As one of the key technologies of 5G wireless communication technology, cooperative multi-access edge computing allows one device to associate multiple edge nodes simultaneously, namely multi-association, which can provide scalable communication services with characteristics of high reliability, massive connectivity and low latency for promising Industrial Internet of Things (IIoT). Effective association between edge nodes and devices is the prerequisite for providing high quality communication services in dense deployed IIoT networks. Most of state of art researches focus on the user association problem in single-association scenario. There are rarely no solutions presented for the considered user association problem with multi-association. In this paper, user association, power allocation and edge node deployment are jointly considered for load balance and energy efficiency under the multi-association mechanism. The problem is formulated as a nested knapsack optimization problem (NKOP) with energy efficiency and load balancing as objective functions and power and signal quality as constraints. Differential evolution with Monte Carlo and sequential quadratic programming (DMS) algorithm is proposed to solve this problem, which decouples the problem into three parts, user association, power allocation and optimizing the location of edge nodes. Numerical results show that: (1) Compared with the single-association, multi-association with power allocation can provide better signal quality and improve energy efficiency; (2) Proposed DMS algorithm is feasible and stable for optimal deployment of edge nodes. These works together provide good reference for edge node deployment of high-density IIoT application scenarios.

协同多址边缘计算作为5G无线通信技术的关键技术之一，允许一台设备同时关联多个边缘节点，即多关联，可以提供具有高可靠、海量连接、低时延等特点的可扩展通信服务。为有前途的工业物联网 (IIoT)。边缘节点和设备之间的有效关联是在密集部署的 IIoT 网络中提供高质量通信服务的先决条件。大多数最先进的研究都集中在单关联场景中的用户关联问题上。对于所考虑的多关联用户关联问题，很少有解决方案。在本文中，用户关联，在多关联机制下，联合考虑功率分配和边缘节点部署以实现负载平衡和能源效率。该问题被表述为嵌套背包优化问题 (NKOP)，以能源效率和负载平衡为目标函数，以功率和信号质量为约束。针对该问题，提出了采用蒙特卡罗差分进化和序列二次规划（DMS）算法解决该问题，将问题解耦为用户关联、功率分配和边缘节点位置优化三个部分。数值结果表明：（1）与单联相比，多联配功率分配可以提供更好的信号质量，提高能效；(2) 所提出的DMS算法对于边缘节点的优化部署是可行且稳定的。