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With the drastic development of Internet of things, the number of connected mobile users (MUs) is increasing at an unprecedented speed. The increasing popularity of MUs has triggered more and more new mobile applications. However, these applications are sensitive to latency, which inevitably increases pressure on MUs. Fortunately, computation offloading of mobile edge computing is becoming a promising technology that can improve quality of service for MUs. However, it becomes much difficult when there are multiple edge servers (ESs) near to the MU, even to the multiple MUs. On the other hand, as the resources of ESs are heterogeneous and finite, and thus it is challenge to design effective offloading strategies for multiple MUs. To tackle the above challenges, we firstly establish a multi-objective optimization model concerning time consumption and energy consumption of MUs, and resource utilization of ESs. Moreover, we devise an end-edge-cloud collaborative computing offloading method based on improved Strength Pareto Evolutionary Algorithm 2 for addressing this mode. Finally, compared to benchmark methods, numerous experiments have proved that our proposed method is effective and efficient and can be widely used for the scenario of multiple MUs and multiple heterogeneous ESs. [ABSTRACT FROM AUTHOR]