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In this paper, a novel approach is proposed to improve the classification performance of a polynomial neural network (PNN). In this approach, the partial descriptions (PDs) are generated at the first layer based on all possible combinations of two features of the training input patterns of a dataset. The set of PDs from the first layer, the set of all input features, and a bias constitute the chromosome of the real-coded genetic algorithm (RCGA). A system of equations is solved to determine the values of the real coefficients of each chromosome of the RCGA for the training dataset with the mean classification accuracy (CA) as the fitness value of each chromosome. To adjust these values for unknown testing patterns, the RCGA is iterated in the usual manner using simple selection, crossover, mutation, and elitist selection. The method is tested extensively with the University of California, Irvine benchmark datasets by utilizing tenfold cross validation of each dataset, and the performance is compared with various well-known state-of-the-art techniques. The results obtained from the proposed method in terms of CA are superior and outperform other known methods on various datasets. [ABSTRACT FROM PUBLISHER]