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Decomposition Method for Solving the Quadratic Programming Problem in the Aircraft Assembly Modeling

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Optimization and Applications (OPTIMA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13781))

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Abstract

Aircraft assembly modeling requires solving the contact problem which can be reduced to the Quadratic Programming (QP) problem with dense ill-conditioned Hessian. For dozens of thousands of variables solving the QP problem requires huge time and RAM space. This paper suggests decomposing the problem into several sub-QP problems according to the geometric regions to reduce both solving time and memory requirements. The important feature of the considered QP problem is the density of the Hessian matrix which means that decomposed regions have mutual interference not only along their common boundary but instead on their whole areas. Suggested decomposition method solves sub-QP problems iteratively until the solution of the original QP is found. Convergence is proved under certain conditions. The results for test models of fuselage section joint and simultaneous joint of the upper and lower wing panels are presented.

The research was supported by Russian Science Foundation (project No. 22-19-00062, https://rscf.ru/en/project/22-19-00062/).

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Acknowledgments

The research was supported by Russian Science Foundation (project No. 22-19-00062, https://rscf.ru/en/project/22-19-00062/).

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Authors and Affiliations

  1. Peter the Great St.Petersburg Polytechnic University, St.Petersburg, 195251, Russia

    Stanislav Baklanov, Maria Stefanova, Sergey Lupuleac, Julia Shinder & Artem Eliseev

Authors
  1. Stanislav Baklanov
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  2. Maria Stefanova
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  3. Sergey Lupuleac
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  4. Julia Shinder
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  5. Artem Eliseev
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Corresponding author

Correspondence to Stanislav Baklanov .

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Editors and Affiliations

  1. Dorodnitsyn Computing Centre, Moscow, Russia

    Nicholas Olenev

  2. Dorodnitsyn Computing Centre, Moscow, Russia

    Yuri Evtushenko

  3. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  4. Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  5. Dorodnitsyn Computing Centre, Moscow, Russia

    Vlasta Malkova

  6. Dorodnitsyn Computing Centre, Moscow, Russia

    Igor Pospelov

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Baklanov, S., Stefanova, M., Lupuleac, S., Shinder, J., Eliseev, A. (2022). Decomposition Method for Solving the Quadratic Programming Problem in the Aircraft Assembly Modeling. In: Olenev, N., Evtushenko, Y., Jaćimović, M., Khachay, M., Malkova, V., Pospelov, I. (eds) Optimization and Applications. OPTIMA 2022. Lecture Notes in Computer Science, vol 13781. Springer, Cham. https://doi.org/10.1007/978-3-031-22543-7_1

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  • DOI: https://doi.org/10.1007/978-3-031-22543-7_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22542-0

  • Online ISBN: 978-3-031-22543-7

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