Multi-criteria approach to the construction of fully connected two-factor regressions based on the modelling of the gdp of russia

Abstract

This paper studies two strategies to protect bodies located in the nodes of a square lattice (the network structure of bodies) from extraneous objects. The focus is on the protection by self-moving devices that move along the border of the area where the network structure is located. This paper considers not only circular areas, but also areas of an arbitrary type, namely, areas with piecewise linear and convex-concave smooth borders. It was proved that the model with the group protection of bodies (devices move along the border of a large radius area) is more advantageous to the model with the individual protection of each body (devices move along a circle with a diameter equal to the grid step). It was shown that the ratio of the minimum number of devices used for the individual protection strategy to the minimum number of devices used for the group protection strategy is proportional to the linear dimension of the area. The obtained results are based on the parametrisation of the model by the linear dimension of the region, on the proof of asymptotic relations for regions with different borders, and on the idea of calculating the area of the inner band of the considered width regions equal to the length of the diagonal of the lattice square. In case of group strategy for protecting the network structures of bodies there is a single probability to detect an extraneous object if self-moving vehicles move along the border at the distance of the locator’s field of vision between neighbouring vehicles (along the trajectory of movement) equal to a double radius of vision. This task arose due to the intensive study of structures generated by self-moving particles. The number of self-moving particles is assumed to be quite large, which causes certain difficulties in their technical implementation.