Mobile devices (MDs) cannot fully run all computation/delay-sensitive tasks due to their limited computing resources. Mobile edge computing (MEC) meets the demand by providing massive resources for MDs and offloading task partitions to MEC servers. However, task offloading also brings communication delay and energy consumption. Therefore, it is challenging to associate resource-constrained MDs with appropriate MEC servers to minimize power consumption. To address this problem, a constrained mixed integer nonlinear program is formulated to optimize the total energy consumption of the system including MDs and MEC servers. To solve this problem, this work designs an improved meta-heuristic optimization algorithm called Self-adaptive and Multi-population Differential Annealed Optimization (SMDAO). Experimental results demonstrate that compared with its two state-of-the-art peers, the proposed SMDAO yields the best solution with the smallest total energy consumption in the least time.