Multicommodity routing optimization for engineering networks

Area of Science:

• Transportation Engineering
• Network Science
• Applied Mathematics

Background:

• Optimizing passenger routes is essential for efficient transportation networks.
• Optimal transport (OT) offers a promising alternative to standard optimization methods.
• Empirical validation of OT on real-world engineering networks is needed.

Purpose of the Study:

• To assess the empirical validity of optimal transport formulations on engineering networks.
• To investigate the impact of different passenger interaction functions on network dynamics.
• To compare OT performance against Dijkstra's algorithm and analyze network resilience.

Main Methods:

• Implemented optimal transport formulation with two distinct coupling functions for passenger fluxes (sum and sum of squares).
• Applied the models to the Paris metro network.
• Analyzed traffic bottlenecks, infrastructure resilience to node removal, and compared with Dijkstra's algorithm.

Main Results:

• The two coupling functions yield equivalent results in congested transport regimes but differ in branched regimes.
• One function promotes route consolidation, potentially leading to traffic overload in branched networks.
• Optimal transport networks demonstrate efficient recovery of shortest-path-like graphs and lie on the Pareto front of energy dissipation and infrastructure cost.

Conclusions:

• Optimal transport is empirically valid for engineering networks, with coupling functions influencing network behavior.
• The choice of coupling function significantly impacts traffic flow distribution and bottleneck formation.
• OT provides a robust framework for analyzing network efficiency, resilience, and trade-offs between operational cost and infrastructure investment.