Formalized method of the solution of multi-criteria problems

Abstract

Multi-criteria (vector) optimization involves finding a set (Pareto area) of acceptable solutions. You usually only need to choose one of them. Since the points of the Pareto set are formally incomparable, in order to solve the problem, it is fundamentally necessary to involve information about the preferences of the person making the decision. When solving a specific problem of vector optimization, the decision-maker creates his own model of the objective function (utility function) according to his preferences. Thus, the solution of multi-criteria problems is subjective in nature. The article proposes a formalized method for solving multi-criteria problems.
 A model of multi-criteria optimization is obtained, which allows the object to realize all the goals set in the entire range of possible situations. A systematic approach to the problem of vector optimization made it possible to combine models of individual trade-off schemes into a single integral structure that adapts to the situation of making a multi-criteria decision. The advantage of the concept of a non-linear trade-off scheme is the possibility of making a multi-criteria decision formally, without the direct participation of a person. At the same time, on a single ideological basis, both tasks that are important for general use, and those which main content essence is the satisfaction of individual preferences of decision makers, are solved. The apparatus of the nonlinear trade-off scheme, developed as a formalized tool for studying systems with conflicting criteria, makes it possible to practically solve multi-criteria problems of a wide class.