  In the aftermath of a sudden catastrophe, First Responders (FR) strive to
promptly reach and rescue immobile victims. Simultaneously, other mobile
individuals take roads to evacuate the affected region, or access shelters. The
escalated traffic congestion significantly hinders critical FR operations if
they share some of the same roads. A proposal from the Turkish Ministry of
Transportation and Infrastructure being discussed for implementation is to
allocate a subset of road segments for use by FRs only, mark them clearly, and
pre-communicate them to the citizens. For the FR paths under consideration: (i)
there should exist an FR path from designated entry points to each demand point
in the network, and (ii) evacuees try to leave the network (through some exit
points following the selfish routing principle) in the shortest time possible
when they know that certain segments are not available to them. We develop a
mixed integer non-linear programming formulation for this First Responder
Network Design Problem (FRNDP). We solve FRNDP using a novel hybrid
quantum-classical heuristic building on the Graver Augmented Multi-Seed
Algorithm (GAMA). Using the flow-balance constraints for the FR and evacuee
paths, we use a Quadratic Unconstrained Binary Optimization (QUBO) model to
obtain a partial Graver Bases to move between the feasible solutions of FRNDP.
To efficiently explore the solution space for high-quality solutions, we
develop a novel bi-level nested GAMA within GAMA: GAGA. We test GAGA on random
graph instances of various sizes and instances related to an expected Istanbul
earthquake. Comparing GAGA against a state-of-the-art exact algorithm for
traditional formulations, we find that GAGA offers a promising alternative
approach. We hope our work encourages further study of quantum (inspired)
algorithms to tackle complex optimization models from other application
domains.
