Global optimization of truss topology with discrete bar areas-Part II: Implementation and numerical results

Wolfgang Achtziger, Mathias Stolpe

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    A classical problem within the field of structural optimization is to find the stiffest truss design subject to a given external static load and a bound on the total volume. The design variables describe the cross sectional areas of the bars. This class of problems is well-studied for continuous bar areas. We consider here the difficult situation that the truss must be built from pre-produced bars with given areas. This paper together with Part I proposes an algorithmic framework for the calculation of a global optimizer of the underlying non-convex mixed integer design problem. In this paper we use the theory developed in Part I to design a convergent nonlinear branch-and-bound method tailored to solve large-scale instances of the original discrete problem. The problem formulation and the needed theoretical results from Part I are repeated such that this paper is self-contained. We focus on the implementation details but also establish finite convergence of the branch-and-bound method. The algorithm is based on solving a sequence of continuous non-convex relaxations which can be formulated as quadratic programs according to the theory in Part I. The quadratic programs to be treated within the branch-and-bound search all have the same feasible set and differ from each other only in the objective function. This is one reason for making the resulting branch-and-bound method very efficient. The paper closes with several large-scale numerical examples. These examples are, to the knowledge of the authors, by far the largest discrete topology design problems solved by means of global optimization.
    Original languageEnglish
    JournalComputational Optimization and Applications
    Volume44
    Issue number2
    Pages (from-to)315-341
    ISSN0926-6003
    DOIs
    Publication statusPublished - 2009

    Keywords

    • Branch-and-bound
    • Truss topology optimization
    • Global optimization

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