Abstract
We consider the minimum compliance topology design problem with a volume constraint and discrete design variables. In particular, our interest is to provide global optimal designs to a challenging benchmark example proposed by Zhou and Rozvany. Global optimality is achieved by an implementation of a local branching method in which the subproblems are solved by a special purpose nonlinear branch-and-cut algorithm. The convergence rate of the branch-and-cut method is improved by strengthening the problem formulation with valid linear inequalities and variable fixing techniques. With the proposed algorithms, we find global optimal designs for several values on the available volume. These designs can be used to validate other methods and heuristics for the considered class of problems.
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Notes
There is an ambiguity with the word node, since it can also refer to a finite element node. Throughout this paper, unless explicitly stated, a node refers to a part of the enumeration tree.
By hidden solutions, we mean optimal designs that are found, by the heuristics, at great depths in the search tree.
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Acknowledgements
The authors sincerely thank the three anonymous reviewers and the editor for many perceptive and constructive suggestions and comments which improved the presentation.
The computer resources were funded by the Danish Center for Scientific Computing (www.dcsc.dk) grant CPU-0107-07 “Optimal design of composite structures”.
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This article is a significantly extended and revised version of the conference proceedings article: Stolpe M, Bendsøe MP (2007).
Appendix
Appendix
In Table 4 we list the best found objective function value and the corresponding design for the studied values on V.
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Stolpe, M., Bendsøe, M.P. Global optima for the Zhou–Rozvany problem. Struct Multidisc Optim 43, 151–164 (2011). https://doi.org/10.1007/s00158-010-0574-y
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DOI: https://doi.org/10.1007/s00158-010-0574-y