Data is often thought of as the resource of the future. The enormous amount of data that is currently available leads to new scientific and economic questions, such as: “How can companies extract useful information from the available data to support their business processes,“ or “How can analysis of the available data improve medical diagnostics?“ The field of research that concerns itself with such questions is called ‘”Analytics” and can be divided into the following areas:
- Descriptive Analytics (“What is the current state?”)
- Predictive Analytics (“What developments are most likely?”)
- Prescriptive Analytics (“What should we do?”)
At present “Analytics” combined with buzzwords like “Big Data”, “Internet of Things” or “Smart Data” is a widely discussed topic in the scientific world as well as in business. However, most of the discussions focus just on the first two of the above mentioned subfields: How can we gather this data? How can we recognize its essential characteristics? How will it evolve in the future? Yet the underrepresented third subject is the one with the biggest potential: How can we use this data to assist us in decision making and how can we choose among different alternatives in order to optimize processes or even identify completely new business segments or develop new business models. In other words, what better ways are there to make use of data in mathematical optimization? In our working group we address exactly this question. The following projects provide further insight into our work on this topic.
ADA Lovelace Center for Analytics, Data and Applications
Artificial Intelligence (AI) has long left behind its character as a solely theoretic discipline and permeates more and more our daily life. It enables digital assistants, cooperating robots as well as vastly autonomous vehicles and production facilities. The ADA Lovelace Center for Analytics, Data and Applications has been founded by the Fraunhofer Institute for Integrated Circuits (IIS), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) and Ludwig-Maximilians-Universität München (LMU). It is a partner for the national and international industry whose aim it is to help them benefit from these developments and to make them economically usable.
Optimal Control of Electrical Distribution Networks with Uncertain Solar Feed-In
“Areic modelling, simulation and optimization of solar feed-in, power flow and control of electrical distribution networks with uncertain feed” is a collaborative project of the BMBF-funding measure “Mathematics for Innovations”. The project will be funded from January 01, 2018 to Dezember 31, 2020.
- Kevin-Martin Aigner, Frauke Liers, Alexander Martin
For further details about this project please contact Kevin-Martin Aigner (firstname.lastname@example.org).
- Universität Ulm, Institut für Stochastik (Prof. Dr. Volker Schmidt, project coordinator)
- Universität Duisburg-Essen, Lehrstuhl für Energiewissenschaft (Prof. Dr. Christoph Weber)
Optimization of medical care in rural environments
HealthFaCT – Health: Facility Location, Covering, and Transport is a collaborative project of the BMBF-funding measure “Mathematics for Innovations in Industry and Services”.
HealthFaCT will be funded from December 01, 2016 to November 30, 2019.
The main goal of HealthFaCT is the development of an innovative and software-aided system for optimization and decision making to improve three essential pillars of medical care: pharmacies, emergency physicians as well as scheduling of ambulances. The main focus of this project lies on rural environments. Mathematical methodologies can make an important contribution in terms of data-driven facts rather than political argumentation. Detailed information about the contents of this project can be found here.
HealthFaCT is executed by
- University of Erlangen-Nuremberg (Dennis Adelhütte, Prof. Dr. Frauke Liers (project coordinator), Sebastian Tschuppik),
- RWTH Aachen University (Prof. Dr. Christina Büsing, Timo Gersing),
- TU Kaiserslautern (Prof. Dr. Sven O. Krumke, Eva Schmidt, Manuel Streicher)
- Fraunhofer Institute for Industrial Mathematics ITWM (Melanie Heidgen, Dr. Neele Leithäuser, Johanna Schneider).
Furthermore, Apothekerkammer Nordrhein, Kreisverwaltung Mainz-Bingen, Stadtverwaltung Kaiserslautern, Gesundheitsamt der StädteRegion Aachen, Informatikgesellschaft für Software-Entwicklung mbH and Gesundheitsregion plus Erlangen-Höchstadt & Erlangen take also part in HealthFaCT. The HealthFaCT team also cooperates with IBOSS.
