Journal of Global Optimization

, Volume 74, Issue 4, pp 803–838 | Cite as

Critical nodes in interdependent networks with deterministic and probabilistic cascading failures

  • Alexander Veremyev
  • Konstantin Pavlikov
  • Eduardo L. Pasiliao
  • My T. Thai
  • Vladimir BoginskiEmail author


We consider optimization problems of identifying critical nodes in coupled interdependent networks, that is, choosing a subset of nodes whose deletion causes the maximum network fragmentation (quantified by an appropriate metric) in the presence of deterministic or probabilistic cascading failure propagations. We use two commonly considered network fragmentation metrics: total number of disabled nodes and total number of disabled pair-wise connectivities. First, we discuss computational complexity issues and develop linear mixed integer programming (MIP) formulations for the corresponding optimization problems in the deterministic case. We then extend these problems to the case with probabilistic failure propagations using Conditional Value-at-Risk measure. We develop a scenario-based linear MIP model and propose an exact Markov chain-based algorithm to solve these problems. Finally, we perform a series of computational experiments on synthetic and semi-synthetic networks and discuss some interesting insights that illustrate the properties of the proposed models.


Combinatorial optimization Interdependent networks Cascading failures Critical nodes Vulnerability assessment Conditional value-at-risk 



This material is based upon work supported by the AFRL Mathematical Modeling and Optimization Institute. M.T. Thai’s and V. Boginski’s research is supported in part by NSF award EFRI-1441231.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Management SystemsUniversity of Central FloridaOrlandoUSA
  2. 2.Department of Business and EconomicsUniversity of Southern DenmarkOdense MDenmark
  3. 3.Munitions DirectorateAir Force Research LaboratoryEglin AFBUSA
  4. 4.Department of Computer and Information Science and EngineeringUniversity of FloridaGainesvilleUSA

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