The application of discrete programming to structural optimization permits the use of tabulated section properties and eliminates the need for approximate relations, such as between weight and section modulus, which may obscure the optimal solution. Linear discrete programming techniques are applied to elastic design problems by linearizing the constraint functions. The AISC Code formulae for allowable compression stresses in truss members are included exactly in the formulation. The program can also select the best material from various grades of structural steel. For computational economy, tables of structural sections are truncated, so that the solution may be restricted to a local optimum. For this reason, a fast approximate procedure may be as effective as an exact, but slower, implicit enumeration algorithm. Since the local optima depend upon the initial design, a search for the global optimum can be made by generating random starting points. Decision rules based on Bayesian statistics are developed to determine the optimal number of alternate designs to be investigated in the design process.