Dvirna O. The models and solving’s methods of discrete optimization’s vector problems on combinatorial configurations

The subject of research is the process of modeling and solving vector problems of discrete optimization on combinatorial configurations. The purpose of the dissertation is to develop effective methods for solving vector problems on Euclidean combinatorial configurations. The research methods are vector optimization methods for solving vector problems on combinatorial configurations; the main criterion method is the method of solving a vector problem on combinatorial configurations without further restrictions; combinatorial optimization methods – in the combined method of solving a vector problem on combinatorial configurations; graph theory methods – for constructing a structural graph and grid graph; function localization methods as ideas for methods for solving vector problems in combinatorial configurations. The scientific novelty of the work is: for the first time a grid-graph of Euclidean combinatorial configurations is defined and studied; first developed a horizontal method for solving vector combinatorial optimization problems; first developed a coordinate method for solving vector combinatorial optimization problems; the formulation of vector combinatorial problems has been further developed, namely, the formulation of a vector problem on Euclidean combinatorial configurations and the isolated problem of vector linear Euclidean combinatorial optimization; studying the properties of graphs of Euclidean combinatorial configurations, namely, the generalized concept of a structural graph and investigating its properties; the method of combinatorial clipping, namely, developed an approach that allows to integrate and implement the combined method, which is a synthesis of the vector optimization method and the combinatorial clipping method, which unlike existing combines the vector properties of the problem and the combinatorial nature of the set, which allowed to apply the specified method to the ulcerating vector problems on combinatorial configurations; vector and combinatorial optimization models. The practical implications of the results are the ability to use the proposed methods for solving vector problems on combinatorial configurations for applications in different industries, including to determine the effectiveness of real estate contributions, production planning, and more. Methods for solving such problems in the educational process of the Higher educational institution of Poltava University of Economics and Trade for teaching the subjects "Mathematical bases of information activity" and "System analysis of information activity".