Abstract
Methods for mixed discrete-integer-continuous variable nonlinear optimization are reviewed for structural design applications with focus on problems having linked discrete variables. When a discrete value for such a variable is specified from an allowable set, the values for other variables linked to it must also be used in all the calculations. Optimum design of steel frames using commercially available sections is an example of this class of problems. A general formulation for this type of problems is developed. Approaches for solving such practical optimization problems are described and classified into single and multiple design variable formulations. Many approaches use two phases in their solution process before the final discrete design is obtained: In the first phase, a continuous variable optimum is usually obtained, and in the second phase, the continuous solution is somehow utilized to obtain the final discrete solution. Some of the basic optimization methods used in these approaches are also described.
