Usually, for economic reasons, the physical infrastructure for transmission networks is designed as 2-connected graphs, i.e. interconnected rings. However, the increment of both, the traffic and the dependency of our professional and personal lives on ICT, demands more reliable transmission and distribution networks. Network interconnection problems are in general costly and complex to solve, categorized as NP-hard computational complexity. In addition, structural constraints such as 3-connectivity increase the time and resources utilized in the optimization search process. This paper presents and evaluates novel strategies in order to simplify the optimization process when planning the physical network interconnection as 3-connected with nodal degree 3. These strategies are applied in a case study and the results, using this and other approaches, are compared in terms of path distances, path length, network length, processing time, and number of iterations to find the solution.