UDC 519.85

N.V. Semenova
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine,  nvsemenova@meta.ua

L.M. Koliechkina
University of Lodz, Lodz, Poland,  lkoliechkina@gmail.com

O.A. Dvirna
National University "Yuri Kondratyuk Poltava Polytechnic," Poltava, Ukraine,
 lenadvirna@gmail.com

SOLVING A MULTI-OBJECTIVE OPTIMIZATION PROBLEM
ON COMBINATORIAL POINT CONFIGURATIONS

REFERENCES

• 1. Papadimitriou C.H., Steiglitz K. Combinatorial optimization: Algorithms and complexity. Mineola, N.Y.: Dover Publications, Inc., 1998. 496 p.
• 2. Bóna M. Combinatorics of permutations. Boca Raton: Chapman & Hall/CRC, 2004. 337 р.
• 3. Berge C. Principes de combinatoire. Paris: Dunod, 1968. 146 p.
• 4. Sergienko I.V., Hulianytskyi L.F., Sirenko S.I. Classification of applied methods of combinatorial optimization. Cybernetics and Systems Analysis. 2009. Vol. 45, N 5. P. 732–741. https://doi.org/10.1007/s10559-009-9134-0.
• 5. Gulyanitskii L.F., Sergienko I.V. Metaheuristic downhill simplex method in combinatorial optimization. Cybernetics and System Analysis. 2007. Vol. 43, N 6. P. 822–829. https://doi.org/10.1007/s10559-007-0106-y.
• 6. Sergienko I.V., Shylo V.P., Roshchin V.O. Discrete optimization. Algorithms and their effective use [in Ukrainian]. Kyiv: Nauk. Dumka, 2020. 219 p.
• 7. Shor N.Z., Setstyuk P.I. Lagrangian bounds in multiextremal polynomial and discrete optimization problems. Journal of Global Optimization. 2002. Vol. 23. P. 1–41. https://doi.org/10.1023/A:1014004625997.
• 8. Onwubolu G.C., Davendra D. (Eds.) Differential evolution: A handbook for global permutation-based combinatorial optimization. Studies in Computational Intelligence. Berlin; Heidelberg: Springer, 2009. Vol. 175. 213 p. https://doi.org/10.1007/978-3-540-92151-6.
• 9. Korte B., Vygen J. Combinatorial optimization: Theory and algorithms. 5th ed. Berlin; Heidelberg: Springer, 2012. https://doi.org/10.1007/978-3-642-24488-9.
• 10. Pardalos P.M., Du D., Graham R.L. Handbook of combinatorial optimization. New York: Springer, 2013. 648 p.
• 11. Stetsyuk P.I., Donets G.P., Nenakhov E.I. et al. Subgradient algorithms and problems on combinatorial configurations [in Ukrainian]. Kyiv: Pulsary, 2019. 234 p.
• 12. Zgurovskyi M.Z., Pavlov O.A. Hard-to-solve combinatorial optimization problems in planning and decision-making [in Ukrainian]. Kyiv: Nauk. Dumka, 2016. 716 p.
• 13. Aardal K., Hoesel S. Polyhedral techniques in combinatorial optimization II: Theory. Statistica Neerlandica. 1999. Vol. 59, N 2. P. 131–177. https://doi.org/10.1111/1467-9574.00104.
• 14. Stoyan Yu.G., Yemets. O.O. Theory and methods of Euclidean combinatorial optimization [in Ukarainian]. Kyiv: Institute of Systems. Research of Education, 1993. 188 p.
• 15. Semenova N.V., Kolechkina L.M. Vector problems of discrete optimization on combinatorial sets: Methods of research and solution [in Ukrainian]. Kyiv: Nauk. Dumka, 2009. 266 p.
• 16. Donets G.P., Kolechkina L.M. Extremal problems on combinatorial configurations [in Ukrainian]. Poltava: RVV PUET, 2011. 309 p.
• 17. Grebennik I.V., Chorna O.S. Special transpositions of permutation elements and properties of their composition. Cybernetics and Systems Analysis. 2017. Vol. 53, N 1. P. 67–77. https://doi.org/10.1007/s10559-017-9907-9.
• 18. Grebennik I., Chorna O. Elements transpositions and their impact on the cyclic structure of permutations. Econtechmod: An International Quarterly Journal on Economics of Technology and Modelling Processes. 2015. Vol. 4, N 3. P. 33–38.
