We consider the NP-hard problem of synthesis of optimal spanning communication subgraph in a given arbitrary simple edge-weighted graph. This problem occurs in the wireless networks while minimizing total transmission power consumptions. We propose a new method based on the variable neighborhood decomposition search metaheuristic for the approximate solution to the problem. We have performed a numerical experiment where the proposed algorithm was executed on the randomly generated test instances. For these instances, on average, our algorithm significantly outperforms the previously known heuristics, comparing solutions obtained after the same run time. The advantage of the proposed algorithm becomes more noticeable with increasing dimensions of the problem.