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Frauke Liers

Prof. Dr. Frauke Liers

Department of Mathematics
Professorship of Applied Mathematics (Integer and Robust Optimization) (Prof. Dr. Liers)

Room: Room 03.345
Cauerstraße 11
91058 Erlangen

Research Interests

I am interested in combinatorial and mixed-integer linear and non-linear optimization. A recent interest of mine is optimization under uncertainty, especially robust optimization.

Projects

  • Design of particulate products

    (Third Party Funds Group – Overall project)

    Term: 01-01-2020 - 31-12-2023
    Funding source: DFG / Sonderforschungsbereich (SFB)
    URL: https://www.crc1411.research.fau.eu/

    The objective is the targeted design of particulate products by rigorous optimisation based on predictive structure-property and process-structure functions. Particulate products consist in the simplest case of dis-persed single particles and in more complex cases of hierarchically organised assemblies of particles in the form of supraparticles, thin films and stationary phases for chromatographic separation. We target break-throughs in the product engineering of nanoparticles (NPs) with optimised optical properties produced by continuous synthesis directly coupled to property-specific classification of NPs by chromatography. These challenges will be addressed in four strongly interlinked research areas (RAs), and by the development of joint methodologies.In RA A, we will focus on the continuous liquid-phase formation of NPs, whose properties will be designed with respect to the absorption, emission and scattering of light. We will study metallic, semiconducting and metal organic framework NPs as well as their self-assembly. In RA B, we will establish NP chromatography as novel classification technology with respect to size, shape or surface properties for NPs from RA A. This requires the tailoring of stationary phases with optimal pore sizes and interactions with the NPs and the de-sign of powerful processes with enhanced performance at preparative scale. RA C applies a comprehensive toolbox for property and process characterisation for single particles and particle ensembles by in situ analysis and by the advancement of high-end ex situ methodologies. Modelling and mathematical optimisa-tion in RA D will establish a coherent framework based on a unifying population balance equation for the evolution of property distributions. The key parameters for interactions and transport will be obtained from molecular models of NPs and SPMs and from lattice Boltzmann simulations. The resulting NPs and their assembled superstructures provide the basis for the optimisation of their optical properties. Protection against unavoidable process uncertainties will be developed via robust optimisation methodologies opening new avenues for quality control in product design. Finally, NP formation, assembly and classification will be combined and optimised all at once to achieve our ambitious goal for the true engineering design of par-ticulate properties. The first class environment at the universities of Erlangen-Nürnberg and Duisburg-Essen as well as the Helmholtz Institute Erlangen-Nürnberg for Renewable Energy provides the ideal platform for CRC 1411. We are firmly committed to establishing a highly visible hub for the design of particulate products. Four Merca-tor fellows will support our activities. CRC 1411 includes a package of strategic measures for the promotion of early career researchers, gender equality and science communication. The integrated research training group will set new standards for doctoral training in particle science and technology.

  • Quality control by robust optimisation

    (Third Party Funds Group – Sub project)

    Overall project: SFB 1411: Design of particulate products
    Term: since 01-01-2020
    Funding source: DFG / Sonderforschungsbereich (SFB)

    The objective is the development, algorithmic design, implementation and validation of robust mathematical optimisation methods for protecting the design of particulate products against uncertainties. Global solution methods will be investigated for optimal robust chromatography as well as synthesis processes, develop-ing methods based on reformulation and decomposition. The obtained results will be validated with the projects. Information on which uncertainties are most relevant and should be reduced, together with recommendations on robust optimum design and quality control, will be returned to the experimental Projects.

  • Holistische Optimierung von Trajektorien und Runway Scheduling

    (Third Party Funds Group – Sub project)

    Overall project: Holistische Optimierung von Trajektorien und Runway Scheduling
    Term: 01-09-2018 - 31-08-2021
    Funding source: Bundesministerium für Wirtschaft und Technologie (BMWi)
    URL: https://en.www.math.fau.de/edom/projects-edom/logistics-and-production/holistic-optimization-of-trajectrories-and-runway-schedul

    Efficient runway utilization is a major issue in airport operation, as capacities are (nearly) reached in many aiports. But planing is highly affected by uncertainties arising from weather changes or disruptions in the operative business. Furthermore, the planing of flight trajectories in the terminal region is by now often neglected in runway scheduling, as time efficient solution methods are mathematically challenging. The overall goal of this project is to combine trajectory and runway schedule computation including resilience against uncertainties in order to obtain stable optimal solutions.

