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We consider the microaggregation problem (MAP) that involves partitioning a set of individual records in a microdata file into a number of mutually exclusive and exhaustive groups. This problem, which seeks for the best partition of the microdata file, is known to be NP-hard and has been tackled using many heuristic solutions. In this paper, we present the first reported fixed-structure-stochastic-automata-based solution to this problem. The newly proposed method leads to a lower value of the information loss (IL), obtains a better tradeoff between the IL and the disclosure risk (DR) when compared with state-of-the-art methods, and leads to a superior value of the scoring index, which is a criterion involving a combination of the IL and the DR. The scheme has been implemented, tested, and evaluated for different real-life and simulated data sets. The results clearly demonstrate the applicability of learning automata to the MAP and its ability to yield a solution that obtains the best tradeoff between IL and DR when compared with the state of the art.