Dear colleagues,A reminder that our next ENRE online event takes place this Thursday April 28, 2022, starting at 15:00 (UK time). Please feel free to forward this invitation to anyone who might be interested. For more information and recordings of past seminars, see blogs.ed.ac.uk/enreWe hope to see many of you next week,Miguel Anjos and Lars Schewe
=============================================================
28 April 2022 15:00-16:30 UK time (on Zoom) | Martin Schmidt & Johannes Thürauf (Universität Trier)
Join Zoom Meeting https://ed-ac-uk.zoom.us/j/88468647768
Meeting ID: 884 6864 7768
Passcode: Ex1jWp3E
On Convex Lower-Level Black-Box Constraints in Bilevel Optimization with an Application to Gas Market Models with Chance Constraints (Martin Schmidt)
Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this talk, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this setup, we develop a cutting-plane algorithm that computes approximate bilevel-feasible points. We apply this method to a bilevel model of the European gas market in which we use a joint chance constraint to model uncertain loads. Since the chance constraint is not available in closed form, this fits into the black-box setting studied before. For the applied model, we use further problem-specific insights to derive bounds on the objective value of the bilevel problem. By doing so, we are able to show that we solve the application problem to approximate global optimality. In our numerical case study we are thus able to evaluate the welfare sensitivity in dependence of the achieved safety level of uncertain load coverage.
Martin Schmidt studied Mathematics and Computer Science at the Leibniz Universität Hannover and received his PhD in 2013 in the area of algorithmic optimization. From 2014 to 2018 he was junior professor for the optimization of energy systems at the Friedrich-Alexander-Universität Erlangen-Nürnberg and the Energy Campus Nürnberg, before he moved to Trier University. His research interests are mixed-integer nonlinear as well as bilevel optimization. He develops novel algorithms for solving these problems for real-world and large-scale instances. His application focus is on the energy sector.
A bilevel optimization approach to decide the feasibility of bookings in the European gas market (Johannes Thürauf)
The European gas market is organized as a so-called entry-exit system with the main goal to decouple transport and trading. To this end, gas traders and the transmission system operator (TSO) sign so-called booking contracts that grant capacity rights to traders to inject or withdraw gas at certain nodes up to this capacity. On a day-ahead basis, traders then nominate the actual amount of gas within the previously booked capacities. By signing a booking contract, the TSO guarantees that all nominations within the booking bounds can be transported through the network. In this talk, we consider networks with linearly modeled active elements such as compressors or control valves. Since these active elements allow the TSO to control the gas flow, the single-level approaches for passive networks from the literature are no longer applicable. We thus present a bilevel model to decide the feasibility of bookings in networks with active elements. While this model is well-defined for general active networks, we focus on the class of networks for which active elements do not lie on cycles. This assumption allows us to reformulate the original bilevel model such that the lower-level problem is linear for every given upper-level decision. Consequently, we derive several single-level reformulations for this case. Besides the classic Karush– Kuhn–Tucker reformulation, we obtain three problem-specific optimal-value-function reformulations. The latter also lead to novel characterizations of feasible bookings in networks with active elements that do not lie on cycles. We compare the performance of our methods by a case study based on data from the GasLib.
Johannes Thürauf is a postdoctoral researcher at the University of Trier since end of 2021. He studied Mathematics at the Friedrich-Alexander Universität (FAU) Erlangen-Nürnberg and received his MSc degree in 05/2017. Afterward, he worked as a PhD student at the FAU Erlangen-Nürnberg and got his PhD at the end of 2021. His research topics include optimization under uncertainty, network optimization with a focus on energy networks, as well as combinatorial and algorithmic optimization.
------------------------------
Miguel F. Anjos, Ph.D., P.Eng., FHEA, SMIEEE, FEUROPT, FCAE
President, INFORMS Section on Energy, Natural Resources, and the Environment (ENRE)
Vice-President, INFORMS International Activities
Chair of Operational Research, School of Mathematics, University of Edinburgh, U.K.
Schöller Senior Fellow, University of Erlangen-Nürnberg, Germany
http://www.miguelanjos.com/------------------------------