  Multilayer networks have been found to be prone to abrupt cascading failures
under random and targeted attacks, but most of the targeting algorithms
proposed so far have been mainly tested on uncorrelated systems. Here we show
that the size of the critical percolation set of a multilayer network is
substantially affected by the presence of inter-layer degree correlations and
edge overlap. We provide extensive numerical evidence which confirms that the
state-of-the-art optimal percolation strategies consistently fail to identify
minimal percolation sets in synthetic and real-world correlated multilayer
networks, thus overestimating their robustness. We propose two new targeting
algorithms, based on the local estimation of path disruptions away from a given
node, and a family of Pareto-efficient strategies that take into account both
intra-layer and inter-layer heuristics, and can be easily extended to multiplex
networks with an arbitrary number of layers. We show that these strategies
consistently outperform existing attacking algorithms, on both synthetic and
real-world multiplex networks, and provide some interesting insights about the
interplay of correlations and overlap in determining the hyperfragility of
real-world multilayer networks. Overall, the results presented in the paper
suggest that we are still far from having fully identified the salient
ingredients determining the robustness of multiplex networks to targeted
attacks.
