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The Adaptation of Interior Point Method for Solving the Quadratic Programming Problems Arising in the Assembly of Deformable Structures

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Optimization and Applications (OPTIMA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12422))

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Abstract

The simulation of the airframe assembly process implies the modelling of contact interaction of compliant parts. As every item in mass production deviates from the nominal, the analysis of the assembly process involves the massive solving of contact problems with varying input data. The contact problem may be formulated in terms of quadratic programming. The bottleneck is the computation time that may be reduced by the use of specially adapted optimization methods. The considered problems have an ill-conditioned Hessian and a sparse matrix of constraints. It is necessary to solve a large number of problems with the same constraint matrix and Hessian. This work considers the primal-dual interior-point method (IPM) and proposes its adaptation to the solving of assembly problems. A method is proposed for choosing a feasible starting point based on a physical interpretation for reducing the number of IPM iterations. The numerical comparison of the approaches to solve a system of linear equations at each iteration of IPM is presented, i.e. an augmented system and a normal equation (its reduction) using various preconditioners. Finally, IPM is compared by computation time with an active-set method, a Newton projection method and Lemke’s method on a number of aircraft assembly problems.

Supported by RFBR, project number 20-38-90023\(\backslash \)20.

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Acknowledgments

The authors would like to thank our colleagues from both Airbus SAS and Peter the Great St.Petersburg Polytechnic University for numerous discussions and helpful suggestions. We also want to express our gratitude to Prof. J. Gondzio for his valuable advices that have helped us improve the quality of the research. We thank O. Tarunina and T. Pogarskay for careful reading of our manuscript and giving useful comments.

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Authors and Affiliations

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

    Maria Stefanova & Sergey Lupuleac

Authors
  1. Maria Stefanova
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  2. Sergey Lupuleac
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Correspondence to Maria Stefanova .

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Editors and Affiliations

  1. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  4. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Stefanova, M., Lupuleac, S. (2020). The Adaptation of Interior Point Method for Solving the Quadratic Programming Problems Arising in the Assembly of Deformable Structures. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2020. Lecture Notes in Computer Science(), vol 12422. Springer, Cham. https://doi.org/10.1007/978-3-030-62867-3_19

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