Maximum dynamic network flow interdiction problem: New formulation and solution procedures

Rad, maria Afshari; Kakhki, Hossein Taghizadeh

doi:10.1016/j.cie.2013.04.014

Cited by 34 publications

(9 citation statements)

References 22 publications

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“…NIP is also a useful model for researching the protection of IoT, e.g., the defensive resource allocation [15] and adversarial outbreak detection [19]. Numerous variations of NIP have been proposed and studied to meet different hypotheses under particular scenarios [16,17,[20][21][22][23][24]. Among the many types of NIP, SPNI is a classic and important branch.…”

Section: Introductionmentioning

confidence: 99%

Bi-Layer Shortest-Path Network Interdiction Game for Internet of Things

Yan

Xiao

Zhu

et al. 2020

Sensors

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Network security is a crucial challenge facing Internet-of-Things (IoT) systems worldwide, which leads to serious safety alarms and great economic loss. This paper studies the problem of malicious interdicting network exploitation of IoT systems that are modeled as a bi-layer logical–physical network. In this problem, a virtual attack takes place at the logical layer (the layer of Things), while the physical layer (the layer of Internet) provides concrete support for the attack. In the interdiction problem, the attacker attempts to access a target node on the logical layer with minimal communication cost, but the defender can strategically interdict some key edges on the physical layer given a certain budget of interdiction resources. This setting generalizes the classic single-layer shortest-path network interdiction problem, but brings in nonlinear objective functions, which are notoriously challenging to optimize. We reformulate the model and apply Benders decomposition process to solve this problem. A layer-mapping module is introduced to improve the decomposition algorithm and a random-search process is proposed to accelerate the convergence. Extensive numerical experiments demonstrate the computational efficiency of our methods.

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Section: Introductionmentioning

confidence: 99%

Bi-Layer Shortest-Path Network Interdiction Game for Internet of Things

Yan

Xiao

Zhu

et al. 2020

Sensors

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“…In the literature, scholars have studied CIS vulnerability under different types of disruptive events, including (1) random failures, which are modeled by randomly selecting a certain fraction of system components to make them fail (Motter and Lai, ; Crucitti et al., ; Albert et al., ; Yazdani and Jeffrey, ; Dobson et al., ; Ouyang and Dueñas‐Osorio, ; Carreras et al., ; Dobson et al., ; Ren and Dobson, ; Ouyang et al., ; Newman, ; Hong et al., ); (2) natural hazards, whose scenarios are simulated by hazard generation models (FEMA, ) and their impacts on system components are described by fragility curves (Dueñas‐Osorio et al., ; Adachi and Ellingwood, ; Esposito et al., ; Franchin and Cavalieri, ; Cavallaro et al., ; FEMA, ; Ouyang and Dueñas‐Osorio, ); (3) malicious attacks, which are simulated by removing important components (Hines et al., ; Holmgren, ; Rosas‐Casals et al., ; Holme et al., ; Bompard et al., ; Mishkovski et al., ; Zio et al., ; Alderson et al., ; Ouyang et al., ; Wang et al., ; Afshari Rad and Kakhki, ; Hasani and Khosrojerdi, ; Newell, ; Bogloee et al. ); and (4) some combinations of the above events (Levitin and Hausken, ; Levitin, ; Miller‐Hooks et al., ).…”

Section: Introductionmentioning

confidence: 99%

“…(3) malicious attacks, which are simulated by removing important components (Hines et al, 2010;Holmgren, 2006;Rosas-Casals et al, 2007;Holme et al, 2002;Bompard et al, 2010;Mishkovski et al, 2011;Zio et al, 2012;Alderson et al, 2015;Ouyang et al, 2015;Wang et al, 2016;Afshari Rad and Kakhki, 2013;Hasani and Khosrojerdi, 2016;Newell, 1980;Bogloee et al 2017); and (4) some combinations of the above events (Levitin and Hausken, 2009;Levitin, 2007;Miller-Hooks et al, 2012). Note that the above events do not consider the spatial proximity of the damaged components and should be grouped into nonproximity-based events.…”

Section: Introductionmentioning

confidence: 99%

Vulnerability Mitigation of Multiple Spatially Localized Attacks on Critical Infrastructure Systems

Ouyang

Tao

Huang

et al. 2018

Computer aided Civil Eng

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Recently, many studies have analyzed critical infrastructure vulnerability under spatially localized attack (SLA), which is modeled as the failure of a set of infrastructure components, distributed in a spatially localized area, due to malicious attacks, while other components outside of the area do not directly fail. However, existing studies have only considered one single attack area, and multiple SLAs (MSLAs) with more than one attack area have been seldom investigated. This article addresses this issue and studies vulnerability mitigation of critical infrastructure systems (CISs) against the worst‐case MSLAs. The problem is mathematically formulated as a tri‐level defender‐attacker‐defender model, the exact solution of which is solved by a proposed decomposition algorithm. Case studies on the adapted IEEE 24 bus system and the power transmission systems in Shelby County and Harris County, U.S., indicate that (1) system vulnerability under 2*M localized attack areas might be much larger than two times of the vulnerability under M localized attack areas; (2) small preevent defense investment might mitigate the worst‐case vulnerability by more than 40%; and (3) MSLAs might cause larger vulnerability than nonproximity‐based malicious attacks.

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“…The above classification is not inclusive. There are other variants, some as special cases and some the same but under different names, such as interdiction on planar graphs, , interdiction in any region of a network in the Euclidean space , game theoretic models , matching interdiction , minimum spanning tree interdiction , Matrix interdiction , median and covering facility interdiction , and maximum flow interdiction on dynamic networks . For a taxonomy of different types of these problems the interested reader is referred to .…”

Section: Introductionmentioning

confidence: 99%

Two extended formulations for cardinality maximum flow network interdiction problem

Rad

Kakhki

2017

Networks

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We consider the maximum flow network interdiction problem in its cardinality case. There is an integer programming model for this problem by Wood (Math Comput Model 17 (1993), 1–18). Two types of valid inequalities have also been proposed (Altner et al., Oper Res Lett 38 (2010), 33–38 and Wood, Math Comput Model 17 (1993), 1–18) to strengthen the LP relaxation of the integer model. However, due to their combinatorial nature, the number of these inequalities are exponential. Here, we present an equivalent reformulation (extended formulation) for this problem which has a polynomial number of constraints. We also introduce new valid inequalities, and show that the corresponding reformulation of the LP relaxation of the integer model augmented with these inequalities, significantly decreases the integrality gap for a class of network interdiction problems with proven large integrality gaps. Numerical results for some benchmark as well as randomly generated instances are also reported. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 69(4), 367–377 2017

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Maximum dynamic network flow interdiction problem: New formulation and solution procedures

Cited by 34 publications

References 22 publications

Bi-Layer Shortest-Path Network Interdiction Game for Internet of Things

Bi-Layer Shortest-Path Network Interdiction Game for Internet of Things

Vulnerability Mitigation of Multiple Spatially Localized Attacks on Critical Infrastructure Systems

Two extended formulations for cardinality maximum flow network interdiction problem

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