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In robust optimization, the uncertainty set is used to model all possibleoutcomes of uncertain parameters. In the classic setting, one assumes that thisset is provided by the decision maker based on the data available to her. Onlyrecently it has been recognized that the process of building useful uncertaintysets is in itself a challenging task that requires mathematical support.  In this paper, we propose an approach to go beyond the classic setting, byassuming multiple uncertainty sets to be prepared, each with a weight showingthe degree of belief that the set is a "true" model of uncertainty. We considertheoretical aspects of this approach and show that it is as easy to model asthe classic setting. In an extensive computational study using a shortest pathproblem based on real-world data, we auto-tune uncertainty sets to theavailable data, and show that with regard to out-sample performance, thecombination of multiple sets can give better results than each set on its own.

Mixed Uncertainty Sets for Robust Combinatorial Optimization