Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2018, Volume 14, Issue 4, Pages 378–392
DOI: https://doi.org/10.21638/11701/spbu10.2018.410 (Mi vspui385) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Control processes

Construction and reduction of the Pareto set in asymmetric travelling salesman problem with two criteria

A. O. Zakharova, Yu. V. Kovalenkob

a St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
b Novosibirsk State University, 1, Pirogova ul., Novosibirsk, 630090, Russian Federation
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DOI: https://doi.org/10.21638/11701/spbu10.2018.410
Abstract: We consider the bicriteria asymmetric traveling salesman problem (bi-ATSP). The optimal solution to a multicriteria problem is usually supposed to be the Pareto set, which is rather wide in real-world problems. For the first time, we apply to the bi-ATSP the axiomatic approach of the Pareto set reduction proposed by V. Noghin. We identify series of “quanta of information” that guarantee the reduction of the Pareto set for particular cases of the bi-ATSP. An approximation of the Pareto set to the bi-ATSP is constructed by a new multi-objective genetic algorithm. The experimental evaluation carried out in this paper shows the degree of reduction of the Pareto set approximation for various “quanta of information” and various structures of the bi-ATSP instances generated randomly or from TSPLIB problems.
Keywords: reduction of the Pareto set, decision maker preferences, multiobjective genetic algorithm, computational experiment.
Funding agency Grant number
Russian Foundation for Basic Research 17-07-00371_а
Ministry of Education and Science of the Russian Federation
This work was supported by Russian Foundation for Basic Research (project N 17-07-00371) and by the Ministry of Science and Education of the Russian Federation (under the 5-100 Excellence Programme).
Received: May 18, 2018
Accepted: September 25, 2018
Bibliographic databases:
Document Type: Article
UDC: 519.854
MSC: 90C27, 90C29, 90C59
Language: English
Citation: A. O. Zakharov, Yu. V. Kovalenko, “Construction and reduction of the Pareto set in asymmetric travelling salesman problem with two criteria”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 14:4 (2018), 378–392
Citation in format AMSBIB
\Bibitem{ZakKov18}
\by A.~O.~Zakharov, Yu.~V.~Kovalenko
\paper Construction and reduction of the Pareto set in asymmetric travelling salesman problem with two criteria
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2018
\vol 14
\issue 4
\pages 378--392
\mathnet{http://mi.mathnet.ru/vspui385}
\crossref{https://doi.org/10.21638/11701/spbu10.2018.410}
\elib{https://elibrary.ru/item.asp?id=36687365}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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