When learning a neural network, the weighting factors are adjusted based on minimizing a calculation error. When the objective function has a complex character and a big number of local extremums, network learning using gradient optimization methods does not often guarantee the finding of a global extremum. Nowadays, the solution of this problem for a large class of problems includes using genetic algorithms as the main method for learning backpropagation networks. The development of these algorithms has continued in the study of bioinspired algorithms and their hybrid modifications. The use of bioinspired algorithms, which are based on random search methods, allows solving the problem of bypassing local extremums and has high convergence rate. The paper considers a combined bioinspired algorithm that solves the global optimization problem when there are problems associated with learning artificial neural networks. The network structure and the number of neurons in each hidden layer are important parameters affecting the effectiveness of artificial neural networks learning. Three-layer neural networks can solve many complex problems. However, the effect of the number of neurons in each hidden layer on the convergence rate is underexplored in the general case. The paper studies a combination of the firefly algorithm and gradient descent developed by the authors for the study of three-layer neural networks of various topologies. The conducted research made it possible to identify topology from artificial neural networks. This topology makes it possible to obtain the most optimal solution for fewer steps. The analysis of the learning algorithm performance is based on the exceptional-OR (Xor) function.