<span>With the fifth-generation (5G) networks, Mobile edge computing (MEC) is a promising paradigm to provide near computing and storage capabilities to smart mobile devices. In addition, mobile devices are most of the time battery dependent and energy constrained while they are characterized by their limited processing and storage capacities. Accordingly, these devices must offload a part of their heavy tasks that require a lot of computation and are energy consuming. This choice remains the only option in some circumstances, especially when the battery drains off. Besides, the local CPU frequency allocated to processing has a huge impact on devices energy consumption. Additionally, when mobile devices handle many tasks, the decision of the part to offload becomes critical. Actually, we must consider the wireless network state, the available processing resources at both sides, and particularly the local available battery power. In this paper, we consider a single mobile device that is energy constrained and that retains a list of heavy offloadable tasks that are delay constrained. Therefore, we formulated the corresponding optimization problem, and proposed a Simulated Annealing based heuristic solution scheme. In order to evaluate our solution, we carried out a set of simulation experiments. Finally, the obtained results in terms of energy are very encouraging. Moreover, our solution performs the offloading decisions within an acceptable and feasible timeframes.</span>