name="Alice"), day=Day(name=name))
    # Bob works all days
    Available.add(employee=Employee(name="Bob"), day=Day())
    # Carol works weekends only
    for name in ["Sat", "Sun"]:
        Available.add(employee=Employee(name="Carol"), day=Day(name=name))
    # Dave works Mon/Wed/Fri
    for name in ["Mon", "Wed", "Fri"]:
        Available.add(employee=Employee(name="Dave"), day=Day(name=name))
    # Eve works Tue/Thu/Sat
    for name in ["Tue", "Thu", "Sat"]:
        Available.add(employee=Employee(name="Eve"), day=Day(name=name))

# All possible employee–shift–day combinations
with model.rule():
    Scenario.add(employee=Employee(), shift=Shift(), day=Day())

# Create a SolverModel instance from the model.
solver_model = solvers.SolverModel(model)

# Define solver variables.

# Scenario assignment: binary variable for each employee–shift–day combination.
with model.rule():
    scenario = Scenario()
    solver_model.variable(
        scenario,
        type="zero_one",
        name_args=["assigned", scenario.employee.name, scenario.day.name, scenario.shift.name],
    )

Resource

See the Define Solver Constraints section of the Working with Solver Models guide to learn more about solver expressions.

See Also

• solvers.integer()
• solvers.integer_interval()
• solvers.interval()