Rights statement: The final publication is available at Springer via http://dx.doi.org/10.1007/s11590-019-01456-3
Accepted author manuscript, 318 KB, PDF document
Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Mixed uncertainty sets for robust combinatorial optimization
AU - Dokka, T.
AU - Goerigk, M.
AU - Roy, R.
N1 - The final publication is available at Springer via http://dx.doi.org/10.1007/s11590-019-01456-3
PY - 2020/9/1
Y1 - 2020/9/1
N2 - In robust optimization, the uncertainty set is used to model all possible outcomes of uncertain parameters. In the classic setting, one assumes that this set is provided by the decision maker based on the data available to her. Only recently it has been recognized that the process of building useful uncertainty sets is in itself a challenging task that requires mathematical support. In this paper, we propose an approach to go beyond the classic setting, by assuming multiple uncertainty sets to be prepared, each with a weight showing the degree of belief that the set is a “true” model of uncertainty. We consider theoretical aspects of this approach and show that it is as easy to model as the classic setting. In an extensive computational study using a shortest path problem based on real-world data, we auto-tune uncertainty sets to the available data, and show that with regard to out-of-sample performance, the combination of multiple sets can give better results than each set on its own.
AB - In robust optimization, the uncertainty set is used to model all possible outcomes of uncertain parameters. In the classic setting, one assumes that this set is provided by the decision maker based on the data available to her. Only recently it has been recognized that the process of building useful uncertainty sets is in itself a challenging task that requires mathematical support. In this paper, we propose an approach to go beyond the classic setting, by assuming multiple uncertainty sets to be prepared, each with a weight showing the degree of belief that the set is a “true” model of uncertainty. We consider theoretical aspects of this approach and show that it is as easy to model as the classic setting. In an extensive computational study using a shortest path problem based on real-world data, we auto-tune uncertainty sets to the available data, and show that with regard to out-of-sample performance, the combination of multiple sets can give better results than each set on its own.
KW - Robust optimization
KW - Combinatorial optimization
KW - Uncertainty modeling
KW - Computational study
U2 - 10.1007/s11590-019-01456-3
DO - 10.1007/s11590-019-01456-3
M3 - Journal article
VL - 14
SP - 1323
EP - 1337
JO - Optimization Letters
JF - Optimization Letters
SN - 1862-4472
ER -