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The data distribution problem is a critical one that affects the global performance of the distributed database systems because it directly influences the efficiency of the querying process. Due to the complexity of the problem, most of the proposed solutions divide the design process in two parts: the fragmentation and the allocation of the fragments on the different locations in the network. Here we consider the allocation problem with the possibility to replicate fragments, minimizing the total cost, which is in general NP-complete, and propose a method based on Q-learning to solve the allocation of fragments in the design of a distributed database. As a result we obtain for several cases, logical allocation of fragments in a reasonable time.