Construction of a Mathematical Model of Multiobjective Optimization on Permutations

The article is devoted to the problem of constructing and solving mathematical models of applied problems as multiobjective problems on combinatorial configurations. This question is actual branch because any task of optimal design of complex economic and technical systems, technological devices, planning and management etc. requires that the desired solution be found consider many criteria. It is used transfer to Euclidian combinatorial configurations and using of discrete optimizations methods. Method for solving such problems is considered and it includes the analyzing of structural graph of Euclidean combinatorial configurations sets. These methods can be modified by combining with other multiobjective optimization approaches depending on the initial conditions of the problem. Models for defining real estate contribution plans and production planning as multiobjective discrete problems are proposed. These models can be supplemented as needed by the required functions and, depending on the initial conditions, are presented as tasks on different sets of combinatorial configurations

Решение экстремальных задач с дробно-линейными функциями цели на комбинаторной конфигурации перестановок при условии многокритериальности

The authors consider the extremum optimization problem with linear fractional objective functions on combinatorial configuration of permutations under multicriteria condition. Solution methods for linear fractional problems are analyzed to choose the approach to problem’s solution. A solution technique based on graph theory is proposed. The algorithm of the modified coordinate method’s subprogram with search optimization is described. It forms a set of points that satisfy additional constraints of the problem. The general solution algorithm without linearization of the objective function and it’s block diagram are proposed. Examples of the algorithm are described

Kombinatoryczne konfiguracje punktów i politopy

The monograph is dedicated to exploring combinatorial point configurations derived from mapping a set of combinatorial configurations into Euclidean space. Various methods for this mapping, along with the typology and properties of the resultant configurations, are presented. In addition, the study revolves around combinatorial polytopes defined as convex hulls of combinatorial point configurations. The primary focus lies in examining multipermutation and partial multipermutation point configurations alongside their associated combinatorial polytopes known as multipermutohedra and partial multipermutohedra. Our theoretical contributions are substantiated through the proof of theorems and supporting auxiliary statements. Examples and illustrations are included to enhance the comprehension of the material.Monografia poświęcona jest badaniu kombinatorycznych konfiguracji punktowych uzyskanych z odwzorowania zbioru konfiguracji kombinatorycznych na przestrzeń euklidesową. Przedstawiono różne metody tego mapowania, wraz z typologią i właściwościami powstałych konfiguracji. Ponadto badanie dotyczy wielotopów kombinatorycznych zdefiniowanych jako wypukłe kadłuby kombinatorycznych konfiguracji punktowych. Główny nacisk położony jest na badanie konfiguracji punktów multipermutacji i częściowych punktów multipermutacji wraz z powiązanymi z nimi kombinatorycznymi politopami, znanymi jako multipermutoedry i częściowe multipermutoedry. Nasz wkład teoretyczny jest uzasadniony dowodem twierdzeń i wspierającymi je stwierdzeniami pomocniczymi. Aby ułatwić zrozumienie materiału, załączono przykłady i ilustracje