UDC 519.8
MULTICRITERIA OPTIMIZATION PROBLEMS WITH VECTOR CONVOLUTIONS
OF NON-HOMOGENEOUS CONVOLUTIONS OF CRITERIA
Abstract. Multiсriteria decision-making problems are considered. Advantage orders are determined by criterial orders, which are convolutions of convolutions. The cases are analyzed where the subordination of equal importance or strict ranking subordination is specified on the set of vector criteria. In both cases, the convolutions within each of the partial vector criteria can be heterogeneous. The equivalence of the considered problems to the corresponding multicriteria decision-making problems with homogeneous (same) ranking within partial vector criteria is proved.
Keywords: multicriteria optimization problem, convolutions of criteria, convolutions of convolutions, vector criteria, heterogeneous convolutions of criteria.
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REFERENCES
- Chervak Yu.Yu. Optimization. An unimproved choice [in Ukrainian]. Uzhhorod: Uzhhorod. nat-l unt, 2002. 312 p.
- Brila A.Yu. Achievability of optimal solutions to a linear multicriteria optimization problem with alternative criteria in transitive subordination. International scientific and technical journal "Problems of control and informatics". 2011. N 4. P. 68–72.
- Brila A.Yu. Achievability of optimal solutions to a linear multicriteria optimization problem based on a weighted sum of criteria of different importance in transitive subordination. Kibernetika i sistemnyj analiz. 2008. Vol. 44, N 5. P. 135–138.
- Donets G.A., Kolechkina L.N. An algorithm for searching values of a linear function on lexicographically ordered permutations. Teoriya optymal'nykh ríshen'. 2009. N 8. P. 3–8.
- Sergienko I.V. Mathematical models and methods for solving discrete optimization problems [in Russian]. Kyiv: Nauk. Dumka, 1988. 472 p.
- Sergienko I.V., Lebedeva T.T., Semenova N.V. On the existence of solutions in vector optimization problems. Kibernetika i sistemnyj analiz. 2000. Vol. 36, N 6. P. 39–46.
- Lebedeva T.T., Semenova N.V., Sergienko T.I. The kernel of stability of the vector optimization problem under the conditions of perturbations of criterion functions. Reports of the National Academy of Sciences of Ukraine. 2021. N 1. P. 17–23.
- Lebedeva T.T., Semenova N.V., Sergienko T.I. Stability and regularization of vector optimization problems under possible criteria disturbances. Kibernetyka ta sistemnyi analiz. 2022. Vol. 58, N 5. P. 57–63.
- Sergienko I.V., Shilo V.P. Discrete optimization problems: problems, solution methods, analysis [in Russian]. Kyiv: Nauk. dumka, 2003. 264 p.
- Sergienko I.V., Shilo V.P., Roschyn V.O. Discrete optimization. Algorithms and their effective use [in Ukrainian]. Kyiv: Nauk. dumka, 2020. 144 p.
- Lebedeva T.T., Semenova N.V., Sergienko T.I. Stability of vector integer optimization problems: relationship with the stability of sets of optimal and non-optimal solutions. Kibernetika i sistemnyj analiz. 2005. Vol. 41, N 4. P. 90–100.
- Semenova N.V., Kolechkina L.M. Vector problems of discrete optimization on combinatorial sets: research and solution methods [in Ukrainian]. Kyiv: Nauk. dumka, 2009. 266 p.
- Podinovsky V.V., Nogin V.D. Pareto-optimal solutions to multicriteria problems. Moscow: Nauka, 1982. 256 p.
- Podinovsky V.V., Gavrilov V.M. Optimization according with respect to consistently applied criteria [in Russian]. Moscow: Sov. radio, 1975. 192 p.
- Nogin V.D. Decision-making in a multicriteria environment: a quantitative approach [in Russian]. Moscow: Fizmatlit, 2002. 144 p.
- Ehrgott M. Multicriteria Optimization. Second edition. Heildelberg: Springer Berlin, 2005. 324 p.
- Greco S., Ehrgott M., Figueira J.R. Multiple Criteria Decision Analysis — State of the Art Surveys. New York: Springer, 2016. 1346 p.
