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Truss topology optimization with discrete design variables by outer approximation

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  • Mathias Stolpe

Abstract

Several variants of an outer approximation method are proposed to solve truss topology optimization problems with discrete design variables to proven global optimality. The objective is to minimize the volume of the structure while satisfying constraints on the global stiffness of the structure under the applied loads. We extend the natural problem formulation by adding redundant force variables and force equilibrium constraints. This guarantees that the designs suggested by the relaxed master problems are capable of carrying the applied loads, a property which is generally not satisfied for classical outer approximation approaches applied to optimal design problems. A set of two- and three-dimensional benchmark problems are solved and the numerical results suggest that the proposed approaches are competitive with other special-purpose global optimization methods for the considered class of problems. Numerical comparisons indicate that the suggested outer approximation algorithms can outperform standard approaches suggested in the literature, especially on difficult problem instances. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Mathias Stolpe, 2015. "Truss topology optimization with discrete design variables by outer approximation," Journal of Global Optimization, Springer, vol. 61(1), pages 139-163, January.
  • Handle: RePEc:spr:jglopt:v:61:y:2015:i:1:p:139-163
    DOI: 10.1007/s10898-014-0142-x
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    References listed on IDEAS

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    1. Fred Glover, 1975. "Improved Linear Integer Programming Formulations of Nonlinear Integer Problems," Management Science, INFORMS, vol. 22(4), pages 455-460, December.
    2. Eduardo Muñoz & Mathias Stolpe, 2011. "Generalized Benders’ Decomposition for topology optimization problems," Journal of Global Optimization, Springer, vol. 51(1), pages 149-183, September.
    3. S. Bollapragada & O. Ghattas & J. N. Hooker, 2001. "Optimal Design of Truss Structures by Logic-Based Branch and Cut," Operations Research, INFORMS, vol. 49(1), pages 42-51, February.
    4. Wolfgang Achtziger & Mathias Stolpe, 2009. "Global optimization of truss topology with discrete bar areas—Part II: Implementation and numerical results," Computational Optimization and Applications, Springer, vol. 44(2), pages 315-341, November.
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    Cited by:

    1. Yoshihiro Kanno, 2016. "Global optimization of trusses with constraints on number of different cross-sections: a mixed-integer second-order cone programming approach," Computational Optimization and Applications, Springer, vol. 63(1), pages 203-236, January.

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