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In this paper, we study the problem of dynamically migrating a service in Clouds to satisfy a sequence of mobile batch-request demands in a cost effective way. The service may have a single or multiple replicas, each running on a virtual machine. As the origins of the mobile accesses are frequently changed over time, this problem is particularly important to those time-bounded services to achieve enhanced QoS and cost effectiveness. Moving services closer to client locations not only reduces the service access latency but also minimizes the network cost for service providers. However, these benefits do not come without compromise. The migration comes at cost of bulk data transfer and service disruption, as a result, increasing the overall service costs. To gain the benefits of service migration while minimizing the increased monetary costs, we propose a search-based dynamic migration algorithm that can effectively migrate a single or multiple servers to adapt to the changes of access patterns with minimum service costs. The algorithm is characterized by effective uses of historical access information to conduct virtual moves of a set of servers as a whole under a certain condition so as to overcome the limitations of local search in cost reduction. Our simulation results show that the proposed algorithm can effectively achieve the goal by satisfying service request sequences. Moreover, with moderate migration cost, using a single server is more cost-effective to satisfy the requests in Clouds than deploying multiple servers.