discrete_optimization.workforce.allocation.transformations package

Submodules

discrete_optimization.workforce.allocation.transformations.to_coloring module

Transformation from Workforce Allocation to Graph Coloring (composed transformation).

This module implements WorkforceAllocationToColoringTransformation as a composition of: 1. WorkforceAllocationToListColoringTransformation (direct encoding) 2. ListColoringToColoringTransformation (dummy nodes encoding)

This avoids code duplication and leverages both transformation implementations.

class discrete_optimization.workforce.allocation.transformations.to_coloring.WorkforceAllocationToColoringTransformation[source]

Bases: ProblemTransformation[TeamAllocationProblem, TeamAllocationSolution, ColoringProblem, ColoringSolution]

Transform Workforce Allocation to Graph Coloring (composed transformation).

This transformation is a COMPOSITION of: 1. WorkforceAllocationToListColoringTransformation (direct encoding) 2. ListColoringToColoringTransformation (dummy nodes encoding)

Mapping (via composition): - Allocation → ListColoring: Tasks → Nodes, Teams → Colors, allowed teams → allowed_colors - ListColoring → Coloring: Add dummy team nodes, edges for forbidden colors

Final encoding: - Tasks → Original nodes in coloring graph - Teams → Dummy nodes (one per team), forming a complete clique - Dummy node k fixed to color k - Forbidden allocations → Edges to dummy team nodes - subset_nodes focuses optimization on tasks only

This is LOSSY (calendar & same_allocation constraints lost) but EXACT for supported constraints.

back_transform_solution(solution: ColoringSolution, source_problem: TeamAllocationProblem) → TeamAllocationSolution[source]

Transform Coloring solution back to Workforce Allocation solution.

Parameters:

  • solution – Coloring solution (with dummy nodes)

  • source_problem – Original TeamAllocationProblem

Returns:

Equivalent TeamAllocationSolution

forward_transform_solution(solution: TeamAllocationSolution, target_problem: ColoringProblem) → ColoringSolution | None[source]

Transform Allocation solution to Coloring solution (for warmstart).

Parameters:

  • solution – TeamAllocationSolution

  • target_problem – Target Coloring problem (with dummy nodes)

Returns:

Equivalent ColoringSolution

get_forward_metadata() → TransformationMetadata[source]

Metadata for forward problem transformation (Allocation → Coloring).

This is the composition of two transformations, inheriting losses from step1.

transform_problem(source_problem: TeamAllocationProblem) → ColoringProblem[source]

Transform Workforce Allocation to Coloring via composition.

Parameters:

source_problem – TeamAllocationProblem instance

Returns:

ColoringProblem with dummy nodes

discrete_optimization.workforce.allocation.transformations.to_list_coloring module

Transformation from Workforce Allocation to List Coloring (direct approach).

class discrete_optimization.workforce.allocation.transformations.to_list_coloring.WorkforceAllocationToListColoringTransformation[source]

Bases: ProblemTransformation[TeamAllocationProblem, TeamAllocationSolution, ListColoringProblem, ColoringSolution]

Transform Workforce Allocation to List Coloring (direct approach).

Mapping: - Tasks → Nodes - Teams → Colors (0, 1, 2, …, nb_teams-1) - all_diff_allocation → Edges between tasks - Available teams per task → allowed_colors[task] - Minimize number of teams → Minimize number of colors

This is the cleaner approach using ListColoringProblem directly, without dummy nodes.

This transformation is LOSSY: - Forward (problem): LOSSY - calendar and same_allocation constraints lost - Backward (solution): EXACT - color assignments = team assignments

back_transform_solution(solution: ColoringSolution, source_problem: TeamAllocationProblem) → TeamAllocationSolution[source]

Transform List Coloring solution back to Workforce Allocation solution.

Parameters:

  • solution – List Coloring solution

  • source_problem – Original TeamAllocationProblem

Returns:

Equivalent TeamAllocationSolution

forward_transform_solution(solution: TeamAllocationSolution, target_problem: ListColoringProblem) → ColoringSolution | None[source]

Transform Allocation solution to List Coloring solution (for warmstart).

Parameters:

  • solution – TeamAllocationSolution

  • target_problem – Target ListColoringProblem

Returns:

Equivalent ColoringSolution

get_forward_metadata() → TransformationMetadata[source]

Metadata for forward problem transformation (Allocation → ListColoring).

