Exact Anchoring and a Dualization-Based Matheuristic for Bi-Level Dual-Defense Network Interdiction

Bi-level interdiction models are frequently solved by metaheuristics whose solution quality cannot be assessed, because exact optima are unavailable at the scales tested. We supply them for the bi-level dual-defense attacker model (BDAM), which couples node interdiction, edge destruction and capacitated supply support, and which we previously solved by a hybrid metaheuristic. First, BDAM's dominant attacker-path term admits an exact single-level reformulation by lower-level dualization, a reduction available whenever arc lengths are linear in the defender's binary decisions; the resulting mixed-integer program certifies optimality on all eighteen three-row and five-row configurations of our earlier benchmark, seventeen in under ten seconds, with strong uncertified incumbents out to 15*30 grids. Our published averages sit 3.55% below that frontier, and the gap widens with scale. Second, the supply rule, like any rule priced on a single attacker shortest path, is ill-posed under ties, and our threat-corridor formulation is tie-invariant by construction. The tie-break moves the objective by under 10^(-3) but the realized supply cost by up to 0.83 units, so the defect is suppressed by the objective weight rather than absent. Third, MILP-DA pairs the exact anchor with the corridor decode and a feasibility repair; compared against our published figures with no re-implementation on either side, it wins on thirteen of eighteen certified configurations and on all eighteen larger ones, every loss falling on a three-row grid.