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Number Partitioning API Reference

Data

Data model for NumberPartitioning use case.

NumberPartitioningData

Bases: UcData

Data for the Number Partitioning Problem.

Given a set of integers, the Number Partitioning problem asks to divide them into two subsets such that the difference of their sums is minimized.

Attributes:

  • name (Literal['number_partitioning']) –

    Identifier for this data type.

  • numbers (NumPyArray) –

    1D array of integers to partition.

plot(*, ax: Axes | None = None) -> Axes

Plot the numbers as a bar chart.

Parameters:

  • ax (Axes | None, default: None ) –

    Matplotlib axes to draw on. Creates a new figure if None.

Returns:

  • Axes –

    The axes with the plot.

to_string() -> str

Return a string describing the data.

Returns:

  • str –

    String representation of the data.

from_values(numbers: list[int]) -> NumberPartitioningData staticmethod

Create a NumberPartitioningData instance from explicit values.

Parameters:

  • numbers (list[int]) –

    1D array of integers to partition.

Returns:

generate_random(n_numbers: int = 8, max_value: int | None = None, seed: int | None = None) -> NumberPartitioningData staticmethod

Generate a random number partitioning instance.

Parameters:

  • n_numbers (int, default: 8 ) –

    Number of integers, by default 8.

  • max_value (int | None, default: None ) –

    Maximum value for each integer, by default None, will be set to 2 * n_numbers.

  • seed (int | None, default: None ) –

    Random seed for reproducibility, by default None.

Returns:

Raises:

  • ValueError –

    If n_numbers > max_value, which makes distinct sampling impossible.

Formulation

Formulation for NumberPartitioning use case.

NumberPartitioningFormulation

Bases: UcFormulation[NumberPartitioningData, NumberPartitioningSolution]

Quadratic formulation for the Number Partitioning Problem.

Mathematical Formulation

Decision Variables: x_i in {0,1} for each number i: 1 if number i is in partition 1

Objective: minimize (2 * sum_i numbers[i]*x[i] - S)^2 where S = sum(numbers)

Expanded: sum_{i,j} numbers[i]*numbers[j]*x[i]*x[j]
          - S * sum_i numbers[i]*x[i]
(constant S^2 omitted)

Constraints: None (unconstrained quadratic optimization)

to_string(data: NumberPartitioningData) -> str staticmethod

Return a string describing the formulation.

Parameters:

Returns:

  • str –

    String representation of the formulation.

formulate(data: NumberPartitioningData) -> Model staticmethod

Formulate the Number Partitioning Problem.

Uses a quadratic objective to minimize the squared difference between partition sums. No constraints are needed.

Parameters:

Returns:

  • Model –

    A Luna Model ready to be solved.

interpret(solution: Solution, data: NumberPartitioningData) -> NumberPartitioningSolution staticmethod

Extract solution from quantum result.

Parameters:

Returns:

Solution

Solution model for NumberPartitioning use case.

NumberPartitioningSolution

Bases: UcSolution

Solution for the Number Partitioning Problem.

Attributes:

  • name (Literal['number_partitioning']) –

    Identifier for this solution type.

  • partition_0 (list[int]) –

    Numbers assigned to partition 0.

  • partition_1 (list[int]) –

    Numbers assigned to partition 1.

  • sum_0 (int) –

    Sum of numbers in partition 0.

  • sum_1 (int) –

    Sum of numbers in partition 1.

  • difference (int) –

    Absolute difference between partition sums.

  • is_valid (bool) –

    Whether the difference is 0 (perfect partition).

plot(data: NumberPartitioningData | None = None, *, ax: Axes | None = None) -> Axes

Plot the number partitioning solution.

Parameters:

  • data (NumberPartitioningData | None, default: None ) –

    Problem data for context.

  • ax (Axes | None, default: None ) –

    Matplotlib axes to draw on. Creates a new figure if None.

Returns:

  • Axes –

    The axes with the plot.

to_string() -> str

Return a string describing the solution.

Returns:

  • str –

    String representation of the solution.

Instance

Instance model for NumberPartitioning use case.

NumberPartitioningInstance

Bases: UcInstance[NumberPartitioningData, NumberPartitioningFormulation, NumberPartitioningSolution]

Instance combining data and formulation for NumberPartitioning.

Collection

Collection of NumberPartitioning instances.

NumberPartitioningCollection

Bases: UcInstanceCollection[NumberPartitioningInstance]

Collection of Number Partitioning instances.

This collection provides methods to generate benchmark instances with various characteristics for testing and evaluation.

from_random(min_n_numbers: int, max_n_numbers: int, num_instances: int = 1, *, max_value: int | None = None, seed: int | None = None) -> NumberPartitioningCollection classmethod

Generate random number partitioning instances.

Parameters:

  • min_n_numbers (int) –

    Minimum number of integers per instance.

  • max_n_numbers (int) –

    Maximum number of integers per instance.

  • num_instances (int, default: 1 ) –

    Number of instances per size, by default 1.

  • max_value (int | None, default: None ) –

    Maximum value for each integer, by default 2 * n_numbers.

  • seed (int | None, default: None ) –

    Random seed for reproducibility, by default None.

Returns: