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

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 Chvátal–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.