This direction is LOSSY but cleaner than the dummy node approach.

transform_problem(source_problem: TeamAllocationProblem) → ListColoringProblem[source]

Transform Workforce Allocation to List Coloring.

Parameters:

source_problem – TeamAllocationProblem instance

Returns:

Equivalent ListColoringProblem

Module contents

Transformations from Workforce Allocation to other problems.

class discrete_optimization.workforce.allocation.transformations.WorkforceAllocationToColoringTransformation[source]

Bases: ProblemTransformation[TeamAllocationProblem, TeamAllocationSolution, ColoringProblem, ColoringSolution]

Transform Workforce Allocation to Graph Coloring (composed transformation).

This transformation is a COMPOSITION of: 1. WorkforceAllocationToListColoringTransformation (direct encoding) 2. ListColoringToColoringTransformation (dummy nodes encoding)

Mapping (via composition): - Allocation → ListColoring: Tasks → Nodes, Teams → Colors, allowed teams → allowed_colors - ListColoring → Coloring: Add dummy team nodes, edges for forbidden colors

Final encoding: - Tasks → Original nodes in coloring graph - Teams → Dummy nodes (one per team), forming a complete clique - Dummy node k fixed to color k - Forbidden allocations → Edges to dummy team nodes - subset_nodes focuses optimization on tasks only

This is LOSSY (calendar & same_allocation constraints lost) but EXACT for supported constraints.

back_transform_solution(solution: ColoringSolution, source_problem: TeamAllocationProblem) → TeamAllocationSolution[source]

Transform Coloring solution back to Workforce Allocation solution.

Parameters:

  • solution – Coloring solution (with dummy nodes)

  • source_problem – Original TeamAllocationProblem

Returns:

Equivalent TeamAllocationSolution

forward_transform_solution(solution: TeamAllocationSolution, target_problem: ColoringProblem) → ColoringSolution | None[source]

Transform Allocation solution to Coloring solution (for warmstart).

Parameters:

  • solution – TeamAllocationSolution

  • target_problem – Target Coloring problem (with dummy nodes)

Returns:

Equivalent ColoringSolution

get_forward_metadata() → TransformationMetadata[source]

Metadata for forward problem transformation (Allocation → Coloring).

This is the composition of two transformations, inheriting losses from step1.

transform_problem(source_problem: TeamAllocationProblem) → ColoringProblem[source]

Transform Workforce Allocation to Coloring via composition.

Parameters:

source_problem – TeamAllocationProblem instance

Returns:

ColoringProblem with dummy nodes

class discrete_optimization.workforce.allocation.transformations.WorkforceAllocationToListColoringTransformation[source]

Bases: ProblemTransformation[TeamAllocationProblem, TeamAllocationSolution, ListColoringProblem, ColoringSolution]

Transform Workforce Allocation to List Coloring (direct approach).

Mapping: - Tasks → Nodes - Teams → Colors (0, 1, 2, …, nb_teams-1) - all_diff_allocation → Edges between tasks - Available teams per task → allowed_colors[task] - Minimize number of teams → Minimize number of colors

This is the cleaner approach using ListColoringProblem directly, without dummy nodes.

This transformation is LOSSY: - Forward (problem): LOSSY - calendar and same_allocation constraints lost - Backward (solution): EXACT - color assignments = team assignments

back_transform_solution(solution: ColoringSolution, source_problem: TeamAllocationProblem) → TeamAllocationSolution[source]

Transform List Coloring solution back to Workforce Allocation solution.

Parameters:

  • solution – List Coloring solution

  • source_problem – Original TeamAllocationProblem

Returns:

Equivalent TeamAllocationSolution

forward_transform_solution(solution: TeamAllocationSolution, target_problem: ListColoringProblem) → ColoringSolution | None[source]

Transform Allocation solution to List Coloring solution (for warmstart).

Parameters:

  • solution – TeamAllocationSolution

  • target_problem – Target ListColoringProblem

Returns:

Equivalent ColoringSolution

get_forward_metadata() → TransformationMetadata[source]

Metadata for forward problem transformation (Allocation → ListColoring).

This direction is LOSSY but cleaner than the dummy node approach.

transform_problem(source_problem: TeamAllocationProblem) → ListColoringProblem[source]

Transform Workforce Allocation to List Coloring.

Parameters:

source_problem – TeamAllocationProblem instance

Returns:

Equivalent ListColoringProblem