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ONE APPROACH TO DECISION MAKING IN THE TASK OF MILTI-OBJECT OPTIMIZATION
Abstract
The decision making theory finds its application literally at any field of science, especially at geosciences, because working with natural resources requires the most accurate tools. This paper considers one question of the given theory, which is called the solution priority problem. The priority problem in multi-object optimization is quite complex, many authors understand it in their own way. Perhaps this is because now the theory of multi-purpose optimization is in its infancy: there is no holistic understanding of the priority problem from its definition and task to its consideration. However, this work is not intended to bring final clarity to this issue, this task should be solved in the near future. There are numerous approaches to define improvability of the given solution, but this work considers only one of it. The considered approach can be applied for defining of solution improvability in the field of multi-objective optimization. This approach is based on applying of simple preference relation of one solution to another one. For defining the task of multi-object optimization a vector criteria consisting of solutions of the task is given. After the task of multi-purpose optimization is formulated, the problem arises of determining the principle of choosing the elements that are optimal according to this principle and according to a given priority, or taking into account a given priority when using any principle, depending on which of the following sample set of cases is implemented. Moreover, the conditions under which the given solution is unimprovable (so it is Pareto optimal) have been shown. If the Pareto optimal element is unique, then it is a solution to the problem of multi-purpose optimization; if the set of Pareto optimal elements contains a significant number of elements, then it is here that the problem of narrowing this set arises on the basis of priority, restrictions, etc., finding optimal and super-optimal elements. The results presented in this paper should help solve this problem. At the end of the work, improvability and optimum conditions by given preference relations also have been presented.
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References35
Kolbin V.V. Decision making and programming. World Scientific Publ. Company. Singapore, 2003. 745 p.
Petrov M.M, Kolbin V.V. One Approach to the Problem of Multi-Objective Optimization Solutions Improvement // Process Management and Scientific Developments. Birmingham, UK: Infinity, 2020. р. 45-49.
Petrov M.M, Kolbin V.V. One Approach to Researching the Priority Problem in the Tasks of Multi-object Optimization // Process Management and Scientific Developments. Birmingham, UK: Infinity, 2020. р. 49-54.
Aizerman M.A., Aleskerov F.T. Choosing og the variants: fundamentals of the theory, Moscow, Nauka, 1990.
Wilkas A., I. Optimum in games and solutions, Nauka, Moscow, 1990.
Williams A.C. On stochastic linear programming. J. Soc. Induzt. Appl. MTH. 927- 940, 1965.
Kiruta A.Ya., Maiminas E.Z. Solutions: theory, information, modelling. Radio i svyaz, Moscow, 1981.
Shtoier R. Multi-criteria optimization. Theory, computation and application. Radio i svyaz, Moscow, 1992.
Larichev O.I. Science and the art of decision-making. Nauka, Moscow, 1979.
Main H., Osaki S. Markov processes in decision-making. Nauka, Moscow, 1977.
Truhaev R. I. Models of decision-making under uncertainty. Nauka, Moscow, 1981.
Fishburn, Peter C. Utiliti theory for decision making / Peter C. Fishburn New York, 1970.
Yudin D.B. Computational methods of decision-making theory. Nauka, Moscow, 1989.
Abramov L.M., Kapustin V.F. Mathematical programming. SPbU publ., Leningrad, 1976.
Karlin S. Mathematical methods in game theory, programming and economy. Mir, Moscow, 1964
Germeier Yu.B. Introduction to operation research. Nauka, Moscow, 1972.
Ioffe A.D., Tikhomirov V.M. Theory of extremal problems. SPbU publ., Leningrad 1974.
Zubov V.I., Petrosyan L.A. The problem of capital distribution. SPbU publ., Leningrad 1971.
Zubov V.I., Petrosyan L.A. Mathematical methods for planning. SPbU publ., Leningrad, 1982
Yudin D.B. Mathematical methods of control under conditions of incomplete information. Soviet radio, Moscow, 1989
Demianov V.F. Malozemov V.N. Introduction to minimax. Nauka, Moscow, 1972.
Zhukovin V.E. Multi-criteria models of decision-making under uncertainty. Nauka, Moscow, 1983.
Zhukovin V.E. Models and procedures of decision-making. Nauka, Moscow, 1981.
Karmanov V.G. Mathematical programming. Nauka, Moscow, 1975.
Melamed I. I. Linear convolution in multi-criteria optimization. Avtomatica I telemekhanika, Moscow, 1997, p. 119-125.
Mirzoakhmedov F., Milakhevich M.V. Applied aspects of stochastic programming. Nauka, Moscow, 1989.
Neiman J., Morgenshtern O. Game theory and economic behavior. Nauka, Мoscow, 1970.
Tabak A., Kuo B. Optimal control and mathematical programming. Nauka, Moscow, 1975.
Kozeletskyi Yu. Psicological theory of decisions. Progress, Moscow, 1979.
George F.H. Problem solving, 1980.
Fishburn P.C. General theory of subjective probabilities and expected utilities. Ann. Math. Statistics, 40, 1969.
Fishburn P.C. Even-chance lotteries in social choice theory. Theory and Decision, 18-40, 1972.
Packard D.J. A preference logic minimally complete for expected utility maximization. J. Philosophical logic, 223-235, 1975.
Packard D.J. Preference relations. J. Math. Psych. 295-306, 1979.
Wets R. Stochastic programs with fixed recourse. SIAM Rev., 309-339, 1974.
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