Inserted: 28 oct 2003
Last Updated: 23 sep 2015
Journal: ESAIM Control Optim. Calc. Var.
In the framework of transport theory, we are interested in the following optimization problem: given the distributions $\mu^+$ of working people and $\mu^-$ of their working places in an urban area, build a transportation network (such as a railway or an underground system) which minimizes a functional depending on the geometry of the network through a particular cost function. The functional is defined as the Wasserstein distance of $\mu^+$ from $\mu^-$ with respect to a metric which depends on the transportation network.
Keywords: Optimal Networks, Mass Transportation Problems