Journal article
Global optimization of truss topology with discrete bar areas-Part II: Implementation and numerical results
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.
Language: | English |
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Publisher: | Springer US |
Year: | 2009 |
Pages: | 315-341 |
Journal subtitle: | An International Journal |
ISSN: | 15732894 and 09266003 |
Types: | Journal article |
DOI: | 10.1007/s10589-007-9152-7 |
ORCIDs: | Stolpe, Mathias |