  • Robustification of Physics Parameters in Gas Networks (B06) (2018 - 2022)

    (Third Party Funds Group – Sub project)

    Overall project: TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
    Term: 01-07-2018 - 30-06-2022
    Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)

    The goal of this research project is to study uncertain optimization problems using robust optimization methods. Focusing on transport networks, we aim at the development of tractable robust counterparts for uncertain optimization problems and an analysis of the problem structure. For the arising adjustable robust optimization tasks, good relaxations as well as effective branch-and-bound implementations shall be developed.

  • Optimierte Prozesse für Trajektorie, Instandhaltung, Management von Ressourcen und Abläufen in der Luftfahrt

    (Third Party Funds Single)

    Term: 01-01-2018 - 31-12-2021
    Funding source: Bundesministerium für Wirtschaft und Technologie (BMWi)
    URL: https://www.mso.math.fau.de/edom/projects/ops-timal/
  • Mixed-Integer Non-Linear Optimisation: Algorithms and Applications

    (Third Party Funds Group – Overall project)

    Term: 01-01-2018 - 31-12-2021
    Funding source: Europäische Union (EU)
    URL: https://minoa-itn.fau.de/

    Building upon the achievements of the Marie-Curie ITN Mixed-Integer Non-Linear Optimization (MINO) (2012 - 2016), the goal of the Mixed-Integer Non-Linear Optimisation Applications (MINOA) proposal is to train the next generation of highly qualified researchers and managers in applied mathematics, operations research and computer science that are able to face the modern imperative challenges of European and international relevance in areas such as energy, logistics, engineering, natural sciences, and data analytics. Twelve Early-Stage Researchers (ESRs) will be trained through an innovative training programme based on individual research projects motivated by these applications that due to their high complexity will stimulate new developments in the field. The mathematical challenges can neither be met by using a single optimisation method alone, nor isolated by single academic partners. Instead, MINOA aims at building bridges between different mathematical methodologies and at creating novel and effective algorithmic enhancements. As special challenges, the ESRs will work on dynamic aspects and optimisation in real time, optimisation under uncertainty, multilevel optimization and non-commutativity in quantum computing. The ESRs will devise new effective algorithms and computer implementations. They will validate their methods for the applications with respect to metrics that they will define. All ESRs will derive recommendations, both for optimised MINO applications and for the effectiveness of the novel methodologies. These ESRs belong to a new generation of highly-skilled researchers that will strengthen Europe'e human capital base in R&I in the fast growing field of mathematical optimisation. The ESR projects will be pursued in joint supervision between experienced practitioners from leading European industries and leading optimisation experts, covering a wide range of scientific fields (from mathematics to quantum computing and real-world applications).

  • Optimierung der Netzeingriffe

    (Third Party Funds Group – Sub project)

    Overall project: Flächenbezogene Modellierung, Simulation und Optimierung von Solar-Einspeisung, Lastfluss und Steuerung für Stromverteilnetze, unter Berücksichtigung von Einspeisungsunsicherheiten
    Term: 01-01-2018 - 31-12-2020
    Funding source: Bundesministerium für Bildung und Forschung (BMBF)
    URL: https://en.www.math.fau.de/edom/projects-edom/analytics/optimal-control-of-electrical-distribution-networks-with-uncertain-solar
  • Energiemarktdesign

    (Third Party Funds Group – Sub project)

    Overall project: Energie Campus Nürnberg (EnCN2)
    Term: 01-01-2017 - 31-12-2021
    Funding source: andere Förderorganisation, Bayerische Staatsministerien
    URL: http://www.encn.de/en/forschungsthemen/energiemarktdesign/

