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Categorical data clustering has been gaining significant attention from researchers, because most of the real life data sets are categorical in nature. In contrast to numerical domain, no natural ordering can be found among the elements of a categorical domain. Hence no inherent distance measure, like the Euclidean distance, would work to compute the distance between two categorical objects. In this article, genetic algorithm and simulated annealing based categorical data clustering algorithm has been proposed. The performance of the proposed algorithm has been compared with that of different well known categorical data clustering algorithms and demonstrated for a variety of artificial and real life categorical data sets.