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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 LunaModel 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 | None = None, max_num_elements: int | None = None, num_instances: int = 1, *, sizes: Sequence[int] | None = None, 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 | None, default: None ) –

    Minimum number of elements per instance.

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

    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.

  • sizes (Sequence[int] | None, default: None ) –

    Explicit sizes to generate, e.g. [10, 50, 100], instead of a range. Mutually exclusive with min_num_elements/max_num_elements, by default None.

Returns:

filter_infeasible(max_runtime: float = 3600, *, quiet: bool = True) -> list[bool]

Drop the instances of this collection that have no feasible solution.

Every instance is formulated and handed to SCIP, which stops as soon as it finds the first feasible solution. An instance is removed from the collection when SCIP proves the model infeasible, when no solution turns up within max_runtime, or when formulating it fails altogether. This keeps randomly generated instances from breaking a downstream pipeline.

Parameters:

  • max_runtime (float, default: 3600 ) –

    SCIP time limit per instance in seconds. Must be positive. Defaults to 3600 seconds.

  • quiet (bool, default: True ) –

    Suppress the SCIP solver output.

Returns:

  • list[bool] –

    Feasibility mask over the instances as they were before filtering, in that order: True where the instance was kept, False where it was removed.

Raises: