MATHEMATICAL MODELS FOR DETERMINING THE PARETO FRONT FOR BUILDING TECHNOLOGICAL PROCESSES OPTIONS UNDER THE CONDITIONS OF INTERVAL PRESENTATION OF LOCAL CRITERIA - Beskorovainyi, Vladimir; Kolesnyk, Lyudmyla; Mgbere, Dr. Chinwi (INNOVATIVE TECHNOLOGIES AND SCIENTIFIC SOLUTIONS FOR INDUSTRIES, 2023)
The subject of research in the article is decision-making support processes in the tasks of optimizing technological processes (TP) at the stages of their design or reengineering. The goal of the work is to improve the efficiency of technologies of automated design of TP due to the development of mathematical models of the tasks of selecting subsets of effective design solutions with intervally specified characteristics of options. The following tasks have been solved in the article: review and analysis of the current state of the problem of supporting decision-making in the tasks of optimization of TP at the stages of their design or reengineering; decomposition of the problem of making project decisions; formalization of the task of comparing intervals for selection of Pareto fronts using comparison indices based on the generalized Hukuhari difference; development of a mathematical model of the problem for the method based on Carlin's lemma; development of a mathematical model of the problem for the method based on Hermeyer's theorem; determination of the Pareto front in the task of optimization of TP by the method of pairwise comparisons. The following methods were used: system approach, theories of systems, theories of usefulness, theories of decision-making, system design, optimization and operations research. Results. The place and connections of the problem of determining the Pareto front in the problem of making project decisions are determined. A formalized interval comparison procedure for the selection of Pareto fronts using Hukuhari total difference comparison indices. Mathematical models of the problem of selection of Pareto fronts using methods based on Carlin's lemma and Hermeyer's theorem have been developed for the case of interval publication with the value of local criteria. An example of the formation of the Pareto front in the problem of optimization of the technological process by the method of pairwise comparison according to the indicators of the duration of the technological cycle, reliability and specified costs is given. Conclusions. The proposed mathematical models expand the methodological bases of the automation of TP design processes. They make it possible to correctly reduce the set of alternative options for construction of TP for the final choice, taking into account the knowledge, experience of designers and factors that are difficult to formalize. The practical use of mathematical models will allow to increase the degree of automation of design or control processes, to reduce the time of decision-making in conditions of incomplete certainty of input data and to guarantee their quality by selecting them only from a subset of effective ones.