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Emerging technologies such as Software-Defined Networks (SDN) and Network Function Virtualization (NFV) promise to address cost reduction and flexibility in network operation while enabling innovative network service delivery. To catch up with the time- varying traffic demands, the network changes frequently. We should come up with a sequence of instructions to manipulate the starting network into the goal network, while preserving the network semantics correctness (e.g., freedom of loops, bandwidth guaranteeing). In this case, how to migrate the virtual network functions (VNF) and update the flow forwarding rules efficiently is an important and challenging problem. In this paper, we are motivated to address the migration of VNF and flow update rule problem with joint consideration of migration cost and update delay. The problem is first formulated into a mixed integer non-linear programming (MINLP). By …