Feature selection is one of the most important concepts in data mining when dimensionality reduction is needed. The performance measures of feature selection encompass predictive accuracy and result comprehensibility. Consistency‐based methods are a significant category of feature selection research that substantially improves the comprehensibility of the result using the parsimony principle. In this work, the biobjective version of the algorithm logical analysis of inconsistent data is applied to large volumes of data. In order to deal with hundreds of thousands of attributes, heuristic decomposition uses parallel processing to solve a set covering problem and a cross‐validation technique. The biobjective solutions contain the number of reduced features and the accuracy. The algorithm is applied to omics datasets with genome‐like characteristics of patients with rare diseases.