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 -