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A specialized primal-dual interior point method for the plastic truss layout optimization

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  • Alemseged Gebrehiwot Weldeyesus

    (The University of Edinburgh)

  • Jacek Gondzio

    (The University of Edinburgh
    NNASK Research Institute)

Abstract

We are concerned with solving linear programming problems arising in the plastic truss layout optimization. We follow the ground structure approach with all possible connections between the nodal points. For very dense ground structures, the solutions of such problems converge to the so-called generalized Michell trusses. Clearly, solving the problems for large nodal densities can be computationally prohibitive due to the resulting huge size of the optimization problems. A technique called member adding that has correspondence to column generation is used to produce a sequence of smaller sub-problems that ultimately approximate the original problem. Although these sub-problems are significantly smaller than the full formulation, they still remain large and require computationally efficient solution techniques. In this article, we present a special purpose primal-dual interior point method tuned to such problems. It exploits the algebraic structure of the problems to reduce the normal equations originating from the algorithm to much smaller linear equation systems. Moreover, these systems are solved using iterative methods. Finally, due to high degree of similarity among the sub-problems after preforming few member adding iterations, the method uses a warm-start strategy and achieves convergence within fewer interior point iterations. The efficiency and robustness of the method are demonstrated with several numerical experiments.

Suggested Citation

  • Alemseged Gebrehiwot Weldeyesus & Jacek Gondzio, 2018. "A specialized primal-dual interior point method for the plastic truss layout optimization," Computational Optimization and Applications, Springer, vol. 71(3), pages 613-640, December.
  • Handle: RePEc:spr:coopap:v:71:y:2018:i:3:d:10.1007_s10589-018-0028-9
    DOI: 10.1007/s10589-018-0028-9
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    References listed on IDEAS

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    1. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    2. Gondzio, Jacek, 2012. "Interior point methods 25 years later," European Journal of Operational Research, Elsevier, vol. 218(3), pages 587-601.
    3. W. Achtziger, 1998. "Multiple-Load Truss Topology and Sizing Optimization: Some Properties of Minimax Compliance," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 255-280, August.
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