# PhD Theses

## PhD Theses

PhD Theses treat usually complex mathematical optimization problems, for which there exist no satisfying solution methods so far. The problem results usually from concrete applications in industry and economy or from engineering and scientific questions.

The main interest of our working group lies in optimization problems which contain combinatorial elements or decision-demanding questions, i.e. questions, which permit only yes/no answers. Mathematically, such questions can be formulated as mixed-integer linear or nonlinear problems (short MIP or MINLP). A thesis usually contains the setting of a suitable mathematical model, the analysis of the underlying MIPs and/or MINLPs, the development and extension of suitable solution procedures as well as the application on real and realistic data.

Until 2023 this was a joint website of the group Analytics & Mixed-Integer Optimization and the group Optimization under Uncertainty & Data Analysis.

### Current Works

*Presolving Techniques, Heuristics and Solving Techniques for Mixed-Integer Programs*

Katrin Halbig

### Previous Works

#### 2023

*Contributions to Robust Optimization: Network Flows, Market Equilibria, Linear Complementarity Problems, and Pareto Optimality*

Christian Biefel*Robust Optimization and Decomposition for Assignment Problems in Airline Operations*

Lukas Glomb*Duality theory in the context of market equilibrium problems with integrality constraints – pricing schemes and existence of solutions*

Lukas Hümbs*Decomposition Methods for Time-Dependent Mixed-Integer Nonlinear Optimization Problems on Graphs*

Richard Krug*Mixed-integer nonlinear robust optimization via nonsmooth methods*

Martina Kuchlbauer*Modelling and solving the integrated locomotive scheduling and driver assignment problem with an extension to graph 2-list-colouring problem with compatibility constraints*

Jonasz Staszek

#### 2022

*Clique-Related Structures in Mixed-Integer Programming: Analysis, Recognition, and Application*

Patrick Gemander*Robust and Stochastic Optimization of Assignment Problems for Airport Runway Utilization*

Manu Kapolke*Well-Posedness of Deterministic and Uncertain Linear Complementarity Problems with Applications to Electricity Markets*

Vanessa Krebs*The pooling problem with recipes*

Oskar Schneider*Feasibility for Maximal Uncertainty Sets in Robust Optimization with Application to Gas Networks*

Johannes Thürauf

#### 2021

*Mixed-Integer Optimization for an Integrated Life Cycle Sustainability Assessment in the Automotive Industry – A Case Study Using the Example of Lithium-Ion Cells*

Lucia Bäuml*Algorithms for Mixed-Integer Bilevel Problems with Convex Followers*

Thomas Kleinert

#### 2020

*Stückweise lineare Approximation von bilinearen Nebenbedingungen mit Anwendung auf hybride Energiesysteme ohne Netzanschluss*

Katja Kutzer

#### 2019

*Exact Methods for Two-Stage Robust Optimization with Applications in Gas Networks*

Denis Aßmann*Adaptive Mixed-Integer Refinements for Solving Nonlinear Problems with Discrete Decisions*

#### 2018

*Mathematical Optimization of Matching Problems with Precedence Constraints – An Application to Runway Scheduling*

Andrea Peter*Incorporating Differential Equations into Mixed-Integer Programming for Gas Transport Optimization*

Mathias Sirvent

#### 2017

*Uncertainty Models for Optimal and Robust ATM Schedules – Robuste Optimierungsmodelle für den Flugverkehr*

Andreas Heidt*Integer and Mixed-Integer Reformulations of Stochastic, Resource-Constrained, and Quadratic Matching Problems*

Lena Hupp*Solving Mixed-Integer Linear and Nonlinear Network Optimization Problems by Local Reformulations and Relaxations*

Maximilian Merkert

#### 2016

**Habilitation***Discrete methods for hard mixed-integer nonlinear problems**Computing maximal entry and exit capacities of transportation networks – Complexity analysis and a discrete relaxation applied to gas transmission systems*

Christine Hayn*Optimal Capacity Planning for the Transition of Energy Systems: Mathematical Models, Methods and Solutions**Approaches to Congestion Management in Electricity Networks: Equilibrium Models, Mathematical Analyses, and Computational Results*

Martin Weibelzahl*Solving mixed-integer programs arising in production planning*

Dieter Weninger

#### 2015

*Solving Network Design Problems via Decomposition, Aggregation and Approximation – with an Application to the Optimal Expansion of Railway Infrastructure*

Andreas Bärmann*Discrete Approaches for Optimal Routing of High Pressure Pipes*

Jakob Schelbert*Binary Steiner Trees: Structural Results, Algorithms and an Application in Phylogeny*

Susanne Pape

#### 2014

*Auctions in Exchange Trading Systems: Modeling Techniques and Algorithms*

Johannes Christian Müller

#### 2013

*Mixed-Integer Semidefinite Programming with an Application to Truss Topology Design**Discrete-continuous optimization of complex dynamic water supply and urban drainage systems*

#### 2012

*Routing cars in rail freight service*

#### 2011

*Approximation of Nonlinear Dynamics in Gas Network Optimization*

#### 2010

*Integral Sheet Metal Design by Discrete Optimization**A Scenario Tree-Based Decomposition for Solving Multistage Stochastic Programs with Application in Energy Production**Designing Coupled Energy Carrier Networks by Mixed-Integer Programming Methods*

#### 2008

*Protein Folding and Self-Avoiding Walks – Polyhedral Studies and Solutions*

#### 2007

*Relaxations and Solutions for the Minimum Graph Bisection Problem*

#### 2006

*Optimal Distribution of Block-Structured Grids in Parallel Computing**A Mixed Integer Approach for the Transient Case of Gas Network Optimization*

#### 2005

*The Integrated Optimization of School Starting Times and Public Transport*

#### 2004

**Habilitation***Counting principles of algebraic combinatorics : with an emphasis on topological enumeration.**Mixed Integer Models for the Optimisation of Gas Networks in the Stationary Case**Mathematische Modellierung der Konsistenz und konsistenzerhaltender Erweiterungen von Vererbung in objektorientierten Sprachen**Rapid Mathematical Programming*