Optimierung und algorithmische diskrete Mathematik , Campus Duisburg
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Dr. Uwe Gotzesemail: uwe.gotzes(at)googlemail.com |
Publications
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Two-stage
stochastic
programming models are considered as attractive tools for making
optimal decisions under uncertainty. Traditionally, optimality is
formalized by applying statistical parameters such as the expectation
or the conditional value at risk to the distributions of objective
values.
Uwe Gotzes analyzes an approach to account for risk aversion in two-stage models based upon partial orders on the set of real random variables. These stochastic orders enable the incorporation of the characteristics of whole distributions into the decision process. The profit or cost distributions must pass a benchmark test with a given acceptable distribution. Thus, additional objectives can be optimized. For this new class of stochastic optimization problems, results on structure and stability are proven and a tailored algorithm to tackle large problem instances is developed. The implications of the modelling background and numerical results from the application of the proposed algorithm are demonstrated with case studies from energy trading. |
- U.
Gotzes, R.
Schultz, C. Weber, O. Woll: Verteilte
Erzeugung im liberalisierten Energiemarkt – Analyse von
Investitionsentscheidungen, Modellierung und Optimierung von
Energiesystemen, Schultz, R. and Wagner, H.-J., eds., 2008
- U.
Gotzes, R.
Schultz: Risikoaversion
mittels stochastischer Dominanz mit Anwendungen bei
Optimierungsproblemen in der Energiewirtschaft – Ein innovativer
Modellierungsansatz, VDI-Berichte 2018 - Optimierung in der
Energiewirtschaft, S. 221-235
Abstract: Stochastische Optimierungsprobleme, insbesondere Erwartungswert-Risiko-Modelle, haben sich als nützliche Werkzeuge zur Entscheidungsfindung unter Unsicherheit erwiesen. In der vorliegenden Ausarbeitung wird ein innovativer Alternativzugang zur Behandlung des Risikos in zweistufigen, gemischt-ganzzahligen, linearen, stochastischen Optimierungsproblemen dargestellt, der auf dem Konzept der stochastischen Dominanz beruht. Die algorithmische Behandlung der sich ergebenden hochdimensionalen - jedoch mit Blick auf Lösungsmethoden günstig strukturierten - gemischt-ganzzahligen Optimierungsprobleme wird andiskutiert. Die sich ergebenden Effekte werden anhand von Fallstudien aus dem Bereich der Energiewirtschaft erläutert.
Keywords: Risikoaversion, Stochastische Optimierung, Stochastische Dominanz, Optimierung in der Energiewirtschaft
- M.
Carrión, U.
Gotzes, R. Schultz: Risk Aversion for an Electricity Retailer
with Second-Order Stochastic Dominance Constraints,
Computational Management Science 6, (2009), pp. 233-250
Abstract: In this paper we present the problem faced by an electricity retailer which searches to determine the forward contracting portfolio and the selling price for its clients. This problem is formulated as a two-stage stochastic program including second-order stochastic dominance constraints. The stochastic dominance theory is used in order to reduce the risk suffering from low profits. The resulting deterministic equivalent problem is a mixed-integer linear program which is solved using commercial branch-and-cut software. Numerical results are reported and a realistic case study is solved. Finally, relevant conclusions are drawn.
Keywords: Electricity Retailer, MILP Formulation, Stochastic Dominance, Stochastic Programming
- U.
Gotzes, F.
Neise: User’s
guide to ddsip.vSD—A C Package for the Dual Decomposition of Stochastic
Programs with Dominance Constraints Induced by Mixed-Integer Linear
Recourse
- R.
Gollmer, U.
Gotzes, F. Neise, R. Schultz: Risk Modeling
via Stochastic Dominance in Power Systems with Dispersed Generation,
accepted for presentation at ISAP2007, Taiwan)
Abstract: We propose a new approach to risk modeling in power optimization employing the concept of stochastic dominance. This leads to new classes of large-scale block-structured mixed-integer linear programs for which we present decomposition algorithms. The new methodology is applied to stochastic optimization problems related to operation and investment planning in a power system with dispersed generation.
Keywords: Dispersed storage and generation, Cogeneration, Renewable resources, Mathematical optimization, Uncertainty and risk modeling, Stochastic dominance, Decomposition methods
- R.
Gollmer, U.
Gotzes, R. Schultz: Second-Order Stochastic Dominance
Constraints Induced by Mixed-Integer Linear Recourse,
submitted to Math. Prog.)
Abstract: We introduce stochastic integer programs with dominance constraints induced by mixed-integer linear recourse. Closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is derived. For discrete probability measures, large-scale, block-structured, mixed-integer linear programming equivalents to the dominance constrained stochastic programs are identified. For these models, a decomposition algorithm is proposed. Computational tests with instances from power optimization and Sudoku puzzling conclude the paper.
