@article{2545a6b2-979f-4394-b029-f338c7ffede1,
  abstract     = {{<p>Critical infrastructure networks are susceptible to disruptions, and an imbalanced distribution of component importance can significantly amplify their vulnerability to cascading failures or targeted attacks. This study introduces a novel bi-objective optimization framework designed to enhance network resilience by strategically balancing component importance in multi-commodity spatial networks. The first objective minimizes the total deviation of flow-based, commodity-specific component importance measures (derived from single-link interdiction scenarios) from their respective averages, achieved through targeted capacity augmentations. The second objective minimizes the network’s overall proportional unmet demand, reflecting operational performance. The -constraint method is utilized to generate Pareto-optimal solutions, explicitly quantifying the trade-offs between achieving importance balance and maintaining unmet demands. We demonstrate this approach using a comprehensive case study of the Swedish multi-commodity railway network. The results reveal distinct commodity-specific vulnerability profiles and show that strategic capacity additions can substantially improve importance balance, with the analysis detailing the performance trade-offs under various capacity augmentation limits.</p>}},
  author       = {{Gupta, Himadri Sen and Barker, Kash and González, Andrés D. and Christensen, Mick B and Johansson, Jonas and Zio, Enrico}},
  issn         = {{1566-113X}},
  keywords     = {{Component importance measures; Multi-commodity network; Network balancing; Network interdiction; Swedish railway network}},
  language     = {{eng}},
  publisher    = {{Springer}},
  series       = {{Networks and Spatial Economics}},
  title        = {{Balanced Design of Important Components in Multi-Commodity Networks}},
  url          = {{http://dx.doi.org/10.1007/s11067-026-09750-1}},
  doi          = {{10.1007/s11067-026-09750-1}},
  year         = {{2026}},
}