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We discuss a new design methodology of polynomial neural networks (PNN) in the framework of genetic algorithm (GA). The PNN is based on the ideas of group method of data handling (GMDH). Each node in the network is very flexible and can carry out polynomial type mapping between input and output variables. But the performances of PNN depend strongly on the number of input variables available to the model, the number of input variables, and the type (order) of the polynomials to each node. In this paper, GA is implemented to better use the optimal inputs and the order of polynomial in each node of PNN. The appropriate inputs and order are evolved accordingly and are tuned gradually throughout the GA iterations. We employ a binary coding for encoding key factors of the PNN into the chromosomes. The chromosomes are made of three sub-chromosomes which represent the order, number of inputs, and input candidates for modeling. To construct model by using significant approximation and generalization, we introduce the fitness function with a weighting factor. Comparisons with other modeling methods and conventional PNN show that the proposed design method offers encouraging advantages and better performance.