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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.

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Vehicle routing problems are strategic point to the optimization of logistics processes and for more than half a century have attracted wide attention of researchers due to their complexity and practical significance. This paper focuses on a relatively new area of research on dynamic vehicle routing problems. The authors give prerequisites for its formation, associated with globalization and the development of information and communication technologies. A brief history of this sub-class of problems is presented, with references to the works of authors who have contributed significantly to its research. The principal differences between the dynamic vehicle routing problems and their static counterparts are shown. As examples of a practical application there are considered sales sphere, emergency rescue and repair service companies, courier services, transport ordering systems, emergency services and taxi services. There is a review of varieties of deterministic and non-deterministic problems in the paper. Among the main dynamic parameters of the problems, there are considered the requests for export and delivery, the query time, the quantity of demand, the travel time of the vehicle, and others. The main approaches to solving dynamic vehicle routing problems are considered and the most popular methods and algorithms are specified, including tabu search, variable neighborhood search, insertion methods, nearest neighbor search, column generation, genetic algorithms, ant colony optimization and particle swarm optimization. The conclusion is the current trends of research in this area, related to the formulation of complex variants of dynamic vehicle routing problem and the development of effective methods of global optimization to solve them.