SURVEY OF DISCRETE VARIABLE OPTIMIZATION FOR STRUCTURAL DESIGN

Available methods for discrete variable structural optimization are re viewed in this paper. Methods are classified according to three catego ries: 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 provid e efficiency but do not guarantee an optimum discrete solution. In a m ajority of the discrete optimization problems, approximation methods p rovide useful solutions and have been found to be the most practical. Ad-hoc methods such as simulated annealing and genetic algorithms atte mpt 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 computati onal cost. A stepped cantilever beam example is solved using branch an d bound and approximation methods, to give a computational sense of th e efforts involved in solving discrete variable optimization problems.