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Set Partitioning API Reference

Data

Data model for SetPartitioning use case.

SetPartitioningData

Bases: UcData

Data for the Set Partitioning Problem.

Given a universe of elements, a collection of subsets, and costs per subset, the Set Partitioning problem asks to find a minimum-cost collection of subsets such that every element is covered exactly once.

Attributes:

  • name (Literal['set_partitioning']) –

    Identifier for this data type.

  • subset_matrix (NumPyArray) –

    A 2D NumPy array (int) where each row represents a subset and each column an element. subset_matrix[i][j] = 1 if subset i contains element j, 0 otherwise.

  • costs (NumPyArray) –

    A 1D NumPy array (float) with costs associated with each subset.

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

Plot the subset matrix as a binary heatmap with costs.

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(subset_matrix: list[list[int]], costs: list[float]) -> SetPartitioningData staticmethod

Create a SetPartitioningData instance from explicit values.

Parameters:

  • subset_matrix (NumPyArray) –

    A list of integers where each row represents a subset and each column an element. subset_matrix[i][j] = 1 if subset i contains element j, 0 otherwise.

  • costs (NumPyArray) –

    Costs associated with each subset.

Returns:

generate_random(n_elements: int = 5, n_subsets: int = 8, density: float = 0.4, seed: int | None = None, costs_generation: Literal['random', 'proportional'] = 'random') -> SetPartitioningData staticmethod

Generate a random set partitioning instance.

Parameters:

  • n_elements (int, default: 5 ) –

    Number of elements in the universe, by default 5.

  • n_subsets (int, default: 8 ) –

    Number of subsets, by default 8.

  • density (float, default: 0.4 ) –

    Probability that an element is included in a subset, by default 0.4.

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

    Random seed for reproducibility, by default None.

  • costs_generation (Literal['random', 'proportional'], default: 'random' ) –

    Cost generation strategy. "random" draws from Uniform(1, 10), "proportional" sets costs to subset size +/- Uniform(-0.5, 1.0), by default "random".

Returns:

Formulation

Formulation for SetPartitioning use case.

SetPartitioningFormulation

Bases: UcFormulation[SetPartitioningData, SetPartitioningSolution]

Constraint-based formulation for the Set Partitioning Problem.

Mathematical Formulation

Decision Variables: x_s in {0,1} for each subset s: 1 if subset s is selected

Objective: minimize sum_s costs[s] * x_s

Constraints: For each element e: sum_{s containing e} x_s == 1 (each element must be covered exactly once)

to_string(data: SetPartitioningData) -> str staticmethod

Return a string describing the formulation.

Parameters:

Returns:

  • str –

    String representation of the formulation.

formulate(data: SetPartitioningData) -> Model staticmethod

Formulate the Set Partitioning Problem using constraint-based approach.

Parameters:

Returns:

  • Model –

    A Luna Model ready to be solved.

interpret(solution: Solution, data: SetPartitioningData) -> SetPartitioningSolution staticmethod

Extract solution from quantum result.

Parameters:

  • solution (Solution) –

    The quantum solution.

  • data (SetPartitioningData) –

    The problem data.

Returns:

Solution

Solution model for SetPartitioning use case.

SetPartitioningSolution

Bases: UcSolution

Solution for the Set Partitioning Problem.

Attributes:

  • name (Literal['set_partitioning']) –

    Identifier for this solution type.

  • selected_subsets (list[int]) –

    Indices of selected subsets.

  • total_cost (float) –

    Total cost of selected subsets.

  • is_valid (bool) –

    Whether each element is covered exactly once.

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

Plot the set partitioning solution.

Parameters:

  • data (SetPartitioningData | 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 SetPartitioning use case.

SetPartitioningInstance

Bases: UcInstance[SetPartitioningData, SetPartitioningFormulation, SetPartitioningSolution]

Instance combining data and formulation for SetPartitioning.

Collection

Collection of SetPartitioning instances.

SetPartitioningCollection

Bases: UcInstanceCollection[SetPartitioningInstance]

Collection of Set Partitioning instances.

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

from_random(min_num_elements: int, max_num_elements: int, num_instances: int = 1, *, density: float = 0.4, subset_ratio: float = 1.6, costs_generation: Literal['proportional', 'random'] = 'random', seed: int | None = None) -> SetPartitioningCollection classmethod

Generate random set partitioning instances.

Parameters:

  • min_num_elements (int) –

    Minimum number of elements per instance.

  • max_num_elements (int) –

    Maximum number of elements per instance.

  • num_instances (int, default: 1 ) –

    Number of instances per size, by default 1.

  • density (float, default: 0.4 ) –

    Probability that an element is included in a subset, by default 0.4.

  • subset_ratio (float, default: 1.6 ) –

    Ratio of subsets to elements, by default 1.6.

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

    Random seed for reproducibility, by default None.

Returns: