Resilient Network Design: Disjoint Shortest Path Problem for Power Transmission Application

Path redundancy is essential for safety and reliability in many real-world routing problems, such as the design of networks for power transmission, transportation, etc. These problems are typically posed to find the shortest path on a weighted graph. For the shortest path with path redundancy, particularly in the Disjoint Shortest 2-Path (DS2P) problem, two disjoint paths are desired such that the combined weight of the two paths is minimized while a minimum distance path separation is maintained. The conventional formulation of the above requires a large-scale mixed-integer programming (MIP) model. However, this approach is practically intractable due to the model's complexity and extremely long run-time. We demonstrate why DS2P is NP-complete and propose an efficient heuristic to find an approximate solution to the problem in a much shorter time frame. We demonstrate the approach on a realistic dataset for power transmission routing, integrating the computational methodology with a visualization interface using Google Maps. The resulting prototype software is freely available through GitHub and can be deployed on a cloud platform, such as Amazon AWS.