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Optimal Design of Truss Structures by Logic-Based Branch and Cut

Author

Listed:
  • S. Bollapragada

    (Information Technology Laboratory, General Electric Corporate Research and Development, Schenectady, New York 12301)

  • O. Ghattas

    (Civil and Environmental Engineering Department, Carnegie Mellon University, Pittsburgh, Pensylvania 15213)

  • J. N. Hooker

    (Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

Abstract

The truss design problem is to find the optimal placement and size of structural bars that can support a given load. The problem is nonlinear and, in the version addressed here, the bars must take certain discrete sizes. It is shown that a logic-based method that dispenses with integer variables and branches directly on logical disjunctions can solve substantially larger problems than mixed integer programming, even though the nonlinearities disappear in the mixed integer model. A primary purpose of the paper is to investigate whether advantages of logic-based branching that have been demonstrated elsewhere for linear problems extend to nonlinear programming.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:49:y:2001:i:1:p:42-51
    DOI: 10.1287/opre.49.1.42.11196
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    References listed on IDEAS

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    1. John N. Hooker, 1989. "Input Proofs and Rank One Cutting Planes," INFORMS Journal on Computing, INFORMS, vol. 1(3), pages 137-145, August.
    2. Williams, H. P., 1995. "Logic applied to integer programming and integer programming applied to logic," European Journal of Operational Research, Elsevier, vol. 81(3), pages 605-616, March.
    3. Beaumont, Nicholas, 1990. "An algorithm for disjunctive programs," European Journal of Operational Research, Elsevier, vol. 48(3), pages 362-371, October.
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    Cited by:

    1. Tómasson, Egill & Hesamzadeh, Mohammad Reza & Wolak, Frank A., 2020. "Optimal offer-bid strategy of an energy storage portfolio: A linear quasi-relaxation approach," Applied Energy, Elsevier, vol. 260(C).
    2. John N. Hooker, 2002. "Logic, Optimization, and Constraint Programming," INFORMS Journal on Computing, INFORMS, vol. 14(4), pages 295-321, November.
    3. Srinivas Bollapragada & Michael R. Bussieck & Suman Mallik, 2004. "Scheduling Commercial Videotapes in Broadcast Television," Operations Research, INFORMS, vol. 52(5), pages 679-689, October.
    4. Eduardo Muñoz & Mathias Stolpe, 2011. "Generalized Benders’ Decomposition for topology optimization problems," Journal of Global Optimization, Springer, vol. 51(1), pages 149-183, September.
    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.
    6. 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.
    7. 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.

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