Routing Optimization for Transport and Sustainability

Abstract

Traffic congestion is a major challenge in the transport industry, affecting both the economy and environment. Designing efficient and sustainable transport models requires a multifaceted approach. One of these facets is extracting optimal trajectories for each passenger type, a task well-addressed by the principles of optimal transport theory. By leveraging optimal transport principles, we can model passenger flows in networks to reduce congestion. However, recent research based on optimal transport overlooks crucial factors such as environmental impacts, multilayer transport network analysis, and fails to consider practical constraints such as road capacity limitations.

In response to these gaps, this thesis introduces optimal transport-based methods for modeling flows within multilayer transport networks, with a primary focus on addressing congestion and optimizing traffic flow. Additionally, we extend the application of optimal transport theory to tackle community detection problems within networks. This broader scope allows us to not only enhance our understanding of traffic dynamics but also explore diverse applications of optimal transport in networks.

First, we propose efficient methods, based on optimal transport theory, for modeling passenger flows within multilayer transport networks. Our approach generates both distributed and single-trajectory flows for each passenger types, and shows how these trajectories can alleviate traffic congestion and reduce CO2 emissions. Second, to address the limitation of existing methods on realistic constraints in transport network, we delve into a constrained framework. This framework accommodates nonlinear and non-convex constraints within optimal transport problems, providing a computationally efficient tool for minimizing congestion. As an application, we consider real multilayer transport networks where each layer is associated with a different transport mode, and show how the traffic distribution varies with relevant quantities (such as transport regime, origin-destination pairs, imposed constraints, etc.) across layers.

Lastly, we present an optimal transport-based approach for detecting communities in networks. By incorporating the Ollivier-Ricci curvature, our model provides various transport regimes that allow for better control of information flow between node neighborhoods. The algorithm not only exhibits improved accuracy in identifying communities, but also outperforms conventional OT-based methods, providing deeper insights into geometric approaches to analyzing complex networks. Overall, the methods presented in this thesis enhance our understanding of traffic dynamics within multilayer transport networks, provides valuable insights that contribute to sustainable transport systems. By addressing congestion through optimal transport-based approaches, we pave the way for more efficient and envi- ronmentally friendly transport systems. Furthermore, extending the application of optimal transport to community detection problems highlights its versatility in analyzing complex networks beyond transportation networks.