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In this paper, we present the problem of appropriate feature selection for constructing a Maximum Entropy (ME) based Named Entity Recognition (NER) system under the multiobjective optimization (MOO) framework. Two conflicting objective functions are simultaneously optimized using the search capability of MOO. These objectives are (i). the dimensionality of features, which is tried to be minimized, and (ii). the corresponding F-measure value of the classifier, trained using the features present, is maximized. The features are encoded in the chromosomes. Thereafter, a multiobjective evolutionary algorithm in the steps of a popular MOO technique, NSGA-II, is developed to determine the appropriate feature subset. The proposed technique is evaluated to determine the suitable feature combinations for NER in a resource-constrained language, namely Bengali. Evaluation results yield the recall, precision and F-measure values of 72.45%, 82.39% and 77.11%, respectively.