Case Studies Discrete / Nonlinear Optimization
The modules Case Studies Discrete Optimization [MA4512] and Case Studies Nonlinear Optimization [MA4513] are a combination of lectures, project work, presentation and soft skills courses: Experience real world optimization problems and apply the skills you have acquired during your degree program to design and implement an optimal solution.
In the Case Studies a small team of students is presented a challenging problem by one of our cooperation partners. Your task is to understand the problem, work out the details together, find a viable way to attack the problem and implement a solution. To do this, you will also have to organize your work as a team, discuss possible solutions and obstacles with your partner and present your challenges and results to a broad audience. Of course, your advisors will be ready to help and guide you through that learning experience. They provide mathematical and methodological input in the form of lecture units and individual consulting sessions and also help you with your presentations and provide constant feedback.
General information about the case studies are also available here.
- For the Case Studies Nonlinear Optimization:Introduction to Numerical Linear Algebra (MA1304), Introduction to Nonlinear Optimization (MA2503) or Einführung in die Optimierung (MA2012), Nonlinear Optimization: Advanced (MA3503) or Modern Methods in Nonlinear Optimization (MA4503) (both recommended). Furthermore recommended: Numerical Methods for Ordinary Differential Equations (MA2304), Fundamentals of Convex Optimization / Linear and Convex Optimization (MA2504)
- For the Case Studies Discrete Optimization: Einführung in die Optimierung (MA2012) or Fundamentals of Convex Optimization / Linear and Convex Optimization (MA2504) or equivalent, Integer Optimization (MA3505) or Discrete Optimization (MA3502) or equivalent. Recommended: Combinatorial Optimization (MA4502), Computer Course Linear Programming or similar.
For the listed lectures it is also sufficient if an equivalent lecture has been attended.
Please note that the lectures from the prerequisites have to be passed, participation alone is not sufficient.
We will hold an online information meeting on February 8 at 16:00 where we will give you some information about the case studies courses in general, what to expect during the courses, this year's projects, important dates and the application process. This is a joint meeting for both the "Case Studies Discrete Optimization" and the "Case Studies Nonlinear Optimization". If you cannot join us there but would still like to take the course, some more information will be published here after the meeting. Please note that application by March 13, 2022 is mandatory! If you have any questions that are not answered here or at the information event, please contact us at michael.ritter (at) tum.de.
A slightly edited version of the presentation slides used for the information meeting is available for download here:
Case Studies Discrete Optimization
Visual Quality Inspection
When components for gear trains are manufactured a thorough quality inspection is performed before the components are shipped to customers for further manufacturing stations to ensure that all parts have the required conditions. Part of this inspection is done visually, by taking photos of the parts from a number of positions. The objective of this project is to find and classify typical faults (e.g. rust on the surface, dents) using these photos. This project is a cooperation with Voith.
Facility Layout Optimization
The production process for a complex product usually requires many processing steps on a number of machines. The number of order of machines and also the available means of transportation from one machine to the next depends on the product and on manufacturing requirements. The objective of this project is to optimize the layout of machines and pathways in a production facility to minimize the transportation efforts and thus the total production time, subject to a number of constraints on machine placement and pathways. This project is a cooperation with Voith.
Examination Staff Scheduling
During examination season most staff members of the department of mathematics have to help out with supervision and grading of a number of exams (especially for the large "service exams"). Allocation of staff members for these duties is done centrally, but currently a largely manual process is used. The objective of this project is to replace the current process by an optimization method that will incorporate a number of additional constraints and data.
Case Studies Nonlinear Optimization
Source Term Estimation
We consider the 2D advection diffusion PDE with a source term modeled by a peak-like distribution with unknown location (e.g. Gaussian Kernel with unknown mean). The process can be interpreted as gas dispersion process driven by a source. The concentration is measured by laser absorption spectroscopy, i.e. the integrated concentrations along multiple lines are known. The goal is to estimate the location of the peak based on the measurements by non-linear optimization. This project is a cooperation with DLR
Robot Cell Optimization
Industrial production is becoming more and more flexible and autonomous, which means that the workspace is no longer always the same, but can and should be adapted depending on the given task. In the case study on “robot cell optimization”, we address this task and consider a workspace including one or possibly multiple robot arms, boxes for product parts, and fixtures and jigs. We are interested in an optimal positioning of the elements regarding, e.g, time or energy, taking into account geometric and kinematic constraints. During the case study, the participants are asked to set up a simplified model for the robot cell and formulate a suitable optimal control problem. The workspace setup is optimized with modern methods of optimal control, which are implemented, analyzed, and possibly adapted. This project is a cooperation with Siemens.
Deformable Shape Correspondance
The similarity and correspondence of shapes is a key problem in computer vision, with a diverse range of applications from statistical shape analysis, texture or deformation transfer, to image co-segmentation. Spectral functional map based frameworks have proven to a flexible and robust framework for tackling a number of these problems. The goal of this project is to explore functional correspondence for deformable shape matching, with the additional possibility of comparing them to hybrid methods, which combine modern deep learning based feature extraction approaches with functional maps to achieve state-of-the-art results on deformable shape correspondence problems. This project is a cooperation with TUM Chair for Computer Aided Medical Procedures & Augmented Reality.
Application for both Case Studies courses is possible until March 13, 2022. It is mandatory and binding. To register, please write a short mail to michael.ritter (at) tum.de providing the following information:
- last name, first name
- your master's program (e.g. Mathematics, Mathematics in Science and Engineering, Mathematical Finance and Actuarial Science, Mathematics in Operations Research, Mathematics in Data Science, others) and your current semester (counting from the beginning of your master's program)
- list of optimization related lectures that you have attended and passed (for lectures from other departments or universities, please give a short description of the topics covered so that we know about your expertise in the field)
- programming skills (programming languages and other programming related skills, experience in using optimization software)
- language skills, especially whether you speak (some) German (as some cooperation partners might only speak German; still, this will not exclude you from any project)
- ranking of the projects (which do you find most interesting, which would be a good alternative etc.); please rank at least three project, preferably all. (You can also submit an application with a "mixed" ranking including projects from discrete and nonlinear optimization, we will then assign you to one of the courses while trying to respect your individual ranking.)
- persons you would like to work with as a team (please ask all these persons to give your name in their application, too)
- any additional information that might be relevant for the choice of your project or your partners.
You may also submit a joint application by ranking all projects for both Case Studies courses (you may even include project for the "Case Studies Life Sciences" - in that case, please email the application to the lecturers for that course, too). We will then try to fit you into one of the courses according to your project preferences. We will send you a short message when we have received your email. If you do not receive an acknowledgement within a few days, please resubmit your application.
After March 13, we still have a limited number of places available for incomings from abroad and for master students coming from other universities and starting at TUM this summer. If this applies to you, please mention that in your email. If not claimed, these places will be freed for applicants a few weeks before summer term starts. If this applies to you, we will inform you about that by email.