The Benefit of Uncertainty Coupling in Robust and Adaptive Robust Optimization
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910908582723584 |
|---|---|
| author | Bertsimas, Dimitris Na, Liangyuan Stellato, Bartolomeo Wang, Irina |
| author_facet | Bertsimas, Dimitris Na, Liangyuan Stellato, Bartolomeo Wang, Irina |
| contents | Despite the modeling power for problems under uncertainty, robust optimization (RO) and adaptive robust optimization (ARO) can exhibit too conservative solutions in terms of objective value degradation compared to the nominal case. One of the main reasons behind this conservatism is that, in many practical applications, uncertain constraints are directly designed as constraint-wise without taking into account couplings over multiple constraints. In this paper, we define a coupled uncertainty set as the intersection between a constraint-wise uncertainty set and a coupling set. We study the benefit of coupling in alleviating conservatism in RO and ARO. We provide theoretical tight and computable upper and lower bounds on the objective value improvement of RO and ARO problems under coupled uncertainty over constraint-wise uncertainty. In addition, we relate the power of adaptability over static solutions with the coupling of uncertainty set. Computational results demonstrate the benefit of coupling in applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_10369 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Benefit of Uncertainty Coupling in Robust and Adaptive Robust Optimization Bertsimas, Dimitris Na, Liangyuan Stellato, Bartolomeo Wang, Irina Optimization and Control Despite the modeling power for problems under uncertainty, robust optimization (RO) and adaptive robust optimization (ARO) can exhibit too conservative solutions in terms of objective value degradation compared to the nominal case. One of the main reasons behind this conservatism is that, in many practical applications, uncertain constraints are directly designed as constraint-wise without taking into account couplings over multiple constraints. In this paper, we define a coupled uncertainty set as the intersection between a constraint-wise uncertainty set and a coupling set. We study the benefit of coupling in alleviating conservatism in RO and ARO. We provide theoretical tight and computable upper and lower bounds on the objective value improvement of RO and ARO problems under coupled uncertainty over constraint-wise uncertainty. In addition, we relate the power of adaptability over static solutions with the coupling of uncertainty set. Computational results demonstrate the benefit of coupling in applications. |
| title | The Benefit of Uncertainty Coupling in Robust and Adaptive Robust Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2302.10369 |