**5. Computational results and discussion**

To the best of the authors' knowledge, there are no efficient optimization algorithms that design robust networks combining the requirement of network reliability and high levels of topological connectivity between pairs of distinguished nodes (topological design of survivable networks). Critical applications such as military communication networks, transport and distribution of highly risky or critical products/substances, or circuit design with high requirements of redundancy (airplanes), among others, were influential factors that facilitated the combination of efficient network design with high levels of connectivity that exceeded a pre-established threshold of reliability. Given the lack/absence of real cases in the literature and plausible instances to be used as a benchmark for the combined problem GSP-SRC, 20 instances of the traveling salesman problem (TSP) from the TSPLIB library have been selected [11], and for each of these, three GSP-SRC instances have been generated by randomly marking 20, 35, and 50% out of the nodes as terminal. The 20 TSP test instances were chosen so that their topologies are heterogeneous and their numbers of nodes (which range from 48 to 225) cover typical applications of the GSP problem in telecommunication settings. The acronyms used for the 20 instances in the TSPLIB library are att48, berlin52, brazil58, ch150, d198, eil51, gr137, gr202, kroA100, kroA150, kroB100, kroB150, kroB200, lin105, pr152, rat195, st70, tsp225, u159, and rd100. The connectivity requirements were randomly set in *rij* ∈{2*,*3*,*4} and ∀*i,j* ∈ *T*.

It is worth noting that in all cases the best solutions attained by the VND algorithm were topologically minimal (i.e., feasibility is lost upon removal of any edge). The improvement percentage of the VND algorithm with respect to the solution cost delivered by the construction phase ranged from 25.25 to 39.84%, depending on the topological features of the instance, showing thus the potential of proposed VND in improving the quality of the starting solution.

For the instances in which the average *T*-terminal reliability of the *L\_Sol* solutions set returned by NetworkDesign was computed, it widely surpassed the 85% prefixed threshold. Particularly, in those instances in which the operation probabilities of nodes and edges were set at 99 and 90%, respectively, the average *T*-terminal reliability was bounded by 86*.*0 and 96*.*7%. On the other hand, when setting the values of the operation probabilities of nodes and edges at 99 and 95%, respectively, the average *T*-terminal reliability was bounded by 99*.*1 and 99*.*6%. In all these evaluated cases, the average variance was small, lower than 1*.*0*E*–05.

The average times per iteration reached by the NetworkDesign approximated algorithm were below 173 seconds in all test cases.
