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

The truss design problem is to find 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 substantially 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. 1 Introduction Engineering design problems often involve both continuous variables and discrete alternatives that can be formulated with disjunctive constraints. If the discrete elements are represented with integer variables, the problems can in principle be solved with the branch-and-cut methods of mixed integer programming. An..