Division of Optimization and Systems Theory
Department of Mathematics
Thereafter, we study a common heuristic method for solving minimum compliance (maximum stiffness) problems. These problems are usually modeled as mixed or pure nonlinear 0-1 programs. Since the number of binary variables needs to be large, solving these nonlinear 0-1 programs becomes a major challenge. A way to find feasible or almost feasible solutions is to use material interpolation models. In this approach the the binary constraints are relaxed and the material behavior is modeled using a nonlinear function. The resulting nonlinear program is then solved using standard optimization techniques. The basic idea with this approach is that variables with non-integer values will have little influence on the stiffness of the structure compared to the volume which is occupied, thus steering the variables to become either zero or one.
Finally, it is shown that a broad range of nonlinear 0-1 topology optimization problems, including stress- and displacement-constrained minimum weight problems, can equivalently be modeled as linear mixed 0-1 programs. This result implies that any of the standard methods available for general linear integer programming can now be used on topology optimization problems.