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Subset Sum API Reference

Data

Data model for SubsetSum use case.

SubsetSumData

Bases: UcData

Data for the Subset Sum Problem.

Given a set of integers and a target value, the Subset Sum problem asks whether there exists a subset whose elements sum to the target.

Attributes:

  • name (Literal['subset_sum']) –

    Identifier for this data type.

  • numbers (NumPyArray) –

    A 1D NumPy array containing the integers to choose from.

  • target (int) –

    The target sum to achieve.

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

Plot the numbers as a bar chart with target line.

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], target: int) -> SubsetSumData staticmethod

Create a SubsetSumData instance from explicit values.

Parameters:

  • numbers (list[int]) –

    A list of integers to choose from.

  • target (int) –

    The target sum to achieve.

Returns:

  • SubsetSumData –

    A SubsetSumData instance with the given values.

generate_random(n_numbers: int = 10, max_value: int | None = None, seed: int | None = None) -> SubsetSumData staticmethod

Generate a random subset sum instance.

Generates random numbers and picks a valid target as the sum of a random subset, ensuring the problem is feasible.

Parameters:

  • n_numbers (int, default: 10 ) –

    Number of integers, by default 10.

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

    Maximum value for each integer, by default None and will be set to 2 time n_number.

  • 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 SubsetSum use case.

SubsetSumFormulation

Bases: UcFormulation[SubsetSumData, SubsetSumSolution]

Constraint-based formulation for the Subset Sum Problem.

Mathematical Formulation

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

Objective: minimize 0 (feasibility problem)

Constraints: sum_i numbers[i] * x_i == target

to_string(data: SubsetSumData) -> str staticmethod

Return a string describing the formulation.

Parameters:

Returns:

  • str –

    String representation of the formulation.

formulate(data: SubsetSumData) -> Model staticmethod

Formulate the Subset Sum Problem using constraint-based approach.

Parameters:

Returns:

  • Model –

    A Luna Model ready to be solved.

interpret(solution: Solution, data: SubsetSumData) -> SubsetSumSolution staticmethod

Extract solution from result.

Parameters:

  • solution (Solution) –

    The solution.

  • data (SubsetSumData) –

    The problem data.

Returns:

Solution

Solution model for SubsetSum use case.

SubsetSumSolution

Bases: UcSolution

Solution for the Subset Sum Problem.

Attributes:

  • name (Literal['subset_sum']) –

    Identifier for this solution type.

  • selected_indices (NumPyArray) –

    Indices of selected numbers.

  • selected_sum (int) –

    Sum of selected numbers.

  • difference (int) –

    Absolute difference |sum - target|.

  • is_valid (bool) –

    Whether the selected sum equals the target.

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

Plot the subset sum solution.

Parameters:

  • data (SubsetSumData | 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 SubsetSum use case.

SubsetSumInstance

Bases: UcInstance[SubsetSumData, SubsetSumFormulation, SubsetSumSolution]

Instance combining data and formulation for SubsetSum.

Collection

Collection of SubsetSum instances.

SubsetSumCollection

Bases: UcInstanceCollection[SubsetSumInstance]

Collection of Subset Sum 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) -> SubsetSumCollection classmethod

Generate random subset sum 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 None.

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

    Random seed for reproducibility, by default None.

Returns: