Advancing Transportation Routing Decisions Using Riemannian Manifold Surfaces

We consider several real-world driving factors such as the time spent at traffic signs (e.g., yield signs and stop signs), speed limits, and the topology of the surface to develop realistic and accurate routing solutions. Though these factors increase the complexity of modeling, they provide the flexibility to evaluate the routing solutions from different perspectives: cost, distance, and time, to name a few. First, we develop a set of algorithms based on the Riemannian manifold surface (RMS) to factor in the Earth's curvature to calculate distances. Second, we present a multiobjective, nonlinear, mixed-integer model (MINLP) that minimizes the distance traveled, time traveled, traveling costs, and time spent on traffic signs to design and evaluate the routes where the waiting times associated with traffic lights, stop signs, and yield signs are stochastic. Finally, we apply MINLP and RMS-based algorithms to a set of real-life and short- and long-distance transportation problems and analyze the results from computational experiments and discrete event simulations. We show that our approaches are on par with the state-of-the-art application, Google Maps, and yield realistic routing solutions that generate significant cost savings.