МОДЕЛІ ТА АЛГОРИТМИ БАГАТОЦІЛЬОВОГО ЛІНІЙНОГО ПРОГРАМУВАННЯ

• Datum: 2020
• 1. Verfasser: Pavlov, A.A.
• Format: Artikel
• Sprache: English
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2020
• Schlagworte: багатоцільове лінійне програмування; невизначеність; компромісні критерії; компромісні розв’язки; ймовірність; нечітка множина; емпірична матриця парних порівнянь
• Online Zugang: https://jais.net.ua/index.php/files/article/view/499
• Назва журналу: Problems of Control and Informatics

This paper examines a special case of the vector optimization problem formulation, the multipurpose linear programming (LP) problem. Its formulation is provided, as well as two most common approaches to its solution. The author uses his results in the field of finding compromise solutions for one class of combinatorial optimization problems under uncertainty. He has modified the results to solve the multipurpose LP problem with the constraints given in the form of a convex compact. As a result of this modification, two statements were proved, which made it possible to obtain the following results: (a) for the multipurpose LP problem in a deterministic formulation: a new property was found of the compromise criterion which is a linear weighted convolution of linear criteria; five new criteria for obtaining a compromise solution are provided; for each of the given compromise criteria, the LP problems are formulated, their solution is the optimal compromise solution for the corresponding criterion; (b) the problems of a multipurpose LP under uncertainty are formulated (the uncertainty is formalized both in terms of probability theory by introducing multidimensional discrete random variables, and in terms of fuzzy sets theory by introducing the corresponding membership functions of fuzzy discrete sets); compromise criteria and algorithms for obtaining compromise solutions by solving the corresponding LP problems for both types of uncertainty are presented; (c) mixed models of multipurpose LP are also given for the case when some of the linear criteria are deterministic, and the rest are specified uncertainly. The proposed criteria use expert weights, which are proposed to be found by the empirical matrix of paired comparisons using optimization models and the corresponding criteria for finding the best solution developed by the author and his students.