Global optimization of discrete truss topology design problems using a parallel cut-and-branch method

Authors:
M. H. Rasmussen;M. Stolpe
Affiliations:
Department of Mathematics, Technical University of Denmark, Matematiktorvet, Building 303 S, DK-2800 Kgs. Lyngby, Denmark;Department of Mathematics, Technical University of Denmark, Matematiktorvet, Building 303 S, DK-2800 Kgs. Lyngby, Denmark
Venue:
Computers and Structures
Year:
2008

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Abstract

The subject of this article is solving discrete truss topology optimization problems with local stress and displacement constraints to global optimum. We consider a formulation based on the Simultaneous ANalysis and Design (SAND) approach. This intrinsically non-convex problem is reformulated to a mixed-integer linear program, which is solved with a parallel implementation of branch-and-bound. Additional valid inequalities and cuts are introduced to give a stronger representation of the problem, which improves convergence and speed up of the parallel method. The valid inequalities represent the physics, and the cuts (Combinatorial Benders' and projected Chvatal-Gomory) come from an understanding of the particular mathematical structure of the reformulation. The impact of a stronger representation is investigated on several truss topology optimization problems in two and three dimensions.