A working-set approach for sizing optimization of frame-structures subjected to time-dependent constraints

Abstract

Document Version Peer reviewed versionLink back to DTU Orbit Citation (APA): Verbart, A., & Stolpe, M. (2018). A working-set approach for sizing optimization of frame-structures subjected to time-dependent constraints. Structural and Multidisciplinary Optimization, 58(4), 1367-1382. CITATION 1 READS 118 2 authors, including: Some of the authors of this publication are also working on these related projects: Structural optimization of offshore windturbine support structures View project Topology Optimization with Stress Constraints View project Alexander Verbart Ramboll 8 PUBLICATIONS 70 CITATIONS SEE PROFILE All content following this page was uploaded by Alexander Verbart on 03 September 2018. The user has requested enhancement of the downloaded file.Structural and Multidisciplinary Optimization: Post-print. The final publication is available via http://dx. AbstractIn this paper, we propose a working-set approach for sizing optimization of structures subjected to time-dependent loads. The optimization problems we consider have a very large number of constraints while relatively few design variables and degrees of freedom. Instead of solving the original problem directly, we solve a sequence of smaller sub-problems. The sub-problems consider only constraints in the working set, which is a small sub-set of all constraints. After each sub-problem, we compute all constraint function values for the current design and add critical constraints to the working set. The algorithm terminates once an optimal point to a sub-problem is found that satisfies all constraints of the original problem. We tested the approach on several reproducible problem instances and demonstrate that the approach finds optimal points to the original problem by only considering a very small fraction of all constraints. The proposed approach drastically reduces the memory storage requirements and computational expenses of the linear algebra in the optimization solver and the computational cost of the design sensitivity analysis. Consequently, the approach can efficiently solve large-scale optimization problems with several hundred millions of constraints.

Fail‐safe optimization of viscous dampers for seismic retrofitting

“…This strategy is inspired by the one presented by Verbart and Stolpe. 53 In particular, we present the relaxed formulation of the optimization subproblems considered, the strategy for updating the set of constraints considered between consecutive subproblems k and k + 1, and the stopping criterion for the optimization process. Instead of solving the full optimization problem 13, we solve a sequence of relaxed subproblems that consider a subset of failure scenarios:…”

“…In the case of a number of design variables smaller than the number of constraints, it would have been recommended to adopt the direct differentiation method for calculating the constraints' gradients. 53 Moreover, to ensure the consistency of the sensitivity calculated, we rely on the so called discretize-then-differentiate adjoint variable method. [65][66][67] According to this method, the discrete version of the governing equilibrium (Equation A1) is considered in the gradient calculation.…”

“…In this section, we discuss the working‐set strategy adopted in order to reduce the number of failure scenarios (hence constraints) actually considered in the optimization analysis and, as a consequence, the overall computational cost. This strategy is inspired by the one presented by Verbart and Stolpe 53 . In particular, we present the relaxed formulation of the optimization subproblems considered, the strategy for updating the set of constraints considered between consecutive subproblems k and k +1, and the stopping criterion for the optimization process.…”

“…In general, this results in an optimization problem with a large number of constraints, which requires a high computational effort during the optimization process. The computational cost is reduced using a working‐set strategy, similarly to Verbart and Stolpe 2018 53 : a sequence of relaxed subproblems each defined by an expanding subset of the constraints is solved cyclically. In every cycle, new constraints that are active in correspondence of the current optimized solution are added, and the updated optimization subproblem is solved again.…”

Fail-safe truss topology optimization

“…In this work, we pursue another possibility which is based on a constraint generation approach. It is similar to the working-set approach developed in Verbart and Stolpe (2018) for sizing optimization of frame structures subjected to time-dependent loads and local strength constraints. Rather than solving a sequence of non-convex problems as in Verbart and Stolpe (2018), the proposed algorithm is based on solving a sequence of convex problems of increasing size by selecting a number of relevant constraints to include.…”