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The Relative Formulation of 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 mass solving of quadratic programming (QP) problems. Thus, reducing the computation time becomes a very urgent task. Earlier [12], it was shown that a significant reduction in time can be achieved by reformulating the original QP problem in the so-called form of the relative QP problem. The current paper discusses the aspects of using relative QP problem related to the accuracy of the computations. Data preparation for the relative QP problem involves the matrix inversions. Since the Hessian in the considered QP problems is ill-conditioned, this operation leads to a rapid accumulation of roundoff errors. The paper proposes to use the error-free operations of addition and multiplication to increase the accuracy of the QP problem solution and to maintain high computation speed for QP problem solving. Finally, a comparison of the primal, dual, and relative QP problem formulations in terms of computation time and result accuracy for assembly problems is 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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Acknowledgements

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

    Maria Stefanova & Stanislav Baklanov

Authors
  1. Maria Stefanova
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  2. Stanislav Baklanov
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Corresponding author

Correspondence to Maria Stefanova .

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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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Stefanova, M., Baklanov, S. (2022). The Relative Formulation of 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_3

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  • DOI: https://doi.org/10.1007/978-3-031-22543-7_3

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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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