EWave – Water supply energy management system
The joint research project EWave, supported by the German ministry of education and research (BMBF), aims to develop and implement a prototype for an energy management decision support system based on mathematical optimization.
Over the past few years, requirements for drinking water supply in Germany have become more and more demanding. While the secure supply of high-quality drinking water for the public was the priority during the past decades, rising energy costs and the energy reform being implemented by the German Federal Government now also require that energy is used efficiently. Water suppliers must therefore rise to the challenge of continuing to prioritize a secure supply of high-quality drinking water while coping with the increasing demand for energy efficiency.
A core feature developed and implemented in the EWave project is a mixed-integer nonlinear programming model for the optimization of operative planning including the processes of water collection, treatment, and distribution. This includes a detailed hydraulic model to adequately describe the predicted state of the network as well as further technical and especially operational restrictions. The main objective is to minimize overall energy consumption mainly arising from active raw and pure water pumps. The computation of an energy efficient proposal of the network control is performed for a fixed time period by a receiding horizon strategy, e.g., every 15 minutes for the next 24 hours. To obtain solutions for the resulting mixed-integer nonlinear nonconvex programming problem we combine state of the art methods from the fields of discrete and continuous optimization. On the one hand mixed-integer linear programming relaxations are computed and solved, which draw on piecewise linear approximation of nonlinear nonconvex functions with a predefined error tolerance. Resulting discrete controls such as on/off switching states of pumps and open/closed states of valves are fixed in a complementary stage where optimal control based methods and continuous nonlinear programming techniques are applied.
For more information, please visit our joint project website.
Alexander Martin (EWave project coordinator)
The research collaboration EWave is supported within the funding program “Future-oriented Technologies and Concepts for an Energy-efficient and Resource-saving Water Management – (ERWAS)” by the German Federal Ministry of Education and Research (BMBF) from 2014 to 2017 under the grants 02WER1323A – 02WER1323F.
Angewandte Mathematik 2 (FAU Erlangen-Nuernberg)
Numerik und wissenschaftliches Rechnen (Technische Universität Darmstadt)
Elektrotechnik, Maschinenbau und Technikjournalismus (Hochschule Bonn-Rhein-Sieg)
RWW Rheinisch-Westfälische Wasserwerksgesellschaft mbH
Bilfinger GreyLogix Aqua GmbH
Wissenschaftliches Rechnen, Universität Mannheim
Solving MINLPs on Loosely-Coupled Networks with Applications in Water and Gas Network Optimization.
Ph.D. thesis, University of Erlangen-Nuremberg, 2013.
A. Morsi, B. Geißler, A. Martin.
Mixed Integer Optimization of Water Supply Networks.
In A. Martin, K. Klamroth, J. Lang, G. Leugering, A. Morsi, M. Oberlack, M. Ostrowski, R. Rosen (Eds), Mathematical Optimization of Water Networks, Vol. 162 of International Series of Numerical Mathematics, pp 35-54, Springer Basel, 2012.
O. Kolb, A. Morsi, J. Lang, A. Martin.
Nonlinear and Mixed-Integer Linear Programming.
In A. Martin, K. Klamroth, J. Lang, G. Leugering, A. Morsi, M. Oberlack, M. Ostrowski, R. Rosen (Eds), Mathematical Optimization of Water Networks, Vol. 162 of International Series of Numerical Mathematics, pp 55-65, Springer Basel, 2012.
A. Martin, K. Klamroth, J. Lang, G. Leugering, A. Morsi, M. Oberlack, M. Ostrowski, R. Rosen (Eds).
Mathematical Optimization of Water Networks.
Vol. 162 of International Series of Numerical Mathematics, Springer Basel 2012.
B. Geißler, A. Martin, A. Morsi, L. Schewe.
Using Piecewise Linear Functions for Solving MINLPs.
In Jon Lee and Sven Leyffer (Eds), Mixed Integer Nonlinear Programming, Vol. 154 of The IMA Volumes in Mathematics and its Applications, pp 287-314, Springer, 2012.
