Case Studies in Optimization 2020
The Case Studies modules
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.
There was a preliminary meeting for both case studies courses on Thursday, February 6th, at 16:00 in room MI 02.08.011.
At this meeting, we gave 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. It was a joint meeting for both the "Case Studies Discrete Optimization" and the "Case Studies Nonlinear Optimization". You can find the slides below.
Please note that application by March 1st, 2020 is mandatory! If you have any questions that are not answered here or at the preliminary meeting, please contact Ulf Friedrich at firstname.lastname@example.org or Florian Lindemann at email@example.com, respectively.
Case Studies in Nonlinear Optimization
Topology Optimization - The Acoustic Behavior (BMW):
One fundamental challenge in the automotive industry (but also in further industrial sectors) is the development and design of new mechanical components which are statically or dynamically loaded. Basic design criteria/aims could be minimal weight or minimal compliance (maximal stiffness) while keeping certain restrictions such as constraints on the stiffness or the volume, respectively. More sophisticated aims/constraints comprise the acoustic (the dynamical response for a given driving frequency or frequency range) of the mechanical component. It is desirable that driving and resonance frequencies do not match (in order to limit the noise induced by vibrations or, in extreme sitatuations, to avoid the resonance disaster). However, in many situations this is not always possible. In those cases, the consideration of the damping behavior of the mechanical system is indispensable and a proper mathematical model incorporating the damping becomes necessary. The general goal of this case study is to mathematically describe, to analyze (regarding plausibility), and to numerically solve problems in that context using concepts from topology optimization.
Attack Detection in Energy Grids (Siemens)
Several recent blackouts have revealed that cyber attacks on power systems are an increasing threat that can cause power fluctuations or even grid breakdowns. In this case study, we want to develop and analyze mathematical methods to detect malicious attacks in large dynamic systems such as energy grids. For this purpose, you will consider a flow network with several interacting nodes and simple dynamics to model the approximate behavior of a power grid. As a next step, you will implement detection methods that use model knowledge to compute a sophisticated suspicion of an attacker. Such a method could for example use ideas from sparse signal recovery and compute a sparse attack signal that explains the observed system behavior best.
Semi-Smooth Newton Method for Model Predictive Control (Siemens)
Renewable Energies increase the demand fast control algorithms to assure stability and maximize revenue. This project addresses a smart home where a battery and a PV element can be used to minimize costs while fulfilling the energy demand. Consequently, one needs an online optimization method to solve optimal control problems in real time. Model Predictive Control (MPC) is an advanced control strategy where at every sampling time an optimization problem is solved. Thereby, we must solve a series of quadratic programs (QP) in real time. So far mostly active-set and interior point methods were used to solve the QPs online. If inequality constraints are present, the non-smooth complementary conditions in the first order necessary optimality conditions hinder us of using the classic Newton method. To circumvent this issue, semi-smooth Newton methods, studied intensively in the early nineties, gained recently attention again. The task of this project involves investigation of the performance of recent, semi-smooth Newton based QP solvers on benchmark problems and of different nonlinear complementarity formulations (NCP). The focus is also on understanding the semi smooth Newton method and its application in quadratic programming.
Improved stability analysis of electrical powertrains using Neural Networks (IAV)
All components of an electric power train are subject to stochastic tolerances. These tolererances have to be taken into acount in the design of a robust control strategy such that the controlled variable (here the desired torque) satisfies the required precision and is dynamically stable. More precisely, we are interested in the boundaries in the parameter space of the components so that the deviation of the controlled variable is less than a prescribed quantity. The main challanges are the numerous combinations of different components as well as the nonlinear system behavior which make it practically impossible to conduct a Monte-Carlo simulation for the full parameter space. For these reasons, the goal of the case studies in nonlinear optimization is to find a surrogate model using Neural Networks. Once trained, these models can be evaluated very fast. Moreover, they can be used to find good sampling points for the original model in order to improve the surrogate model. The method has to be implemented in Python. We will provide a model of the electric power train and its components and a metric to measure the system stability and precision.
Acoustic optimization of a hydraulic pump (HAWE):
Radial piston pumps are versatile hydraulic pumps that produce high pressures up to 700 bar while being durable, long-lasting and efficient. Their use cases range from handheld tools to circuits, which precisely move thousand ton heavy radio telescopes. One downside is the high noise emmission of these types of pumps. This emmission can be greatly influenced by changing the pressure signal, that induces the vibrations of the housing. Mathematically this translates to optimizing parameters of an ODE, which models the pressure signal inside one pump element. For each parameter configuration the resulting noise level is computed via Fourier Transform and a dynamic 3D Finite Element simulation of the remaining pump structure.
