The increasing complexity of intelligent services requires new paradigm to overcome the problems caused by resource-limited mobile devices. Mobile edge computing systems with energy harvesting devices is such a promising technology. By offloading the computation tasks from the mobile devices to the MEC servers, users could experience services with low latency. In addition, energy harvesting technology releases the tension between high energy consumption of intelligent services and capacity-constrained mobile device batteries. However, in multi-user and multi-server scenarios where mobile devices can move arbitrarily, computation offloading strategies are faced with new challenges because of resource competition and server selection. In this paper, we will develop an intelligent computation offloading strategy. The quality of user experience cost and the cell capacity in terms of the ratio of computation tasks offloaded will be adopted as the performance metrics. An online algorithm, namely, the LODCO-Based Genetic Algorithm with Greedy Policy, will be proposed. Specifically, the algorithm is based on Lyapunov Optimization and the LODCO Algorithm. By choosing the execution mode among local execution, offloading execution and task dropping for each mobile device, our algorithm can asymptotically obtain the optimal results for the whole system. The algorithm proposed is low-complexity and could work without too much priori knowledge. Moreover, the algorithm not only inherits every advantage from the LODCO Algorithm but also adapts perfectly to the more complex environment. Simulation results illustrate that the algorithms could improve the ratio of offloading computation tasks by more than 10% while the QoE is guaranteed.