B. Geißler, O. Kolb, J. Lang, G. Leugering, A. Martin, A. Morsi.
Mixed Integer Linear Models for the Optimization of Dynamical Transport Networks.
Mathematical Methods of Operations Research, Volume 73, Number 3, pp 339-362, 2011
Robust Power Load Balancing in Railway Networks
The aim of this project are robust train schedules with respect to the power consumption from the power supply stations. The input is a given schedule which is slightly adapted to desynchronize simultaneous train departures. On the other hand, train departures are synchronized with the recuperation phases of other trains to make use of their braking energy. Preliminary results show that significant savings with respect to the provision of reserve power can be achieved.
Participants: Andreas Bärmann
Optimization of Hybrid Energy Systems
Hybrid energy systems usually consist of two or more energy sources with at least one renewable source and one completely controllable source. In our case the hybrid system also comprises of energy storages, different types of energy consumers and a mini-grid connecting a small number of households. The aim of the project is the optimization of the internal and external power distribution, i. e. inside the individual households as well as between the different households, in order to minimize the energy costs while satisfying the demands.
Participants: Katja Kutzer, Björn Geißler
LeOpIn – Life-cycle oriented optimization for a resource- and energy-efficient infrastructure
The goal of the project LeOpIn is to devise methods for life-cycle oriented planning and evaluation of buildings and related infrastructure. To this end we develop simulation and optimization tools which can cope with this task. A concrete application is the planning of a building and pipes undergoing high pressure scenarios for which a software solution will be prototypically developed. The development of the planning and evaluation procedures demands a tight interaction between mathematical and engineering techniques. We plan to employ methods of numerical simulation and of discrete and nonlinear optimization. The main focus lies on integration of these techniques since only by this the high complexity of the treated problems can be handled appropriately.
Participants: Alexander Martin, Stefan Schmieder (Project A) and Lars Schewe, Jakob Schelbert (Project B)
Robust Schedules for Air Traffic Management
Increasing air traffic and new procedures in air traffic management require a very efficient use of limited ATM resources. It is impossible to create schedules for future use which never need to be adapted. Reasons are e.g., unexpected weather conditions, late passengers, and intended and unintended deviations from schedules. We tackle scheduling problems in ATM, like the planning of airplanes on runways. Therefore, the focus of the assigned task lies on modeling, understanding and controlling uncertainty in ATM problems. So it is important to concern with Resilience and Adaptation to continue having air transport and to be competitive to alternative transportation. Thus we have to accept these phenomena and have to incorporate uncertainty into the model.
Participants: Andreas Heidt
Expansion of the German Rail Freight Network
In recent years, rail freight traffic in Germany has attained a significant growth. In contrast, the expansion of the available transportation capacities in the German railway network has always dragged behind this development. The short term drop in demand due to the economic crisis offers the opportunity to make up for this deficit. The goal is to prepare the railway network for the demand growth forecasted for the upcoming years. Recent studies predict annual growth rates of 5% within the next 15 years, which would result in a freight traffic more than twice as high as nowadays. This requires extensive investments in the construction of new tracks and the expansion of existing ones.
Participants: Andreas Bärmann
RobustATM: Robust Optimization of ATM Planning Processes by Modelling of Uncertainty Impact
As possibilities of enlarging airport capacities are limited, one has to enhance the utilization of existing capacities in Air Traffic Management (ATM) to meet the continuous growth of traffic demand. Therefore, it is crucial for the performance of the whole ATM System that the traffic on a runway is planned efficiently. However, uncertainty, inaccuracy and non-determinism almost always lead to deviations from the actual plan or schedule. A typical strategy to deal with these changes is a regular re-computation or update of the schedule. These adjustments are performed in hindsight, i.e. after the actual change in the data occurred. The challenge is to incorporate uncertainty into the initial computation of the plans so that these plans are robust with respect to changes in the data, leading to a better utilization of resources.
Participants: Andreas Heidt, Manu Kapolke, Frauke Liers