Optimal Interdiction of Unreactive Markovian Evaders

The interdiction problem arises in a variety of areas including military logistics, infectious disease control, and counter-terrorism. In the typical formulation of network interdiction, the task of the interdictor is to find a set of edges in a weighted network such that the removal of those edges would maximally increase the cost to an evader of traveling on a path through the network. Our work is motivated by cases in which the evader has incomplete information about the network or lacks planning time or computational power, e.g. when authorities set up roadblocks to catch bank robbers, the criminals do not know all the roadblock locations or the best path to use for their escape. We introduce a model of network interdiction in which the motion of one or more evaders is described by Markov processes and the evaders are assumed not to react to interdiction decisions. The interdiction objective is to find an edge set of size B, that maximizes the probability of capturing the evaders. We prove that similar to the standard least-cost formulation for deterministic motion this interdiction problem is also NP-hard. But unlike that problem our interdiction problem is submodular and the optimal solution can be approximated within 1-1/e using a greedy algorithm. Additionally, we exploit submodularity through a priority evaluation strategy that eliminates the linear complexity scaling in the number of network edges and speeds up the solution by orders of magnitude. Taken together the results bring closer the goal of finding realistic solutions to the interdiction problem on global-scale networks.Comment: Accepted at the Sixth International Conference on integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2009

Network interdiction approaches for diminishing misinformation spread in social networks

Network interdiction has many applications in many domains, including telecommunications, epidemic control, and social network analysis. In this dissertation, we use network interdiction to devise strategies for the problem of misinformation dissemination in online social networks. These platforms provide the opportunity of quick communication between users, which in a network with malicious accounts can result in the fast spread of rumors and harmful content. We study this topic based on two different approaches. The first approach focuses on interdicting cohesive subgroups of malicious accounts. We use s-clubs, which are subsets of vertices that induce subgraphs of diameter at most s to model the cohesive social subgroups. We consider a defender that can disrupt the vertices of the adversarial network to minimize its threat, which leads us to consider a maximum s-club interdiction problem. Using a new notion of H-heredity in s-clubs, we provide a mixed-integer linear programming formulation for this problem that uses far fewer constraints than the formulation based on standard techniques. We further relate H-heredity to latency-s connected dominating sets and design a decomposition branch-and-cut algorithm for the problem. The second methodology that is studied in this dissertation is to delay the spread of misinformation in the network using first passage times interdiction. The first passage times are defined as the first time each user is exposed to a post shared by another user in the network and is computed using a discrete time Markov chain model. Vertices are interdicted to modify the transition probabilities and increase the propagation times between users who share misinformation and harmful content, and vulnerable users. We show that the problem is NP-hard and provide a mixed-integer linear programming formulation for it. Computational experiments on benchmark instances are conducted for both interdiction approaches based on cohesive subgroups and first passage times in order to assess the computational capabilities of the methods we introduced

Patrolling security games: Definition and algorithms for solving largeinstances with single patroller and single intruder

Security games are gaining significant interest in artificial intelligence. They are characterized by two players (a defender and an attacker) and by a set of targets the defender tries to protect from the attacker\u2bcs intrusions by committing to a strategy. To reach their goals, players use resources such as patrollers and intruders. Security games are Stackelberg games where the appropriate solution concept is the leader\u2013follower equilibrium. Current algorithms for solving these games are applicable when the underlying game is in normal form (i.e., each player has a single decision node). In this paper, we define and study security games with an extensive-form infinite-horizon underlying game, where decision nodes are potentially infinite. We introduce a novel scenario where the attacker can undertake actions during the execution of the defender\u2bcs strategy. We call this new game class patrolling security games (PSGs), since its most prominent application is patrolling environments against intruders. We show that PSGs cannot be reduced to security games studied so far and we highlight their generality in tackling adversarial patrolling on arbitrary graphs. We then design algorithms to solve large instances with single patroller and single intruder

Doctor of Philosophy

dissertationA safe and secure transportation system is critical to providing protection to those who employ it. Safety is being increasingly demanded within the transportation system and transportation facilities and services will need to adapt to change to provide it. This dissertation provides innovate methodologies to identify current shortcomings and provide theoretic frameworks for enhancing the safety and security of the transportation network. This dissertation is designed to provide multilevel enhanced safety and security within the transportation network by providing methodologies to identify, monitor, and control major hazards associated within the transportation network. The risks specifically addressed are: (1) enhancing nuclear materials sensor networks to better deter and interdict smugglers, (2) use game theory as an interdiction model to design better sensor networks and forensically track smugglers, (3) incorporate safety into regional transportation planning to provide decision-makers a basis for choosing safety design alternatives, and (4) use a simplified car-following model that can incorporate errors to predict situational-dependent safety effects of distracted driving in an ITS infrastructure to deploy live-saving countermeasures

Vertex-pursuit in random directed acyclic graphs

We examine a dynamic model for the disruption of information flow in hierarchical social networks by considering the vertex-pursuit game Seepage played in directed acyclic graphs (DAGs). In Seepage, agents attempt to block the movement of an intruder who moves downward from the source node to a sink. The minimum number of such agents required to block the intruder is called the green number. We propose a generalized stochastic model for DAGs with given expected total degree sequence. Seepage and the green number is analyzed in stochastic DAGs in both the cases of a regular and power law degree sequence. For each such sequence, we give asymptotic bounds (and in certain instances, precise values) for the green number

GIS routing and modelling of residential waste collection for operational management and cost optimization

In this paper, optimum routing was developed based on the travel salesman method and integrated in ArcInfo GIS using linear programming. The results of the optimized travel distances and times for residential waste collection and routing to disposal site were used to calculate the number and type of required track collection, labour requirement, costing of waste collection and to determine the overall solid waste management efficiency through waste management operation research methods. The objective of the study was to optimize residential collection and hauling to disposal site through operation cost minimization for Petaling Jaya Municipality in the state of Selangor, Malaysia. The study determined that with optimized routes and recycling possibilities, the total cost of waste collections could be reduced from RM90,372 to RM20,967, with a reduction of 76.8%. It was also revealed that optimum routes might not necessarily be the shortest distance from point A to point B as travel time maybe high on short distances due to traffic congestion and the presence of many traffic lights. Techniques and methods developed using general GIS have proven effective in route optimization and allowed management of data to suit local conditions and limitations of waste management for the studied area. Thus, scenarios of travel distances, time and waste quantity value generated from the GIS enabled appropriate determination of the number of waste trucks and labour requirements for the operation and the overall calculation of costs of waste management based on the operation research methods used in the study

Multiple Allocation Hub Interdiction and Protection Problems: Model Formulations and Solution Approaches

In this paper, we present computationally efficient formulations for the multiple allocation hub interdiction and hub protection problems, which are bilevel and trilevel mixed integer linear programs, respectively. In the hub interdiction problem, the aim is to identify a subset of r critical hubs from an existing set of p hubs that when interdicted results in the maximum post-interdiction cost of routing flows. We present two alternate ways of reducing the bilevel hub interdiction model to a single level optimization problem. The first approach uses the dual formulation of the lower level problem. The second approach exploits the structure of the lower level problem to replace it by a set of closest assignment constraints (CACs). We present alternate sets of CACs, study their dominance relationships, and report their computational performances. Further, we propose refinements to CACs that offer computational advantages of an order-of-magnitude compared to the one existing in the literature. Further, our proposed modifications offer structural advantages for Benders decomposition, which lead to substantial computational savings, particularly for large problem instances. Finally, we study and solve large scale instances of the trilevel hub protection problem exactly by utilizing the ideas developed for the hub interdiction problem