The complexity of procedures for determining minimum weight trusses with discrete member sizes

This paper addresses the problem of minimising the weight of a structural truss subject to static constraints and member sizes only being available from a discrete set of commercially available gauges. Substantial theoretical evidence is advanced to suggest that, given current mathematical techniques, it is not possible to solve this problem exactly in all cases. More specifically, the problem under consideration, even in simple cases, is shown to be equivalent to a large number of other problems that are notorious for their computational intractability. In practical terms, such a result justifies the development of methods that approximately solve the problem and consequently, algorithms for solving it to within specified absolute accuracy are considered. It is subsequently shown that such methods are equivalent in complexity to those for solving the original problem.