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As a relatively new information theory, network coding has already resulted in a significant influence on many research areas such as communication system, network protocol, wireless network, and network security. The optimization of network coding, which aims to minimize network coding resources such as coding nodes and links, has recently attracted the attention of some researchers, who have so far focused their efforts mainly on static network coding problem (SNCP). For instance, they make the common assumption that a target rate is always achievable at every sink as long as coding is allowed at all nodes, which is unrealistic due to the dynamic nature of most real-world networks, where any link could be disconnected at any time. This paper is concerned with how to address the dynamic network coding problem (DNCP). To this end, a general formulation of DNCP is described, and then the design of an effective Genetic Algorithm (GA) for the DNCP is reported. The new problem formulation not only considers the minimization of network coding resources, but also takes into account the maximization of the rate actually achieved. The proposed GA adopts a new permutation representation, which not only makes evolutionary operations free of feasibility problems, but also makes it easy to integrate useful problem-specific heuristic rules into the algorithm. Experimental results illustrate the effectiveness of the proposed model and algorithm for DNCP.