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The issue of feature selection is particularly critical for the application of monitoring and "on condition" diagnostic techniques to complex plants, like the nuclear power plants, where hundreds of parameters are measured. Indeed, irrelevant and noisy features unnecessarily increase the complexity of the problem and can degrade the diagnostic performance. In this paper, the problem of choosing among the several measured plant parameters those to be used for efficient, early transient diagnosis is tackled by means of genetic algorithms. Three different schemes for simultaneously performing the feature selection and the training of an empirical diagnostic classifier are presented. The first approach employs a single objective genetic algorithm to search the vector of features optimal with respect to the classification performance of a Fuzzy K-Nearest Neighbors classifier. With reference to the same classifier, the second and third approaches embrace a multi-objective perspective to find feature sets that achieve high classification performances with low numbers of features. In all cases, validation of the performance of the classifiers based on the optimal feature subsets identified by the genetic algorithm is successively carried out with respect to transients never used during the feature selection phase. The effectiveness of the proposed approaches is tested on a diagnostic problem regarding the classification of simulated transients in the feedwater system of a Boiling Water Reactor.