• 19. Semenova N.V., Kolechkina L.N., Nagornaya A.N. Solution and investigation of vector problems of combinatorial optimization on a set of polypermutations. Journal of Automation and Information Sciences. 2008. Vol. 40, N 12. P. 27–42. https://doi.org/10.1615/JAutomatInfScien.v40.i12.30.
• 20. Semenova N.V., Kolechkina L.N. A polyhedral approach to solving multicriterion combinatorial optimization problems over sets of polyarrangements. Cybernetics and Systems Analysis. 2009. Vol. 45, N 3. P. 438–445. https://doi.org/10.1007/s10559-009-9110-8.
• 21. Stoyan Y.G., Yakovlev S.V. Theory and methods of Euclidean combinatorial optimization: Current status and prospects. Cybernetics and Systems Analysis. 2020. Vol. 56, N 3. P. 366–379. https://doi.org/10.1007/s10559-020-00253-6.
• 22. Yakovlev S., Pichugina O., Koliechkina L. Combinatorial point configurations and polytopes. Lodz University Press. 2023. 232 p. https://doi.org/10.18778/8331-391-7.
• 23. Emmerich M.T.M., Deutz A.H. A tutorial on multiobjective optimization: fundamentals and evolutionary methods. Natural Computing. 2018. Vol. 17, N 1–2. P. 585–609. https://doi.org/10.1007/s11047-018-9685-y.
• 24. Ehrgott M., Wiecek M.M. Mutiobjective programming. In: Multiple Criteria Decision Analysis: State of the Art Surveys. International Series in Operations Research & Management Science. Springer, New York, 2005. Vol. 78. P. 667–708. https://doi.org/10.1007/0-387-23081-5_17.
• 25. Steuer R. Multiple criteria optimization: Theory, computation and application. New York: John Wiley, 1986. 546 p.
• 26. Sergienko I.V., Lebedeva T.T., Semenova N.V. Existence of solutions in vector optimization problems. Cybernetics and Systems Analysis. 2000. Vol. 36, N 6. P. 823–828. https://doi.org/10.1023/A:1009401209157.
• 27. Lebedeva T.T., Semenova N.V., Sergienko T.I. Regularization of the vector problem with quadratic criteria of Pareto optimization. Cybernetics and Systems Analysis. 2023. Vol. 59, N 4. P. 561–566. https://doi.org/10.1007/s10559-023-00591-1.
• 28. Lebedeva T.T., Semenova N.V., Sergienko T.I. Stability and regularization of vector optimization problems under possible criteria disturbances. Cybernetics and Systems Analysis. 2022. Vol. 58, N 5. P. 721–726. https://doi.org/10.1007/s10559-022-00505-7.
• 29. Donec G.A., Kolechkina L.M. Construction of Hamiltonian paths in graphs of permutations polyhedral. Cybernetics and Systems Analysis. 2010. Vol. 46, N 1. P. 7–13. https://doi.org/10.1007/s10559-010-9178-1.
• 30. Koliechkina L.N., Dvirna O.A. Solving extremum problems with linear fractional objective functions on the combinatorial configuration of permutations under multicriteriality. Cybernetics and Systems Analysis. 2017. Vol. 53, N 4. P. 590–599. https://doi.org/10.1007/s10559-017-9961-3.
• 31. Pichugina O., Yakovlev S. Functional and analytic representations of the general permutations. Eastern-European Journal of Enterprise Technologies. 2016. Vol. 1, N 4. P. 27–38. https://doi.org/10.15587/1729-4061.2016.58550.
• 32. Yakovlev S. Convex extensions in combinatorial optimization and their applications. In: Springer Optimization and its Applications. 2017. Vol. 130. P. 567–584. https://doi.org/10.1007/978-3-319-68640-027.
• 33. Yakovlev S.V., Pichugina O.S. Properties of combinatorial optimization problems over polyhedral-spherical sets. Cybernetics and Systems Analysis. 2018. Vol. 54, N 1. P. 99–109. https://doi.org/10.1007/s10559-018-0011-6.
• 34. Berge C. Graphs. 2nd ed. Amsterdam: Elsevier Science, 1985. 413 p.
• 35. Bondy J.A., Murty U.S.R. Graph theory with applications. New York: Springer, 2008. 264 p.