Shunting Inhibitory Artificial Neural Networks (SIANNs) are biologically inspired networks in which the synaptic interactions are mediated via a nonlinear mechanism called shunting inhibition, which allows neurons to operate as adaptive nonlinear filters. In this article, The architecture of SIANNs is extended to form a generalized feedforward neural network (GFNN) classifier. Two training algorithms are developed based on stochastic search methods, namely genetic algorithms (GAs) and a randomized search method. The combination of stochastic training with the GFNN is applied to four benchmark classification problems: the XOR problem, the 3-bit even parity problem, a diabetes dataset and a heart disease dataset. Experimental results prove the potential of the proposed combination of GFNN and stochastic search training methods. The GFNN can learn difficult classification tasks with few hidden neurons; it solves perfectly the 3-bit parity problem using only one neuron.