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The Internet of Vehicles (IoV) has gained worldwide attentions as it provides the service of collecting real-time traffic information to improve the road safety. The IoV users can offload their computing tasks to the edge computing devices (ECDs) for low latency execution and the cloud can be engaged to process big data with sufficient computing resources. Though galactic convenience brought by the IoV cloud-edge computing system, it remains a challenge to manage the resource of ECDs by reducing the energy and time consumption while avoiding the situation of overload or underload of the ECDs to maintain the system-stability. Moreover, during the movement of the vehicles, the computing tasks and data may be uploaded to different ECDs and the data continuity may be destroyed. In this paper, a multi-objective computation offloading method (MOC) for IoV in cloud-edge computing is proposed to deal with the challenges above. A vehicle-to-vehicle communication-based route obtaining algorithm is designed first. Then, in order to ensure the trustworth of the IoV data, which ECD to upload the computing tasks to is selected. Under the case that all ECDs are overloaded, the computation offloading between ECDs and cloud is considered. In addition, non-dominated sorting genetic algorithm III is adopted to realize the multi-objective optimization of decreasing the load balancing rate and reduce the energy consumption in ECDs and shorten the time during processing the computing tasks. Furthermore, we employ the simple additive weighting and multiple criteria decision making to evaluate the solutions of our proposed method. Finally, experimental evaluations are conducted to validate the efficiency and effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]