Keywords: Stochastic integer programming, stochastic dominance, mixed-integer optimization
- Master's thesis: Betriebsoptimierung eines Systems mit dezentralen Energieumwandlungsanlagen mittels gemischt-ganzzahliger linearer Modelle, Advisor: Prof. Dr. R. Schultz
Talks
March
5 – March 9, 2012
High Performance Scientific Computing (Hanoi)
Participation on behalf of Open Grid Europe GmbH
July
12 – July 14, 2011
Jornadas RSME de Transferencia y Matemática Industrial (Santiago de Compostela)
Successful Transfer of Mathematics to Industry – Open Grid Europe's Project "Research Cooperation Network Optimization" (on behalf of Open Grid Europe GmbH)
May
23 – May 27, 2011
8th International Conference on Integration of Artificial Intelligence and Operations Research, CPAIOR 2011 (Berlin)
Gas Network Optimization (on behalf of Open Grid Europe GmbH)
May
16 – May 19, 2011
SIAM Coference on Optimization (Darmstadt)
Mathematical Optimization at Open Grid Europe (on behalf of Open Grid Europe GmbH)
November
3, 2008
Seminar über Technomathematik, Prof. Dr. J. Donig (Universität
Duisburg-Essen)
Vorstellung der Dissertation
October
30, 2008
Research seminar (University of Duisburg-Essen)
Masters Thesis Topic Suggestions: Revenue Management—Some Aspects of
Airline Seat Inventory Control
September
3 – September 5, 2008
CARIPLO Workshop on Numerical Linear and Nonlinear Stochastic
Programming (Edinburgh)
Increasing Convex Order Constraints Induced by Mixed-Integer Linear
Recourse
June
26, 2008
Research seminar (University of Duisburg-Essen)
Risk-Aversion Modeling with Second-Order Stochastic Dominance
Constraints: Electricity Retailer Problem
June
17 – 19, 2008
Miniworkshop Stochastische Optimierung (Haus Mühlenblick, Walbeck)
June
13, 2008
Seminar of the Electric Energy Systems Group at the Universidad de
Castilla-La Mancha (Ciudad Real)
Increasing convex order constraints induced by mixed integer linear
recourse
May
8, 2008
Increasing convex order constraints induced by mixed integer linear
recourse—recent developments
November
27 – November 28, 2007
Risikoaversion mittels stochastischer Dominanz – mit Anwendungen bei
Optimierungsproblemen in der Energiewirtschaft
November
11 – November 13, 2007
5.
Siemens Workshop Angewandte Diskrete Optimierung (Fulda, BMBF
Network-Meeting at the Math. Dept. of the Humbolt-University Berlin
Risikoaversion durch stochastische Dominanznebenbedingungen beim
Elektrizitätshandel
August
27 – August 31, 2007
11th Conference on Stochastic Programminig (SPXI) Vienna
Algorithmic aspects of decomposition under dominance constraints—with
applications in dispersed generation systems
July
8 – July 11, 2007
INFORMS International Puerto Rico 2007
Second-Order Sochastic Dominance Constraints Induced by Mixed-Integer
Linear Recourse
May
29 – May 31, 2007
Cologne-Twente Workshop 2007 (Enschede)
Stochastic Programs with Dominance Constraints Induced by Mixed-Integer
Linear Recourse
October
5 – October 6, 2006
BMBF Network-Meeting at the Math. Dept. of the University of Darmstadt
Optimierung unter stochastischen Dominanznebenbedingungen an Beispielen
aus der Energiewirtschaft
July
30 – August 4, 2006
International Symposium on Mathematical Programming, UFRJ Rio de
Janeiro, Brazil
Investment
Planning for Electricity Generation under Second Order Stochastic
Dominance Constraints (Due to the Varig crisis it was unfortunately not
possible to participate in the conference for our group)
June
5 – June 9, 2006
Cologne-Twente Workshop 2006 (Lambrecht)
Optimal Investments in Distributed Generation Units under Uncertainty
May
17, 2006
Research seminar (University of Duisburg-Essen)
Zweistufige Optimierungsprobleme mit Dominanznebenbedingungen
March
9 – March 10, 2006
Workshop at IER (University of Stuttgart)
Optimale Auslegung eines Systems zur dezentralen Energieversorgung mit
Methoden der stochastischen Optimierung
June
2005
Research seminar (University of Duisburg-Essen)
Betriebsoptimierung eines Systems mit dezentralen
Energieumwandlungsanlagen mittels gemischt-ganzzahliger linearer Modelle
last modified 23.04.2009 by Ralf Gollmer