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A new Branch and Bound method for a discrete truss topology design problem

Author

Listed:
  • Adelaide Cerveira
  • Agostinho Agra
  • Fernando Bastos
  • Joaquim Gromicho

Abstract

Our paper considers a classic problem in the field of Truss Topology Design, the goal of which is to determine the stiffest truss, under a given load, with a bound on the total volume and discrete requirements in the cross-sectional areas of the bars. To solve this problem we propose a new two-stage Branch and Bound algorithm. In the first stage we perform a Branch and Bound algorithm on the nodes of the structure. This is based on the following dichotomy study: either a node is in the final structure or not. In the second stage, a Branch and Bound on the bar areas is conducted. The existence or otherwise of a node in this structure is ensured by adding constraints on the cross-sectional areas of its incident bars. In practice, for reasons of stability, free bars linked at free nodes should be avoided. Therefore, if a node exists in the structure, then there must be at least two incident bars on it, unless it is a supported node. Thus, a new constraint is added, which lower bounds the sum of the cross-sectional areas of bars incident to the node. Otherwise, if a free node does not belong to the final structure, then all the bar area variables corresponding to bars incident to this node may be set to zero. These constraints are added during the first stage and lead to a tight model. We report the computational experiments conducted to test the effectiveness of this two-stage approach, enhanced by the rule to prevent free bars, as compared to a classical Branch and Bound algorithm, where branching is only performed on the bar areas. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:54:y:2013:i:1:p:163-187
    DOI: 10.1007/s10589-012-9487-6
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    References listed on IDEAS

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    1. 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.
    2. 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. Ken Kobayashi & Yuich Takano, 2020. "A branch-and-cut algorithm for solving mixed-integer semidefinite optimization problems," Computational Optimization and Applications, Springer, vol. 75(2), pages 493-513, March.
    2. de Meijer, Frank, 2023. "Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization," Other publications TiSEM b1f1088c-95fe-4b8a-9e15-c, Tilburg University, School of Economics and Management.
    3. Kobayashi, Ken & Takano, Yuichi & Nakata, Kazuhide, 2023. "Cardinality-constrained distributionally robust portfolio optimization," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1173-1182.
    4. 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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