Optimal networks for mass transportation problems

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.