Measurement and ranking of important link combinations in the analysis of transportation network vulnerability envelope buffers under multiple-link disruptions

Yu Gu, Anthony Chen, Xiangdong Xu

Research output: Journal article publicationJournal articleAcademic researchpeer-review


This study proposes an optimization-based approach to rank the importance of link combinations and analyze network vulnerability in extreme and near-extreme cases of disruption under the simultaneous disruption of multiple links. A vulnerability envelope concept is used, which considers the worst and best network performance under multiple-link disruptions. This study goes a step further than previous studies, which have focused on the extreme cases that form the boundary of a vulnerability envelope, to investigate the near-extreme cases inside an envelope and the network performance buffers (i.e., the differences in network performance) between different cases. A flexible framework based on combinatorial optimization modeling is used to determine the most important link combinations and the lower and upper bounds of network performance under their disruptions, which form the vulnerability envelope. A constraint-based method is developed to iteratively identify sub-important link combinations that lead to the formation of buffers of the lower and upper bounds of the vulnerability envelope. Numerical experiments are conducted to illustrate the properties and applicability of the proposed method. The results demonstrate that the consideration of near-extreme cases yields additional valuable information that is not generated by the traditional vulnerability analysis, which is focused on extreme cases. Ranking of the most and sub-most important link combinations enables the identification of non-unique worst/best cases, thereby revealing alternative link combinations to better inform decision-making. Consideration of the network performances in extreme and near-extreme cases affords a less conservative vulnerability assessment and reveals the potential cost of considering only extreme cases in decision-making processes.

Original languageEnglish
Pages (from-to)118-144
Number of pages27
JournalTransportation Research Part B: Methodological
Publication statusPublished - Jan 2023


  • Importance ranking
  • Multiple-link disruption
  • N most important link combination
  • Network vulnerability
  • Vulnerability envelope buffer

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


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