Protecting critical infrastructure from deliberate attacks or large-scale failures is a major concern in network management. This paper addresses the Facility Interdiction Problem(FIP), which seeks to identify the set of k facilities whose loss would maximally degrade system performance, thereby revealing critical vulnerabilities for fortification. We model the adversarial interaction as a bilevel optimization problem: an upper-level attacker selects facilities to disable, and a lower-level defender reassigns demand to surviving facilities to minimize cost. To solve this NP-hard problem, we propose a Genetic Algorithm (GA) that encodes candidate interdiction sets and evaluates fitness by solving the resulting assignment subproblem. Experiments on five benchmark instances demonstrate the ability of the proposed solution method to identify high-impact failure scenarios.