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

Adelhütte D, Aßmann D, Gonzàlez Grandòn T, Gugat M, Heitsch H, Liers F, Henrion R, Nitsche S, Schultz R, Stingl M, Wintergerst D (2020)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2020

Journal

URI: https://link.springer.com/article/10.1007/s10013-020-00434-y

DOI: 10.1007/s10013-020-00434-y

Abstract

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 introduce a class of joint probabilistic/robust constraints as its appears in optimization problems under uncertainty. Focussing 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.

Authors with CRIS profile

Involved external institutions

Universität Duisburg-Essen (UDE) Germany (DE) Humboldt-Universität zu Berlin Germany (DE) Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) - Leibniz-Institut im Forschungsverbund Berlin e. V. Germany (DE)

How to cite

APA:

Adelhütte, D., Aßmann, D., Gonzàlez Grandòn, T., Gugat, M., Heitsch, H., Liers, F.,... Wintergerst, D. (2020). Joint model of probabilistic/robust (probust) constraints with application to gas network optimization. Vietnam Journal of Mathematics. https://doi.org/10.1007/s10013-020-00434-y

MLA:

Adelhütte, Dennis, et al. "Joint model of probabilistic/robust (probust) constraints with application to gas network optimization." Vietnam Journal of Mathematics (2020).

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