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Global optimization of trusses with constraints on number of different cross-sections: a mixed-integer second-order cone programming approach

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  • Yoshihiro Kanno

Abstract

In design practice it is often that the structural components are selected from among easily available discrete candidates and a number of different candidates used in a structure is restricted to be small. Presented in this paper is a new modeling of the design constraints for obtaining the minimum compliance truss design in which only a limited number of different cross-section sizes are employed. The member cross-sectional areas are considered either discrete design variables that can take only predetermined values or continuous design variables. In both cases it is shown that the compliance minimization problem can be formulated as a mixed-integer second-order cone programming problem. The global optimal solution of this optimization problem is then computed by using an existing solver based on a branch-and-cut algorithm. Numerical experiments are performed to show that the proposed approach is applicable to moderately large-scale problems. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:63:y:2016:i:1:p:203-236
    DOI: 10.1007/s10589-015-9766-0
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    References listed on IDEAS

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    1. Juan Pablo Vielma & Shabbir Ahmed & George L. Nemhauser, 2008. "A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed-Integer Conic Quadratic Programs," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 438-450, August.
    2. 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.
    3. 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.
    4. Adelaide Cerveira & Agostinho Agra & Fernando Bastos & Joaquim Gromicho, 2013. "A new Branch and Bound method for a discrete truss topology design problem," Computational Optimization and Applications, Springer, vol. 54(1), pages 163-187, January.
    5. 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.
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