International Workshop on Resource Risk Management
DGF Research Center MATHEON, Technical University Berlin, Berlin, Germany &
Dept. of Optimization, Zuse-Institut Berlin (ZIB), Berlin, Germany
An introduction to Optimization under Uncertainty
Classical optimization assumes that the values of all input data of a problem are known exactly. However, most real-world optimization problems involve uncertain data, i.e. data whose values are not known exactly when the problem is solved. Data uncertainty may arise for several reasons, such as using forecasts or measurements subject to errors and adopting approximated numerical representations. Neglecting data uncertainty may have very bad effects: even small deviations in the input data may compromise the optimality of produced solutions, whereas feasible solutions may turn out to be infeasible and thus totally meaningless in practice.
In this talk, we provide an introduction to the topic of data uncertainty in optimization and an overview of the main methodologies (e.g., Stochastic Programming) developed over the years to deal with data uncertainty.
Robust Optimization: bridging the gap between theory and practice in modern optimization under uncertainty
Over the last decade, Robust Optimization (RO) has emerged as an effective and efficient methodology to tackle data uncertainty in real-world optimization problems. RO takes into account uncertainty in the shape of hard constraints that restrict the feasible set and maintain only robust solutions, i.e. solutions that remain feasible even when the values of the input data change. In this talk, we provide an overview of theory and applications of RO, focusing in particular on Multiband Robustness, a new model for RO that we have recently proposed to generalize and refine the classical Bertsimas-Sim robustness model. We also provide an overview of applications of the Multiband model to real-world problems in telecommunications and energy network management that we have considered in past and ongoing industrial cooperations with major European companies.