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Introduction.The estimation of efficiency of methods and algorithms for solving optimization problems with a vector criterion and a set of nonlinear constraints is considered. The approach that allows proceeding to an optimization problem with a single objective function (i.e., an unconditional optimization problem) after equivalent transformations is described. However, the objective function obtained in this way has properties (nonlinearity, multimodality, ravine, high dimension) that do not allow classical methods to be used to solve it. The presented work objective is to develop hybrid methods, based on combinations of the algorithms inspired by wildlife with other approaches (gravitational and gradient) for the solution to this problem.Materials and Methods.New methods to solve the specified problem are developed. A computer experiment was conducted on a number of test functions; its analysis was performed, showing the efficiency of various combinations on various functions.Research Results.The efficiency of hybrid algorithms that combine the following approaches is evaluated: genetic and immune; methods of swarm intelligence and genetic and immune; immune and swarm with gravity and gradient.Discussion and Conclusions.The hybrid algorithms in optimization problems are studied. In particular, decisions can be made on their basis under the management of compound objects in the military and industrial sectors, in the creation of innovative projects related to the digital economy. It is established that the type of the objective function affects the result much more than the combination of algorithms.

Introduction. The sediment transportation is one of the major processes that define the magnitude and back surface changing rate for water bodies. The most used prognostic studies in this field are based on the mathematical models that allow reducing, and in some cases, eliminating the expensive and often environmentally burdensome experiments. Spatially one-dimensional models are mainly used to predict changes in bottom topography. For actual coastal systems with irregular coastal configuration, the flow vector is generally not orthogonal to the tangent line for the coastline at each of its points. It also may not coincide with the wind stress vector. Therefore, to solve lots of practically important problems associated with the prediction of the dynamics of the back surface of water basins, it is necessary to use spatially two-dimensional models of sediment transportation and effective numerical methods of their implementation. Materials and Methods. The authors (A.I. Sukhinov, A.E. Chistyakov, E.A. Protsenko, and V.V. Sidoryakina) have earlier proposed a spatially two-dimensional model of sediment transport that satisfies the basic conservation laws (of material balance and momentum) which is a quasilinear equation of parabolic type. The linear difference schemes are constructed and studied; model and some practically important tasks are solved. However, the theoretical study on the proximity of solutions for the original nonlinear initial-boundary value problem and the linearized continuous task - on which basis a discrete model (difference scheme) was built - remained in the shadow. The study of the linearized problem correctness and the determination of sufficient conditions for positivity of solutions are of special interest because only positive solutions to this sediment transport problem have physical value within the framework of the considered models. Research Results. The investigated nonlinear two-dimensional model of sediment transport in the coastal zone of shallow reservoirs takes account of the following physically significant factors and parameters: soil porosity; critical value of the tangent stress at which load transport starts; turbulent interaction; dynamically varying of the bottom geometry; wind currents; and bottom friction. Linearization is carried out on the time grid - nonlinear coefficients of the parabolic equation are taken for the previous time grid step. Next, a chain of tasks connected by the initial data - final solutions of the linearized mixed Cauchy problems chain on a uniform time grid is constructed, and thus, the linearization for the initial 2D nonlinear model is carried out in large. Earlier, the authors have proved the existence and uniqueness of the solution to a linear tasks chain. Prior estimate of the proximity of the linearized problem chain solution to the initial non-linear task solution has been also obtained. The conditions of its solution positivity and their convergence to the nonlinear sediment transport problem are defined in the norm of the Hilbert space L1 with the rate O(τ) where τ is a time step. Discussion and Conclusions. The obtained research results of the spatially two-dimensional nonlinear sediment transport model can be used for predicting the nonlinear hydrodynamic processes, improving their accuracy and reliability due to the availability of new accounting functionality of physically important factors, including the specification of the boundary conditions.