Optimal Design of Truss Structures by Logic-Based Branch and Cut

The truss design problem is to nd the optimal placement and size of structural bars that can support a given load The problem is nonlinear and in the version addressed here the bars must take certain discrete sizes It is shown that a logic based method that dispenses with integer variables and branches directly on logical disjunctions can solve sub stantially larger problems than mixed integer programming even though the nonlinearities disappear in the mixed integer model A primary purpose of the paper is to investigate whether advantages of logic based branching that have been demonstrated elsewhere for linear problems extend to nonlinear programming