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The FIRST (Faint Images of the Radio Sky at Twenty-cm) survey is an ambitious project scheduled to cover 10,000 square degrees of the northern and southern galactic caps. Until recently, astronomers associated with FIRST identified radio-emitting galaxies with a bent-double morphology through a visual inspection of images. Besides being subjective, prone to error and tedious, this manual approach is becoming increasingly infeasible: upon completion, FIRST will include almost a million galaxies. This paper describes the application of six methods of evolving neural networks (NNs) with genetic algorithms (GAs) to the identification of bent-double galaxies. The objective is to demonstrate that GAs can successfully address some common problems in the application of NNs to classification problems, such as training the networks, choosing appropriate network topologies, and selecting relevant features. We measured the overall accuracy of the networks using the arithmetic and geometric means of the accuracies on bent and non-bent galaxies. Most of the combinations of GAs and NNs perform equally well on our data, but using GAs to select feature subsets produces the best results, reaching accuracies of 90% using the arithmetic mean and 87% with the geometric mean. The networks found by the GAs were more accurate than hand-designed networks and decision trees.