  We model the formation of multi-layer transportation networks as a
multi-objective optimization process, where service providers compete for
passengers, and the creation of routes is determined by a multi-objective cost
function encoding a trade-off between efficiency and competition. The resulting
model reproduces well real-world systems as diverse as airplane, train and bus
networks, thus suggesting that such systems are indeed compatible with the
proposed local optimization mechanisms. In the specific case of airline
transportation systems, we show that the networks of routes operated by each
company are placed very close to the theoretical Pareto front in the
efficiency-competition plane, and that most of the largest carriers of a
continent belong to the corresponding Pareto front. Our results shed light on
the fundamental role played by multi-objective optimization principles in
shaping the structure of large-scale multilayer transportation systems, and
provide novel insights to service providers on the strategies for the smart
selection of novel routes.
