Joint model of probabilistic/robust (probust) constraints applied to gas network optimization

  • Optimization tasks under uncertain conditions abound in many real-life applications. Whereas solution approaches for probabilistic constraints are often developed in case the uncertainties can be assumed to follow a certain probability distribution, robust approaches are usually used in case solutions are sought that are feasible for all realizations of uncertainties within some pre-defined uncertainty set. As many applications contain different types of uncertainties that require robust as well as probabilistic treatments, we deal with a class of joint probabilistic/robust constraints as its appears in optimization problems under uncertainty. Focusing on complex uncertain gas network optimization problems, we show the relevance of this class of problems for the task of maximizing free booked capacities in an algebraic model for a stationary gas network. We furthermore present approaches for their solution. Finally, we study the problem of controlling a transient system that is governed by the wave equation. The task consists in determining controls such that a certain robustness measure remains below some given upper bound, with high probability.
Author:Dennis Adelhütte, Denis Aßmann, Tatiana Gonzàlez Grandòn, Martin Gugat, Holger Heitsch, Frauke Liers, René Henrion, Sabrina Nitsche, Rüdiger Schultz, Michael Stingl, David Wintergerst
Document Type:Preprint
Date of Publication (online):2017/11/20
Date of first Publication:2017/11/20
Release Date:2017/11/20
Tag:chance constraints; optimal control; robust optimization; spheric-radial decomposition
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik
Universität Duisburg-Essen