The object of this investigation is to develop a procedure for the optimization of a roof system to yield minimum cost. The roof system is composed of parallel chord, steel trusses, with purlins and decking. The variables considered are geometry, topology, and member size. The optimal values of the geometry and topology variables are determined by the application of Box's Complex Method. A fully stressed design criterion is used in selecting the member sizes. It is shown that the optimization scheme always converges to a low cost region, although not necessarily to the global optimum. A cost model is developed that includes member-related costs and weight-related costs. Parameter studies demonstrate the importance of selecting the proper ratios of fixed and weight-related costs. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate