Tymofijeva N. Theoretical-Numerical Methods Used to Solve Combinatorial Optimization Problems

The thesis is devoted to working out а methodology used to reveal the objective function properties within combinatorial optimization problems. With the use of such properties, a method is developed aimed at modelling of a structure of input data represented the functions of natural argument, one the functions is combinatorial. The properties of different-type combinatorial configurations as the objective function of argument are described, the conformities with the natural laws of their formation and regulation are stated. The periodicity property, typical for generation of different-type combinatorial configurations, is described. A generalized method of their regulation and a new method solving enumeration problems in combinatorics are proposed. A local method is elaborated that is used to solve combinatorial optimization problems without sorting out of variants, called a structure-alphabetical search method, by recognition of a structure of input data and ordering of combinatorial configurations. Anew subclass of solvable problems is extracted out of a class of combinatorial optimization problems. A new type of crosspoint switch is constructed. It is volumetric. A mathematical model of speech recognition and synthesis problems is proposed as combinatorial optimization problems.