Uncertainty feature optimization: an implicit paradigm for problems with noisy data

Optimization problems due to noisy data are usually solved us-ing stochastic programming or robust optimization approaches. Both requiring the explicit characterization of an uncertainty set that mod-els the nature of the noise. Such approaches tightly depend on the modeling of the uncertainty set. In this paper, we introduce a framework that implicitly models the uncertain data. We define the general concept of Uncertainty Features (UF) which are structural properties of a solution. We show how to formulate an uncertain problem using the Uncertainty Feature Opti-mization (UFO) framework as a multi-objective problem. We prove that stochastic programming and robust optimization are particular cases of the UFO framework. We present computational results for the Multi-Dimensional Knapsack Problem (MDKP) and discuss the application to the airline scheduling problem. Computational results show a stability of the solutions in variations of the noise’s nature, unlike methods based on an explicit uncertainty set.