The objective of the research is two-fold. First, algorithms will be developed for solving nonlinear optimization problems in which some of the variables may assume certain combinations of discrete values. These algorithms must be efficient in terms of minimizing the amount of analysis required to solve the problem. Second, these algorithms will be tested by implementing them into a general-purpose computer program for selecting beams and columns for rectangular steel-framed buildings. The approach for solving optimization problems with related discrete variables consists of: (1) executing a pre-processing algorithm which generates constraints enclosing the available combinations of discrete values, (2) executing standard nonlinear programming software to obtain the continuous optimun, and (3) executing a post-processing algorithm to find the discrete optimum within a neighborhood of the continuous optimum.
