Industrial Robot Monitoring System (IRMS) is an important guarantee to maintain the normal operation of industrial robot systems. For IRMSs in the edge-cloud environment, live migration technology enables them to improve system resource utilization and reliability such as dynamic resource management or fault tolerance without interrupting monitoring services. Therefore, it is important to research the optimization of live migration for IRMS. For multi-container migration, parallel migration can reduce service downtime, serial migration can reduce pre-copy migration time, and hybrid migration with a reasonable serial-parallel relationship can combine the advantages of both. In this paper, we propose a multi-container migration architecture based on shared bandwidth, which considers the resource-constrained characteristics of the edge-cloud environment. Moreover, we present a multi-container hybrid migration planning model with the total migration time as the optimization objective, which uses a matrix representation of serial-parallel relationship. To solve this model, we develop a heuristic algorithm based on a hybrid Tabu-Evolutionary algorithm. The algorithm can find the dominant solution quickly by global search and improve the solution quality by subspace search. The experimental results show that the proposed algorithm can quickly give the hybrid migration strategy for a set of containers, effectively reducing the total migration time.