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Keywords:

  • network interdiction;
  • asymmetric information;
  • bi-level optimization;
  • multiobjective optimization;
  • generalized networks;
  • Benders decomposition

Abstract

This article develops defender-attacker network interdiction models with deception. Here, deception refers to a preemptive and intelligent use of concealed interdiction assets and decoys by the defender, in addition to transparent assets commonly employed in modeling defender-attacker problems. These models can help security planners to locate a limited number of checkpoints and sensors of various types to, for example, detect the smuggling of illegal products. The problem is complex, in part, because the objective functions of the defender and the attacker are different, and because the latter (which represents the attacker's behavior) is difficult to predict by the defender. First, we use duality theory and a generalized network flow model to devise an equivalent mixed-integer programming formulation, and develop its Benders decomposition. We extend this formulation with a multiobjective approach to account for several behaviors simultaneously. The computational effort to solve these models is considerable, as exemplified by our testing on a variety of cases for a medium-sized, notional network. Published 2011 Wiley Periodicals, Inc. NETWORKS, 2012