Soboleva O. Mathematical models and methods for structural-topological optimization for territorial distributed object's synthesis

Object of research - territorial distributed systems. Research objective - development of effective mathematical models, methods, algorithms and software for synthesis of multi-hierarchical territorial distributed systems and based on this the decision of important scientific and practical problem of efficiency raise of CAD-systems for territorial distributed objects. Research methods based on set theory, system theory, graph theory, theory of automatic control and system dynamics methodology, utility theory, statistical analyzing methods. Theoretical and practical results of research are mathematical models and methods for multi-objective synthesis of topology develop methodological basis for creating of effective decision support tools in modern CAD-systems for territorial distributed objects. Scientific novelty are further developed systemological model of territorial distributed system's general structural synthesis problem by consideration of dynamic object's characteristics; first time detected characteristic of optimal hierarchical structures of territorial distributed systems on which proposed the heuristic that significantly reduced the number of design solutions, perfected in time complexity the combinatorial and the coordinatewise methods for topological optimization of hierarchical territorial distributed objects with irregular and regular placement of elements, first time developed system dynamic model for territorial distributed service system that can be used on early design phase for analyzing its resistance to service demand changes; proposed modifications hyperbolic tangent function and Gaussian function for designed solution's utility evaluation by partial criteria that extend benefits in decision maker preference's formalization and more correctly then basic functions reflect his preferences, first time proposed generalized utility models for designed solutions evaluation based on exponential function, information entropy function, additive-multiplicative function and Kolmogorov-Gabor's polynomial that more correctly than basic models reflect the order of decision maker's preferences. The results of the dissertational work realized like software tool, introduced in state budget research works that carried out according to thematic plan of researches in Kharkiv National University of Radio Electronics, funded by the Ministry of Education and Science of Ukraine, in the educational process in Kharkiv National University of Radio Electronics; put into practice in reengineering of supplying system in SEFI "Book Club "Family Leisure Club"", in "Scientific-Production Society "Politech"" Ltd. Scientific theoretical and practical results of the present work can be used in CAD-systems for designing of territorial distributed objects, in the educational process for training specialists in the system engineering field, system dynamics simulation of service systems in demand changing, multi-objective topological optimization of systems and identification for multi-objective decision making problems.