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 A Branch and Bound approach for truss topology design problems with valid inequalities
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/7177

title: A Branch and Bound approach for truss topology design problems with valid inequalities
authors: Cerveira, A.
Agra, A.
Bastos, F.
Varum, H.
keywords: Truss topology design
Semidefinite programming
Global optimization
Branch and bound
Valid inequalities
issue date: 2010
publisher: AIP American Institute of Physics
abstract: One of the classical problems in the structural optimization field is the Truss Topology Design Problem (TTDP) which deals with the selection of optimal configuration for structural systems for applications in mechanical, civil, aerospace engineering, among others. In this paper we consider a TTDP where the goal is to find the stiffest truss, under a given load and with a bound on the total volume. The design variables are the cross-section areas of the truss bars that must be chosen from a given finite set. This results in a large-scale non-convex problem with discrete variables. This problem can be formulated as a Semidefinite Programming Problem (SDP problem) with binary variables. We propose a branch and bound algorithm to solve this problem. In this paper it is considered a binary formulation of the problem, to take advantage of its structure, which admits a Knapsack problem as subproblem. Thus, trying to improve the performance of the Branch and Bound, at each step, some valid inequalities for the Knapsack problem are included.
URI: http://hdl.handle.net/10773/7177
ISBN: 978-0-07354-0836-4
ISSN: 0094-243X
publisher version/DOI: http://dx.doi.org/10.1063/1.3498401
source: ICNAAM 2010: 8th International Conference of Numerical Analysis and Applied Mathematics
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