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With increasing demand for computing and memory, distributed computing systems have attracted a lot of attention. Resource allocation is one of the most important challenges in the distributed systems specially when the clients have Service Level Agreements (SLAs) and the total profit in the system depends on how the system can meet these SLAs. In this paper, an SLA-based resource allocation problem for multi-tier applications in the cloud computing is considered. An upper bound on the total profit is provided and an algorithm based on force-directed search is proposed to solve the problem. The processing, memory requirement, and communication resources are considered as three dimensions in which optimization is performed. Simulation results demonstrate the effectiveness of the proposed heuristic algorithm.