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Optimizing passengers routes is crucial to design efficient transportationnetworks. Recent results show that optimal transport provides an efficientalternative to standard optimization methods. However, it is not yet clear ifthis formalism has empirical validity on engineering networks. We address thisissue by considering different response functions -- quantities determining theinteraction between passengers -- in the dynamics implementing the optimaltransport formulation. Particularly, we couple passengers' fluxes by takingtheir sum or the sum of their squares. The first choice naturally reflectsedges occupancy in transportation networks, however the second guaranteesconvergence to an optimal configuration of flows. Both modeling choices areapplied to the Paris metro. We measure the extent of traffic bottlenecks andinfrastructure resilience to node removal, showing that the two settings areequivalent in the congested transport regime, but different in the branchedone. In the latter, the two formulations differ on how fluxes are distributed,with one function favoring routes consolidation, thus potentially being proneto generate traffic overload. Additionally, we compare our method to Dijkstra'salgorithm to show its capacity to efficiently recover shortest-path-likegraphs. Finally, we observe that optimal transport networks lie in the Paretofront drawn by the energy dissipated by passengers, and the cost to build theinfrastructure.

Multicommodity routing optimization for engineering networks