## 1 Introduction  
The amount of data from mobile smart terminal devices in intelligent factories is growing rapidly as the Industrial Internet age progresses [1]. Due to resource limitations of terminal devices such as logistics handling robots, mobile assembly robots, and unmanned delivery vehicles, they cannot process large amounts of data by themselves [2]. In situations with insufficient bandwidth, traditional cloud computing models have difficulty responding to terminal device requests in real time. Traditional centralized processing is overloaded by the severe bandwidth and energy demands of data transfer from the endpoint to the cloud [3]. It has become a development trend to promote the sinking of cloud computing capabilities and improve the processing capabilities of edge devices, which has led to the emergence of MEC in the Industrial Internet [4; 5; 6]. Intelligent factory scenarios are more sensitive to energy consumption, which require more data computing and higher data security [7]. MEC has a great effect on saving energy consumption [8]. MEC migrates the original cloud computing resources and services of the intelligent factory to a location closer to the terminal, effectively reducing the energy consumption caused by communication and computing [5]. MEC promotes cloud services on the edge to be closer to mobile smart devices by utilizing the capabilities of edge computing servers. Mobile industrial devices constrained by limited battery capacity and computing power are able to offload compute-intensive tasks to MEC servers [9]. In addition, MEC is more adept at handling tasks that require real-time execution than traditional cloud services [10]. Edgecomputing may also be employed in Industrial Internet systems to offload computer tasks and reduce network traffic [11]. MEC is primarily used for real-time processing of large-scale industrial data, but it still faces challenges in communication between mobile devices and MEC servers. This challenge imposes additional costs on the system, including energy consumption and delay. Therefore, in the context of the Industrial Internet, it is crucial to improve resource allocation and unloading strategies, which currently represent a key issue [12]. Moreover, in the field of Industrial Internet, terminal and edge devices have limited computing power. When dealing with complex nonconvex problems, traditional machine learning methods often encounter issues such as nonconvergence or local convergence [13], making the system optimization challenges even more complex. Additionally, factories place high importance on data privacy [14]. In summary, current academic research on edge-terminal collaborative computing offloading and resource allocation for MEC networks has been conducted extensively. However, there is insufficient research on multiedge-terminal collaboration for computing offloading and resource allocation in the intelligent factory of the Industrial Internet scenarios. Therefore, to better facilitate the development of the Industrial Internet and meet business requirements, it is the focus of research to solve the MEC system's multiedge-terminal collaborative computing offloading and resource allocation through cutting-edge machine learning algorithms in the Industrial Internet scenario. Our paper investigates the intelligent factory within the Industrial Internet MEC setting. We propose an algorithm that merges FL and DRL to optimize the system's overall energy consumption. This optimization is achieved through multiedge-terminal collaborative computing offloading and resource allocation. We consider an intelligent factory with an Industrial Internet multiedge-terminal MEC system, which consists of several small base stations connected to edge servers and several mobile smart industrial terminal devices. Tasks can either be run locally on terminal devices or offloaded to edge servers. The overall energy consumption of Industrial Internet multiedge-terminal MEC systems is the focus of our article.