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K-Anonymity is a property for the measurement, management, and governance of the data anonymization. Many implementations of k-anonymity have been described in state of the art, but most of them are not able to work with a large number of attributes in a "Big" dataset, i.e., a dataset drawn from Big Data. To address this significant shortcoming, we introduce and evaluate \textsc{KGen} an approach to K-anonymity featuring Genetic Algorithms. \textsc{KGen} promotes such a meta-heuristic approach since it can solve the problem by finding a pseudo-optimal solution in a reasonable time over a considerable load of input. \textsc{KGen} allows the data manager to guarantee a high anonymity level while preserving the usability and preventing loss of information entropy over the data. Differently from other approaches that provide optimal global solutions catered for small datasets, \textsc{KGen} works properly also over Big datasets while still providing a good-enough solution. Evaluation results show how our approach can still work efficiently on a real world dataset, provided by Dutch Tax Authority, with 47 attributes (i.e., the columns of the dataset to be anonymized) and over 1.5K+ observations (i.e., the rows of that dataset), as well as on a dataset with 97 attributes and over 3942 observations.