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This article describes the project result of modeling and optimizing Radio Access Network. We have proposed a solution for controlling a large number of antennas in the conditions of engineering constraints and a large search space dimension. For estimating the performance, a virtual environment has been developed, that allows changing the parameters of Radio Access antennas to control the coverage and signal quality for all User Equipments. To optimize the Radio Access network, we have analyzed DE, CMA-ES, MOS, self-adaptive surrogate CMA-ES, lq-CMA-ES, BIPOP CMA-ES, sep-CMA-ES, lm-CMA-ES, HMO-CMA-ES, JADE, PSO, which have been adapted to the constraints of the task. To reduce dimension, graph clustering methods - Spectral clustering, Label propagation, Markov Clustering - are compared in dividing the network into groups. The experiments illustrate the efficiency of optimizing a large Radio Access network by the cluster approach.

Structure based partitioning of a system of ordinary differential equations is considered. A general form of the explicit multischeme Runge–Kutta type method for such systems is presented. Order conditions and simplifying conditions are written down. An algorithm of derivation of the sixth order method with seven stages and reuse with two free parameters is given. It embeds a fourth order error estimator. Numerical comparison to the Dormand–Prince method with the same computation cost but of lower order is performed.

Two families of structural four-stage Runge–Kutta methods of order five are considered. The choice of the scheme with the best numerical properties in each family is justified. The comparison of classical and Runge–Kutta–Nystrom fifth order methods is shown and the better performance for some test problems is demonstrated.Two families of structural four-stage Runge–Kutta methods of order five are considered. The choice of the scheme with the best numerical properties in each family is justified. The comparison of classical and Runge–Kutta–Nystrom fifth order methods is shown and the better performance for some test problems is demonstrated.

The so-called structural methods for systems of partitioned ordinary differential equations studied by Olemskoy are considered. An ODE system partitioning is based on special structure of right-hand side dependencies on the unknown functions. The methods are generalization of Runge–Kutta–Nystrom methods and as the latter are more efficient than classical Runge–Kutta schemes for a wide range of systems. Polynomial interpolants for structural methods that can be used for dense output and in standard approach to solve delay differential equations are constructed. The proposed methods take fewer stages than the existing most general continuous Runge–Kutta methods. The orders of the constructed methods are checked with constant step integration of test delay differential equations. Also the global error to computational costs ratios are compared for new and known methods by solving the problems with variable time-step.