**Abstract**

This work is focused on the resolution of a mixed model for the design of largesized networks. An algorithm is introduced, whose initial outcomes are promising in terms of topological robustness regarding connectivity and reliability. The algorithm combines the network survivability and the network reliability approaches. The problem of the topological design has been modeled based on the generalized Steiner problem with node-connectivity constraints (GSPNC), which is NP-hard. The aim of this study is to heuristically solve the GSP-NC model by designing lowcost highly connected topologies and to measure the reliability of such solutions with respect to a certain prefixed lower threshold. This research introduces a greedy randomized algorithm for the construction of feasible solutions for the GSP-NC and a local search algorithm based on the variable neighborhood search (VNS) method, customized for the GSP-NC. In order to compute the built network reliabilities, this work adapts the recursive variance reduction (RVR) technique, as a simulation method since the exact evaluation of this measurement is also NP-hard. The experimental tests were performed over a wide set of testing cases, which contained heterogeneous topologies, including instances of more than 200 nodes. The computational results showed highly competitive execution times, achieving minimal local optimal solutions of good quality fulfilling the imposed survivability and reliability conditions.

**Keywords:** survivability, meta-heuristic, VNS, VND, reliability, simulation, RVR
