Global warming caused by greenhouse gas (GHG) emissions is one of the main concerns for both developed and developing countries. In a fast growing Information and Communication Technology industry, current energy efficiency methodologies are not sufficient for new raising problems such as optimization of complex distributed systems. Therefore, proper methodologies tailored for this type of systems could significantly reduce their GHG emissions. In this paper, a new genetic algorithm (GA) is introduced, namely multi-level grouping GA (MLGGA), which is designed for multi-level bin packing problems such as that of carbon footprint reduction in a distributed cloud over a network of data centers. The new MLGGA algorithm is tested on real data in a simulation platform, and its results are compared with other state-of-the-art methodologies. The results show a significant increase in the performance achieved by the proposed algorithm.