  While new forms of attacks are developed every day to compromise essential
infrastructures, service providers are also expected to develop strategies to
mitigate the risk of extreme failures. In this context, tools of Network
Science have been used to evaluate network robustness and propose resilient
topologies against attacks. We present here a new rewiring method to modify the
network topology improving its robustness, based on the evolution of the
network largest component during a sequence of targeted attacks. In comparison
to previous strategies, our method lowers by several orders of magnitude the
computational effort necessary to improve robustness. Our rewiring also drives
the formation of layers of nodes with similar degree while keeping a highly
modular structure. This "modular onion-like structure" is a particular class of
the onion-like structure previously described in the literature. We apply our
rewiring strategy to an unweighted representation of the World Air
Transportation network and show that an improvement of 30% in its overall
robustness can be achieved through smart swaps of around 9% of its links.
