Survey of Discrete Variable Optimization for Structural Design

Abstract

Available methods for discrete variable structural optimization are reviewed in this paper. Methods are classified according to three categories: branch and bound, approximations using branch and bound, and ad-hoc methods. The branch and bound method is theoretically correct for convex design tasks but is costly to use. Approximation methods provide efficiency but do not guarantee an optimum discrete solution. In a majority of the discrete optimization problems, approximation methods provide useful solutions and have been found to be the most practical. Ad-hoc methods such as simulated annealing and genetic algorithms attempt to solve the discrete variable problem without resorting to branch and bound methods, and do not guarantee an optimum solution. However, ad-hoc methods provide reasonable solution at an acceptable computational cost. A stepped cantilever beam example is solved using branch and bound and approximation methods, to give a computational sense of the efforts involved in solving discrete variable optimization problems.