A Systematic Approach to Multiobjective Optimization
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A SYSTEMATIC APPROACH TO MULTIOBJECTIVE OPTIMIZATION A. N. Voronin1† and A. S. Savchenko1‡
UDC 519.9
Abstract. A systematic approach to solving multiobjective optimization problems is proposed. It allows combining the models of individual schemes of compromises into an integrated structure that adapts to the situation of making multicriteria decisions. An advantage of the concept of nonlinear scheme of compromises is the possibility of making a multicriteria decision formally, without a direct human participation. The apparatus of the nonlinear scheme of compromises, developed as a formalized tool for the analysis of control systems with conflicting criteria, makes it possible to solve practically multicriteria problems of a broad class. Keywords: system, optimization, multicriteria, utility function, scalar convolution, nonlinear scheme of compromises. INTRODUCTION The informative content of many practical problems in different subject domains lies in choosing the conditions that allow the object under study to exhibit its best properties (optimization problems). The conditions on which the object properties depend are qualitatively expressed by certain variables x1 , x 2 , ... , and x n , specified in the domain X and are called optimization arguments. The external influences r do not depend on them; however, they can take their values from the compact set R . It is surmised that calculations are performed when the external influence vector r 0 Î R on which the decision-making situation depends is known and specified. Conversely, each property of the object in the domain Ì is quantitatively described using the variable yk , k Î[1, s] , whose value characterizes the property of the object Î in respect to this property. In the general case, the properties y1 , y2 , ... , ys , which are called quality criteria, form a vector y = { yk }sk =1 Î Ì . Its components quantitatively express the object properties with the specified set of optimization arguments x = {x i }ni =1 Î X . PROBLEM STATEMENT The ideas of system optimization are laid out in [1, 2]. The term “systematic approach” postulates that the real object represented by a system is described as a set of components interacting with each other while realizing a certain objective. From the variety of components of the real object, the final but ordered set of elements and relationships between them is “carved out.” It can be surmised that the system is a model of the real object only in the terms of the objective being realized by it. The object requiring certain functions to be realized determines the composition and structure of the system in terms of them. The objective isolates and defines the outlines of the system in the object. Only the information necessary and sufficient to achieve the objective will be included in this system (the object model). If one object is able to realize 1
National Aviation University, Kyiv, Ukraine, †[email protected]; ‡[email protected]. Translated from Kibernetika i Sistemnyi Analiz, No. 6, November– December, 2020, pp. 160–1
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