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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2025, Volume 65, Number 7, Pages 1110–1117
DOI: https://doi.org/10.31857/S0044466925070043 (Mi zvmmf12007) 		 
General numerical methods

Symmetric triangular decomposition for constructing approximations to solving the quadratic assignment problem

I. E. Kaporin

Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
English version article
DOI: https://doi.org/10.31857/S0044466925070043
Abstract: The permutation matrices that arise in the process of triangular decomposition of shifted symmetric matrices with the choice of the maximum modulo leading element on the diagonal are used as initial approximations for a series of elementary permutations that improve the target value of the quadratic assignment problem. The results of testing the proposed method on 128 test tasks from QAPLIB are presented.
Key words: quadratic assignment problem, symmetrical triangular decomposition, complete selection of the leading element on the diagonal.
Received: 20.03.2025
Accepted: 23.04.2025
English version:
Computational Mathematics and Mathematical Physics, 2025, Volume 65, Issue 7, Pages 1487–1494
DOI: https://doi.org/10.1134/S0965542525700630
Bibliographic databases:
Document Type: Article
UDC: 519.612
Language: Russian
Citation: I. E. Kaporin, “Symmetric triangular decomposition for constructing approximations to solving the quadratic assignment problem”, Zh. Vychisl. Mat. Mat. Fiz., 65:7 (2025), 1110–1117; Comput. Math. Math. Phys., 65:7 (2025), 1487–1494
Citation in format AMSBIB
\Bibitem{Kap25}
\by I.~E.~Kaporin
\paper Symmetric triangular decomposition for constructing approximations to solving the quadratic assignment problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2025
\vol 65
\issue 7
\pages 1110--1117
\mathnet{http://mi.mathnet.ru/zvmmf12007}
\elib{https://elibrary.ru/item.asp?id=82676642}
\transl
\jour Comput. Math. Math. Phys.
\yr 2025
\vol 65
\issue 7
\pages 1487--1494
\crossref{https://doi.org/10.1134/S0965542525700630}
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