  The branched transport problem, a popular recent variant of optimal
transport, is a non-convex and non-smooth variational problem on Radon
measures. The so-called urban planning problem, on the contrary, is a shape
optimization problem that seeks the optimal geometry of a street or pipe
network. We show that the branched transport problem with concave cost function
is equivalent to a generalized version of the urban planning problem. Apart
from unifying these two different models used in the literature, another
advantage of the urban planning formulation for branched transport is that it
provides a more transparent interpretation of the overall cost by separation
into a transport (Wasserstein-1-distance) and a network maintenance term, and
it splits the problem into the actual transportation task and a geometry
optimization.
