Plyekhova G. Modeling and optimization of connections upon restrictions on geometrical parameters of routes

The thesis presents hierarchical mathematical model for the general connection problem being actual for a computer aided laying-out of the networks (water-supply line, railway system, etc.) and routes for vehicles at a rugged terrain. This problem consists in searching of optimal routes and networks in a given non-singly-connected manifold. That are specified on a special functional classes of curves under constraints on curvature and other geometrical and topological restrictions imposed onto connection parameters. For the standard types of curves, constraints, and functionals the basic optimization problems are stated, as well as the standart problems being reduced to the former ones, for which the optimality conditions and respective optimization methods are obtained that show linear time consumption. Adequacy of the proposed models of curves, criterions and constraints to the requirements of the design standards is supported by introduction of the developed algorithms and software.