Fast and Robust Stochastic Structural Optimization

Stochastic structural analysis can assess whether a fabricated object will break under real-world conditions. While this approach is powerful, it is also quite slow, which has previously limited its use to coarse resolutions (e.g., 26 x 34 x 28). We show that this approach can be made asymptotically faster, which in practice reduces computation time by two orders of magnitude, and allows the use of previously-infeasible resolutions. We achieve this by showing that the probability gradient can be computed in linear time instead of quadratic, and by using a robust new scheme that stabilizes the inertia gradients used by the optimization. Additionally, we propose a constrained restart method that deals with local minima, and a sheathing approach that further reduces the weight of the shape. Together, these components enable the discovery of previously-inaccessible designs.