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Binary Integer Linear Programming (BILP) API Reference

Data

Data model for general Binary Integer Linear Programming (BILP) use case.

BilpData

Bases: UcData

Data container for general Binary Integer Linear Programming (BILP).

A BILP is an optimization problem with: - Binary decision variables (0 or 1) - Linear objective function - Linear constraints (equality or inequality)

Attributes:

  • name (Literal['binary_integer_linear_programming']) –

    Constant identifier for this data type.

  • constraint_matrix (NumPyArray) –

    An m x n constraint matrix S where m is the number of constraints and n is the number of variables.

  • rhs (list[float]) –

    Right-hand side vector b of length m.

  • objective_coeffs (list[float]) –

    Coefficient vector c of the linear objective function of length n.

  • constraint_senses (list[Literal['==', '<=', '>=']]) –

    List of constraint types for each row in constraint_matrix. Defines whether the constraint is equality, <=, or >=.

__post_init__() -> None

Ensure constraint_senses is set; default to equality if None.

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

Visualize the BILP data with a constraint matrix heatmap and constraint types.

Parameters:

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

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

Returns:

  • Axes –

    Axes with the plot.

to_string() -> str

Return a string describing the data instance.

from_arrays(constraint_matrix: np.ndarray, rhs: list[float], objective_coeffs: list[float], constraint_senses: list[Literal['==', '<=', '>=']] | None = None) -> BilpData staticmethod

Create a BilpData instance from numpy arrays.

Parameters:

  • constraint_matrix (ndarray) –

    The m x n constraint matrix.

  • rhs (list[float]) –

    Right-hand side vector of length m.

  • objective_coeffs (list[float]) –

    Coefficients for the linear objective function.

  • constraint_senses (list[Literal['==', '<=', '>=']] | None, default: None ) –

    Constraint types for each row. Defaults to equality if None.

Returns:

  • BilpData –

    A populated BilpData instance.

generate_random(n_vars: int = 5, n_constraints: int = 3, size: int | None = None, seed: int | None = None) -> BilpData staticmethod

Generate a random feasible BILP instance.

Ensures feasibility by first generating a random binary solution and computing the RHS from it. Constraint types are chosen randomly.

Parameters:

  • n_vars (int, default: 5 ) –

    Number of binary variables. Default is 5.

  • n_constraints (int, default: 3 ) –

    Number of constraints. Default is 3.

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

    If provided, overrides n_vars for collection compatibility.

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

    Random seed for reproducibility. Default is None.

Returns:

  • BilpData –

    A randomly generated BILP instance.

Formulation

Formulation for general Binary Integer Linear Programming (BILP) use case.

BilpFormulation

Bases: UcFormulation[BilpData, BilpSolution]

Formulation class for general Binary Integer Linear Programming (BILP).

This class translates a BilpData instance into an optimization model suitable for solvers. Supports equality and inequality constraints.

Mathematical Formulation

Decision Variables: x_i in {0,1} for i = 0, ..., n-1

Objective Function: maximize sum_i c_i * x_i

Constraints: For each constraint j: sum_i S[j,i] * x[i] {==, <=, >=} b[j] Where the type is defined in data.constraint_senses[j].

to_string(data: BilpData) -> str staticmethod

Return a detailed string describing the formulation.

Parameters:

  • data (BilpData) –

    The BILP problem data.

Returns:

  • str –

    Multi-line description of the variables, objective, and constraints.

formulate(data: BilpData) -> Model staticmethod

Formulate the general BILP as an optimization model.

Parameters:

  • data (BilpData) –

    Problem data containing the constraint matrix, RHS, objective coefficients, and constraint senses.

Returns:

  • Model –

    An optimization model ready to be solved by a solver.

Notes
  • Supports equality (==, default), less-than-or-equal (<=), and greater-than-or-equal (>=) constraints.
  • All decision variables are binary.

interpret(solution: Solution, data: BilpData) -> BilpSolution staticmethod

Interpret the solver's solution and convert it to a BilpSolution.

Parameters:

  • solution (Solution) –

    The solver's solution object.

  • data (BilpData) –

    The problem data.

Returns:

  • BilpSolution –

    Structured solution containing: - solution vector - objective value - validity flag (all constraints satisfied)

Raises:

Solution

Solution model for BILP use case.

BilpSolution

Bases: UcSolution

Solution for the Binary Integer Linear Programming (BILP) use case.

Attributes:

  • name (Literal['binary_integer_linear_programming']) –

    Identifier for this solution type.

  • solution_vector (list[int]) –

    Binary solution vector x.

  • objective_value (float) –

    Objective value c^T x.

  • is_valid (bool) –

    Whether all equality constraints S x == b are satisfied.

plot(data: BilpData | None = None, *, ax: Axes | None = None) -> Axes | list[Axes]

Visualize the BILP solution with a variable bar chart and optional constraint heatmap.

Parameters:

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

    Problem data providing the constraint matrix and senses. If provided, a heatmap showing which constraints are activated by the solution is displayed below the solution bar chart.

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

    Matplotlib axes or array of axes to draw on. If None, a new figure with two subplots (bars + heatmap) is created.

Returns:

  • Axes | list[Axes] –

    The axes containing the plot(s). Returns a single Axes if only one subplot is used, otherwise a list of two Axes [bar_chart, heatmap].

to_string() -> str

Return a string describing the solution.

Instance

Instance model for Bilp use case.

BilpInstance

Bases: UcInstance[BilpData, BilpFormulation, BilpSolution]

Instance combining data and formulation for Bilp.

Collection

Collection of BILP instances.

BilpCollection

Bases: UcInstanceCollection[BilpInstance]

Collection of BILP instances.

from_random(min_size: int, max_size: int, num_instances: int = 1, *, seed: int | None = None) -> BilpCollection classmethod

Not implemented for BILP.

Random generation cannot reliably produce feasible BILP instances with mixed constraint types, as there is no efficient way to guarantee that a valid binary solution exists for arbitrary constraint matrices and right-hand sides.

Raises: