A Quantum-Inspired Bilevel Optimization Algorithm for the First Responder Network Design Problem.

This article focuses on the First Responder Network Design Problem (FRNDP), a bilevel optimization model developed to improve disaster response and evacuation by reserving lanes exclusively for first responders (FRs) on road networks. The outer problem selects which road links to reserve for FR use to ensure connectivity from entry points to FR demand nodes, while the inner problem models evacuees' selfish routing behavior minimizing their total travel time under these lane reservations. The study introduces GAGA, a novel quantum-inspired bilevel heuristic algorithm based on the Graver augmented multiseed algorithm (GAMA) nested within itself, to efficiently solve FRNDP instances. Computational experiments on synthetic graphs and a realistic Istanbul earthquake scenario demonstrate that GAGA achieves superior solution quality and runtime compared to a state-of-the-art branch-and-bound exact algorithm, highlighting the potential of quantum-inspired methods in complex disaster preparedness network design. The findings emphasize the importance of accounting for evacuees' routing behavior and suggest that predetermined FR lane reservations can be robust across varying disaster severities while balancing first responder accessibility and evacuation efficiency.