    In the project “Energy Markt Design” within EnCN2 a team of researchers from economics, mathematics, and law analyses the economic and regulatory environment for the transformation of the energy system. The main objectives are to enhance the methods in energy market modeling and to contribute with well-grounded analyses to the policy discourse in Germany and Europe. For the electricity market, the focus is on the steering effect of market designs on regulated transmission expansion and private investments, as well as on the identification of frameworks at the distribution level that provide regional stakeholders with business models for the provision of flexibility measures. In order to address these complex issues, mathematical techniques are developed within the project that allow for solving the respective models. Another key research topic results from the advancing sector coupling in energy markets. Within EMD, gas market models, that are developed within DFG Transregio 154 (Simulation and Optimization of Gas Networks) in cooperation with project partners, are applied to evaluate the European gas market design. The long-term objective of the research group is an integrated assessment of the electricity and gas market design and their combined effects on investment decisions.

  • Optimization of medical care in rural environments

    (Third Party Funds Group – Overall project)

  • Integrated graduate school research training group (MGK)

    (Third Party Funds Group – Sub project)

    Overall project: TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks
    Term: since 01-07-2014
    Funding source: DFG / Sonderforschungsbereich / Integriertes Graduiertenkolleg (SFB / GRK)
    The integrated graduate school offers young researchers in the TRR 154 an interdisciplinary scientific education and training in Mathematical Modeling, Simulation und Optimization for Gas Networks by organizing summer and winter schools, excursions to companies, lectures and colloquia. Moreover, it supports the industrial or academic career entry by a mentoring program and soft skill courses.
  • Robustification of Physics Parameters in Gas Networks (B06) (2014 - 2018)

    (Third Party Funds Group – Sub project)

    Overall project: TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks
    Term: since 01-07-2014
    Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
    URL: https://en.www.math.fau.de/edom/projects-edom/energy/robustification-of-physical-parameters-in-gas-networks/
    The goal of this research project is to study uncertain optimization problems using robust optimization methods. Focusing on transport networks, we aim at the development of tractable robust counterparts for uncertain optimization problems and an analysis of the problem structure. For the arising adjustable robust optimization tasks, good relaxations as well as effective branch-and-bound implementations shall be developed.
  • Mixed-Integer Nonlinear Optimization

    (Third Party Funds Group – Sub project)

    Overall project: Mixed-Integer Nonlinear Optimization
    Term: 01-10-2012 - 30-09-2016
    Funding source: EU - 7. RP / People / Initial Training Networks (ITN)
    URL: https://minoa-itn.fau.de/

    Complex decision making in enterprises should involve mathematical optimization methods, because a best choice has to be made out of a huge number of feasible options. A mathematical description of such decision processes typically involves both continuous and discrete decisions. If the latter are present, the customary modelling approach is to use integer variables, which are also used to represent all possible nonlinearities, so that the remaining part of the model is linear. This leads to Mixed-Integer Linear Optimization (MILO) problems, which can be handled nowadays by many packages, but are often very difficult to solve.Difficulty of MILO problems is often due to the fact that objective functions or constraints that are structurally nonlinear (e.g., quadratic) are linearized by introducing new integer variables. In many cases, it was observed that this is not the best way to proceed, as facing the nonlinearity directly without the new variables leads to much better results. Algorithmic technology for the resulting Mixed-Integer Nonlinear Optimization (MINO) problems is still at its early stage.The present situation is that enterprises facing a MINO problem generally give up due to the lack of efficient solvers, or try to convert it to a MILO one often too hard to be solved in practice. On the other hand, in the academia there is now an increasing expertise in MINO, which is however hardly exported outside due to the lack of interaction with the industrial world. It is the purpose of this project to help satisfy the increasing demand for highly qualified researchers receiving, at the same time, a state-of-the-art scientific training from the academia and hands-on experience with real-world applications from the industry.The researchers formed within this project, once recruited by an enterprise at the end of their training, will have the potential to apply all the available knowledge to optimize complex decision making in the real-world.

Publications

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Editorial Activities

  • Associate Editor, Mathematical Methods of Operations Research
  • Associate Editor, Optimization and Engineering

Selected Courses (in German)

  • Robust Optimization
  • Theoretical Foundations of Discrete Optimization
  • Optimization in Industry
  • Project Seminar Optimization
  • Mathematics for Engineers