joint work with Alemseged Gebrehiwot Weldeyesus
We address challenges related to solving real world problems in structural optimization. Such problems arise for example in layout optimization of tall buildings, long bridges or large spanning roofs. We propose to solve such problems with a highly specialized primal-dual interior point method. The problems may be formulated as (very large) linear or, if additional stability concerns are addressed, semidefinite programs. In this talk we will focus on computational challenges arising in such problems and efficient ways to overcome them.
joint work with Michal Kočvara
One of the challenges of topology optimization lies in the size of the problems, which easily involve millions of variables. We consider the example of the variable thickness sheet (VTS) problem and propose a Penalty-Barrier Multiplier (PBM) method to solve it. In each iteration, we minimize a generalized augmented Lagrangian by the Newton method. The arising large linear systems are reduced to systems suitable for a standard multigrid method. We apply a multigrid preconditioned MINRES method. The algorithm is compared with the optimality criteria (OC) method and an interior point (IP) method.
joint work with Mohammad Shahabsafa, Ramin Fakhimi, Luis Zuluaga, Weiming Lei, Joaquim Martins, Sicheng He
We propose a novel mathematical optimization model for Truss Topology Design and Sizing Optimization (TTDSO) problem with Euler buckling constraints. We prove that the proposed model, with probability 1, is delivering a kinematicly stable structure. Computational experiments, using an adaptation of our MILO-moving neighborhood search strategy, shows that our model and computational approach is superior when compared to other approaches.