Generalized Benders’ Decomposition for topology optimization problems

Eduardo Javier Munoz Queupumil, Mathias Stolpe

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    This article considers the non-linear mixed 0–1 optimization problems that appear in topology optimization of load carrying structures. The main objective is to present a Generalized Benders’ Decomposition (GBD) method for solving single and multiple load minimum compliance (maximum stiffness) problems with discrete design variables to global optimality. We present the theoretical aspects of the method, including a proof of finite convergence and conditions for obtaining global optimal solutions. The method is also linked to, and compared with, an Outer-Approximation approach and a mixed 0–1 semi definite programming formulation of the considered problem. Several ways to accelerate the method are suggested and an implementation is described. Finally, a set of truss topology optimization problems are numerically solved to global optimality.
    Original languageEnglish
    JournalJournal of Global Optimization
    Volume51
    Issue number1
    Pages (from-to)149-183
    ISSN0925-5001
    DOIs
    Publication statusPublished - 2011

    Keywords

    • Generalized Benders’ Decomposition
    • Outer-approximation
    • Structural topology optimization
    • Global optimization

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