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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 2, Pages 209–224 (Mi zvmmf9777)  

This article is cited in 19 scientific papers (total in 19 papers)

Nonuniform covering method as applied to multicriteria optimization problems with guaranteed accuracy

Yu. G. Evtushenko, M. A. Posypkin

Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow

Abstract: The nonuniform covering method is applied to multicriteria optimization problems. The $\varepsilon$-Pareto set is defined, and its properties are examined. An algorithm for constructing an $\varepsilon$-Pareto set with guaranteed accuracy $\varepsilon$ is described. The efficiency of implementing this approach is discussed, and numerical results are presented.

Key words: multicriteria optimization, nonuniform covering method, guaranteed accuracy, $\varepsilon$-Pareto set.

DOI: https://doi.org/10.7868/S0044466913020087

Full text: PDF file (301 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:2, 144–157

Bibliographic databases:

UDC: 519.658
Received: 08.08.2012

Citation: Yu. G. Evtushenko, M. A. Posypkin, “Nonuniform covering method as applied to multicriteria optimization problems with guaranteed accuracy”, Zh. Vychisl. Mat. Mat. Fiz., 53:2 (2013), 209–224; Comput. Math. Math. Phys., 53:2 (2013), 144–157

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    This publication is cited in the following articles:
    1. V. E. Berezkin, A. V. Lotov, E. A. Lotova, “Study of hybrid methods for approximating the Edgeworth–Pareto hull in nonlinear multicriteria optimization problems”, Comput. Math. Math. Phys., 54:6 (2014), 919–930  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. Yu. G. Evtushenko, M. A. Posypkin, “Effective hull of a set and its approximation”, Dokl. Math., 90:3 (2014), 791–794  crossref  mathscinet  zmath  isi  elib  scopus
    3. A. Zilinskas, “A one-step worst-case optimal algorithm for bi-objective univariate optimization”, Optim. Lett., 8:7 (2014), 1945–1960  crossref  mathscinet  zmath  isi  scopus
    4. A. Zilinskas, J. Zilinskas, “Adaptation of a one-step worst-case optimal univariate algorithm of bi-objective lipschitz optimization to multidimensional problems”, Commun. Nonlinear Sci. Numer. Simul., 21:1-3 (2015), 89–98  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. A. V. Lotov, “Decomposition of the problem of approximating the Edgeworth–Pareto hull”, Comput. Math. Math. Phys., 55:10 (2015), 1653–1664  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. A. V. Lotov, “Decomposition methods for polyhedral approximation of the edgeworth-pareto hull”, Dokl. Math., 92:3 (2015), 784–787  crossref  mathscinet  zmath  isi  elib  scopus
    7. Ya. I. Rabinovich, “Numerical methods for estimating approximate solutions of multicriteria optimization problems”, Dokl. Math., 91:3 (2015), 384–386  crossref  mathscinet  zmath  isi  elib  scopus
    8. A. Gila Arrondo, J. L. Redondo, J. Fernandez, P. M. Ortigosa, “Parallelization of a non-linear multi-objective optimization algorithm: application to a location problem”, Appl. Math. Comput., 255 (2015), 114–124  crossref  mathscinet  zmath  isi  scopus
    9. A. Zilinskas, A. Zhigljavsky, “Branch and probability bound methods in multi-objective optimization”, Optim. Lett., 10:2 (2016), 341–353  crossref  mathscinet  zmath  isi  scopus
    10. A. M. Thike, S. Lupin, Yu. Vagapov, “Implementation of brute force algorithm for topology optimisation of wireless networks”, 2016 International Conference for Students on Applied Engineering (ICSAE) (Newcastle upon Tyne, United Kingdom), eds. Z. AlShibaany, A. Hameed, IEEE, 2016, 264–268  crossref  isi  scopus
    11. O. V. Khamisov, “Optimization with quadratic support functions in nonconvex smooth optimization”, Proceedings of the 2nd International Conference “Numerical Computations: Theory and Algorithms”, NUMTA 2016 (Pizzo Calabro, Italy, 19–25 June 2016), AIP Conf. Proc., 1776, eds. Y. Sergeyev, D. Kvasov, F. DellAccio, M. Mukhametzhanov, Amer. Inst. Phys., 2016, 050010  crossref  isi  scopus
    12. P. Pardalos, A. Zilinskas, J. Zilinskas, Non-Convex Multi-Objective Optimization, Springer Optimization and Its Applications, 123, Springer, 2017, 192 pp.  crossref  mathscinet  isi
    13. Yu. Evtushenko, M. Posypkin, A. Turkin, L. Rybak, “The non-uniform covering approach to manipulator workspace assessment”, Proceedings of the 2017 IEEE Russia Section Young Researchers in Electrical and Electronic Engineering Conference, ElConRus, IEEE, 2017, 386–389  crossref  isi
    14. G. K. Kamenev, A. V. Lotov, “Approximation of the effective hull of a nonconvex multidimensional set given by a nonlinear mapping”, Dokl. Math., 97:1 (2018), 104–108  mathnet  crossref  crossref  zmath  isi  scopus
    15. Yu. Evtushenko, M. Posypkin, L. Rybak, A. Turkin, “Approximating a solution set of nonlinear inequalities”, J. Glob. Optim., 71:1, SI (2018), 129–145  crossref  mathscinet  zmath  isi  scopus
    16. E. F. Campana, M. Diez, G. Liuzzi, S. Lucidi, R. Pellegrini, V. Piccialli, F. Rinaldi, A. Serani, “A multi-objective DIRECT algorithm for ship hull optimization”, Comput. Optim. Appl., 71:1, SI (2018), 53–72  crossref  mathscinet  isi  scopus
    17. A. V. Lotov, “New external estimate for the reachable set of a nonlinear multistep dynamic system”, Comput. Math. Math. Phys., 58:2 (2018), 196–206  mathnet  crossref  crossref  isi  elib
    18. I. Kaliszewski, J. Miroforidis, “On upper approximations of Pareto fronts”, J. Glob. Optim., 72:3 (2018), 475–490  crossref  mathscinet  isi  scopus
    19. G. K. Kamenev, “Method for constructing optimal dark coverings”, Comput. Math. Math. Phys., 58:7 (2018), 1040–1048  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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