On the Application of Saddle-Point Methods for Combined Equilibrium Transportation Models

Travel demand modeling is an essential tool in urban planning and transportation system management. Existing practically efficient algorithms for solving multistage travel demand problems are variations of the heuristic sequential procedure. We propose a novel approach that applies saddle-point methods to a combined convex optimization formulation of the problem. Unlike all previous methods, our algorithm does not require costly shortest-paths calculations, and can be seamlessly scaled on GPUs. We show that in some cases it drastically outperforms the sequential procedures.