### Abstract

In 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.

Original language | English |
---|---|

Journal | Structural and Multidisciplinary Optimization |

Volume | 58 |

Issue number | 4 |

Pages (from-to) | 1367-1382 |

ISSN | 1615-147X |

DOIs | |

Publication status | Published - 2018 |

### Keywords

- Dynamic response optimization
- Sizing optimization
- Stress constraints
- Time-dependent constraints

### Cite this

}

*Structural and Multidisciplinary Optimization*, vol. 58, no. 4, pp. 1367-1382. https://doi.org/10.1007/s00158-018-2063-7

**A working-set approach for sizing optimization of frame-structures subjected to time-dependent constraints.** / Verbart, Alexander; Stolpe, Mathias.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - A working-set approach for sizing optimization of frame-structures subjected to time-dependent constraints

AU - Verbart, Alexander

AU - Stolpe, Mathias

PY - 2018

Y1 - 2018

N2 - In 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.

AB - In 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.

KW - Dynamic response optimization

KW - Sizing optimization

KW - Stress constraints

KW - Time-dependent constraints

U2 - 10.1007/s00158-018-2063-7

DO - 10.1007/s00158-018-2063-7

M3 - Journal article

AN - SCOPUS:85053039678

VL - 58

SP - 1367

EP - 1382

JO - Structural and Multidisciplinary Optimization

JF - Structural and Multidisciplinary Optimization

SN - 1615-147X

IS - 4

ER -