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Recursive linearization constraint

RecursiveLinearizationConstraint

Bases: Constraint

Recursive (merged-client) linearization for the PC-HLP model.

Reproduces the cubic term:

\[X_{ijkl}^z \;\widehat{=}\; y_{ij}^z \cdot x_{ik} \cdot x_{jl}\]

Same structure as LinearizationConstraint but operates on aggregated client keys from BilevelDataCol.CLIENT_KEY.

Requires: - [AllocationVariable][bilevelpy.models.vars.hlp_vars.AllocationVariable] - RecursiveClientDecisionVariable - RecursiveLinearXYVariable

build(model, **kwargs)

Adds the following constraint to the model:

\[y_{ij}^z = \sum_{k,l \in V} X_{ijkm}^z \quad \forall (i,j,z) \in K\]
\[\sum_{l} X_{ijkm}^z \leq x_{ik} \quad \sum_{k} X_{ijkm}^z \leq x_{jl}\]
Source code in src/oracle_paper/constraints/recursive_linearization_constraint.py 
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def build(self, model: "BaseModel", **kwargs):
    r"""Adds the following constraint to the model:

        $$y_{ij}^z = \sum_{k,l \in V} X_{ijkm}^z \quad \forall (i,j,z) \in K$$

        $$\sum_{l} X_{ijkm}^z \leq x_{ik} \quad \sum_{k} X_{ijkm}^z \leq x_{jl}$$

    """
    nodes = get_nodes(model)
    client_keys = [(i, j, z) for (i, j, z), _ in model.data[BilevelDataCol.CLIENT_KEYS].items()]

    x = model.vars[AllocationVariable]
    q = model.vars[RecursiveLinearXYVariable]
    y = model.vars[RecursiveClientDecisionVariable]

    for (i, j, z) in client_keys:
        model.add_constr(
            quicksum(q[i, j, k, l, z] for k in nodes for l in nodes) == y[i, j, z],
            name=f"lin_y_{i}_{j}_{z}"
        )
        for k in nodes:
            model.add_constr(
                quicksum(q[i, j, k, l, z] for l in nodes) <= x[i, k],
                name=f"lin_x1_{i}_{j}_{z}_{k}"
            )
        for l in nodes:
            model.add_constr(
                quicksum(q[i, j, k, l, z] for k in nodes) <= x[j, l],
                name=f"lin_x2_{i}_{j}_{z}_{l}"
            )