We apply new bilevel and trilevel optimization models to make critical infrastructure more resilient against terrorist attacks. Each model features an intelligent attacker (terrorists) and a defender (us), information transparency, and sequential actions by attacker and defender. We illustrate with examples of the US Strategic Petroleum Reserve, the US Border Patrol at Yuma, Arizona, and an electrical transmission system. We conclude by reporting insights gained from the modeling experience and many “red-team” exercises. Each exercise gathers open-source data on a real-world infrastructure system, develops an appropriate bilevel or trilevel model, and uses these to identify vulnerabilities in the system or to plan an optimal defense.

Abstract-We describe new analytical techniques to help mitigate the disruptions to electric power grids caused by terrorist attacks. New bilevel mathematical models and algorithms identify critical system components (e.g., transmission lines, generators, transformers) by creating maximally disruptive attack plans for terrorists assumed to have limited offensive resources. We report results for standard reliability test networks to show that the techniques identify critical components with modest computational effort.

Abstract-This paper generalizes Benders decomposition to maximize a nonconcave objective function and uses that decomposition to solve an "electric power grid interdiction problem." Under one empirically verified assumption, the solution to this bilevel optimization problem identifies a set of components, limited by cardinality or "interdiction resource," whose destruction maximizes economic losses to customers (and can thereby guide defensive measures). The decomposition subproblem typically incorporates a set of dc optimal power-flow models that cover various states of repair after an attack, along with a load-duration curve. Test problems describe a regional power grid in the United States with approximately 5000 buses, 6000 lines, and 500 generators. Solution time on a 2-GHz personal computer is approximately one hour.Index Terms-Failure analysis, load flow analysis, power system security.

A key strategic issue in pre-disaster planning for humanitarian logistics is the pre-establishment of adequate capacity and resources that enable efficient relief operations. This paper develops a two-stage stochastic optimization model to guide the allocation of budget to acquire and position relief assets, decisions that typically need to be made well in advance before a disaster strikes. The optimization focuses on minimizing the expected number of casualties, so our model includes first-stage decisions to represent the expansion of resources such as warehouses, medical facilities with personnel, ramp spaces, and shelters. Second-stage decisions concern the logistics of the problem, where allocated resources and contracted transportation assets are deployed to rescue critical population (in need of emergency evacuation), deliver required commodities to stay-back population, and transport the transfer population displaced by the disaster. Because of the uncertainty of the event's location and severity, these and other parameters are represented as scenarios. Computational results on notional test cases provide guidance on budget allocation and prove the potential benefit of using stochastic optimization.

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.

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We consider the following problem: Given a set of projects to be executed along a multi-year time horizon, find a sequencing and scheduling feasible solution that optimizes a merit function. A feasible solution should satisfy availability of storable and non-storable resources with budget carrier and non-carrier periods, and precedence, exclusivity and implication relationships among the projects. This is an NP-hard problem. We present several Fix-and-Relax strategies which partition the set of binary variable into clusters in order to selectively explore the branch-and-bound tree. Computational performance is favorably compared with a state-of-the-art optimization engine over a set of real-life cases.

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