Analyzing the Vulnerability of Critical Infrastructure to Attack and Planning Defenses

Abstract

We describe new bilevel programming models to (1) help make the country's critical infrastructure more resilient to attacks by terrorists, (2) help governments and businesses plan those improvements, and (3) help influence related public policy on investment incentives, regulations, etc. An intelligent attacker (terrorists) and defender (us) are key features of all these models, along with information transparency: These are Stackelberg games, as opposed to two-person, zero-sum games. We illustrate these models with applications to electric power grids, subways, airports, and other critical infrastructure. For instance, one model identifies locations for a given set of electronic sensors that minimize the worst-case time to detection of a chemical, biological, or radiological contaminant introduced into the Washington, D.C. subway system. The paper concludes by reporting insights we have gained through forming "red teams," each of which gathers open-source data on a real-world system, develops an appropriate attacker-defender or defender-attacker model, and solves the model to identify vulnerabilities in the system or to plan an optimal defense.

Sometimes There Is No ''Most-Vital'' Arc: Assessing and Improving the Operational Resilience of Systems

“…An important part of this work has been the connection to two-person zero-sum games (Washburn and Wood 1995), and their application to stochastic network interdiction (Cormican et al 1998), shortest path problems (Israeli and Wood 2002), and multicommodity network models (Lim and Smith 2007). Most recently, these ideas have been applied to the study of critical infrastructure systems (e.g., Brown et al 2005Brown et al , 2006, with specific attention toward electric power systems (Salmeró n et al 2004(Salmeró n et al , 2009, facility location problems (e.g., Church 2008), supply chain networks (Snyder et al 2006), telecommunication systems (Murray et al 2007), and transportation problems (Alderson et al 2011). Lunday and Sherali (2012) pose and solve some minmax models depicting interdiction planning to maximize the probability of intercepting a lone evader attempting to traverse a network from some source to some destination.…”

Deception tactics for network interdiction: A multiobjective approach

“…This case is equivalent to a standard DA model with full transparency, as in [5], where the defender's goal is to minimize his worst-case outcome for any possible route the attackers might find. The defender places transparent interdictions on arcs 118-128, 218-228, and 328-335 (indicated by thick arrows in Fig.…”

“…Constraints to establish that x c. As the objectives of defender and attacker are different, the well-known technique of dualization of the "inner" problem to obtain a min-min formulation (see e.g., [5]) is not applicable. However, for every defender choice y, we may use strong duality theory with the attacker's problem (5) and (6) to characterize an optimal x, similar to the technique used in [13]. Specifically, we replace (6) by setting the objective value equal to that of its dual counterpart, and by adding all necessary dual constraints:…”

“…One of these players seeks, for example, to maximize flow through the network, or to minimize cost to supply the demand, while the other player tries to disrupt the network by interdicting selected components [18]. The associated problems are commonly referred to as defender-attacker (DA) and attacker-defender (AD) models (see, e.g., [5] and references therein). In many of these problems, players make their decisions in a specified order, as in bi-level programming and Stackelberg games [16].…”

Models for Reliable Supply Chain Network Design

“…The objective of the interdictor is to maximize the demandweighted total distance with demands assigned to the closest non-interdicted facilities, while the defender attempts to minimize this worst-case cost by defending a subset of the facilities. Brown et al (2005) provide an excellent tutorial on this class of defender/attacker problems. We adopt a somewhat different approach, first suggested by and Daskin et al (2006).…”