Construction of a Mathematical Model of Multiobjective Optimization on Permutations

Abstract

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.