| The oil and gas distribution networks are systems of external pipelines that are suffering from heterogeneous threats. Accordingly, hardening strategies against malicious attacks are discussed, where a tri-level leader-follower-operator game is established for determining the optimum fortification tactics to protect the critical assets considering the defender's limited resources. In addition, the shared cognition concept is mathematically modeled by including defender's deception. The resulted multi-origin(O)-destination(D) mixed integer nonlinear programming problem is decomposed into a master and sub-problem for illustrating the defender-operator and attacker-operator respectively. Furthermore, the bi-level sub-problem is successfully converted to a single level via duality theorem. In light of the linearized model, exact linearization techniques are occupied to reformulate the problem to an efficient bi-level multi-O-D mixed integer linear programming. The constraint-and-column generation methods declared optimum solutions for the antecedent problem's scenarios. The results show that the deception concept is worthwhile plus the cost of attacker's damages diminished significantly. |
