Optimal Transport in Networks: a Physics Perspective
Speaker: Caterina De Bacco
Location: 0.W100 Turing, Building 28
Time: 15:00 - 15:45
Abstract: Optimizing transportation of passengers and resources in complex networks is a central issue in many real-world problems. These range from the compelling design of smart urban transportation systems for cities of the future, which have to meet efficiency, sustainability, and economical requirements, to the study of natural selection mechanisms shaping ecosystems systems, e.g. venation of leaves, deltas of rivers. In this talk we will discuss the problem of optimizing flows and traffic in networks using a dynamical formulation of optimal transport theory. Using analogies with physical systems such as electrical grids or hydraulic networks, we will show how this approach can be used to route passengers of different types in a multi-commodity formulation and how this can be adapted to transportation in multi-modal networks, where passengers can switch between different transportation modes. The ability to arbitrarily tune a parameter that interpolates between different relevant cost functions allows to investigate different transportation regimes. We will show how this can be used to design networks from scratch in a 2D space or how one could simulate scenarios where traffic should be minimized in certain modes (e.g. roads) while it should be consolidated in others (e.g. rails) and how this can result in desirable properties such as decreased carbon emissions.
Constrained Optimisation in Transportation Networks
Speaker: Matteo Canaletti
Location: 0.W100 Turing, Building 28
Time: 15:45 - 16:05
Zoom: link
Abstract: Optimal transport theory is a powerful tool to find optimal flow configurations on networks. Its principled nature and elegant formalism will be briefly addressed at the start of my talk. I will then focus on how realistic constraints such as budget and capacity are applied at the velocity level, leading to optimal solutions.