Case Studies in Discrete Optimization
Algorithm-driven modular production (Audi)
Today, car engines are mainly assembled on assembly lines. A more flexible, modular manufacturing concept is being developed to deal with the wide range of variants of future (electric) engines. In this alternative production system, autonomous transport vehicles carry out the material transports between the island assembly stations. Thus, the fixed sequence along the traditional assembly line is resolved. The flexible manufacturing concept is referred to as modular production. Most importantly, it offers more flexibility since a product can follow several routes through the system. Modular production also allows to react to malfunctions at some island stations by using alternative stations. In order to use this new flexibility efficiently, the production control must use appropriate algorithms with the aim of a throughput-optimized production.
Optimizing bus routes and driver schedules at Flixbus (Flixmobility)
Planning routes and schedules for passengers, buses, and drivers on Europe's largest long-distance bus network is very complex if done by hand. Yet, the optimization potential is immense. Any automation and cost savings would have a huge impact. The goal of this project is to develop an optimization approach that, given a timetable and some constraints, minimizes the number of buses needed. The scope could be extended to assume some flexibility in the timetable. To ensure agility and speed, standard mathematical programming approaches (i.e., MIPs) by themselves may not suffice to solve this problem, so some programming skills to design clever heuristics are recommended.
PRELIMINARY: Logistics of humanitarian OR (World Food Programme)
At the United Nations World Food Programme, several logistic challenges have to be solved. In this project, the warehousing, replenishment, and distribution of staple food is analyzed. The aim is to develop an easy-to-use, lightweight software tool to support the WFP employees and volunteers on site with the logistics. The primary objective is to minimize warehousing and distribution costs while the regular supply of food has to be guaranteed at all times. Additionally, the robustness of the solution and the customization of the model in changed scenarios are considered.
Discrete optimization and machine learning for truck routing (Smartlane)
Efficient logistical operations ensures that the supermarket have fresh produce every day, that pharmacies can order and receive medication fast and that industrial supply chains operate smoothly. It also means less pollution, less traffic and less waste. However, it still largely runs on paper today. Smartlane offers the highest degree of automation and transparency as well as industry-specific configuration capabilities. We develop a transport optimization software based on mathematical programming techniques and machine learning to automate and optimize transport planning as well as data mining of transport-specific processes. At the core of the software is the vehicle routing problem (VRP): a generalization of the well-known traveling salesperson problem (TSP), both of which are NP-hard in general. Modeling real-world constraints that arise from different business models, laws and regulations often lead to models where it can be hard to find feasible solutions. Finding a balance between model complexity and being able to find solutions fast enough, which can mean anything from within 10 minutes to a whole day, depending on the business model, is a challenging task requiring both good modeling, insight into the algorithms used, smart pre-processing and a healthy dose of pragmatism.
The car sequencing problem (Dassault Systèmes)
In the automotive industry, customer orders are transmitted daily to the factories and have to be included in the production plan real-time. For a feasible production plan, a production date hast to be assigned to each ordered vehicle such that it can be delivered before the date promised in the contract, while respecting production line capacities. For all cars assigned to a given production day, the order of cars to be put on the line has to be determined in such a way that the order is feasible for the several production steps in the factory, e.g., at the paint shop and at the assembly lines. The combinatorial challenge of this process results from the fact that in some production steps similar cars should be grouped (e.g., cars of the same color should be painted in a row), whereas in other steps similarities have to be split (e.g., only a small number of sunroofs per hour).
Application is possible until March 1st, 2020. It is mandatory and binding. To register for the Case Studies in Discrete Optimization or the Case Studies in Nonlinear Optimization, please write a short mail to casestudies.or (at) tum.de providing the following information:
- last name, first name
- your master's program (Mathematics, Mathematics in Bioscience, 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).
- transcript of records (including all optimization related lectures that you have attended and passed the exam - for lectures from other faculties 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 per default!)
- ranking of the projects (which do you find most interesting, which would be a good alternative etc.); please rank at least three. You can rank 2 projects at the same place, e.g. [1. project A, 2. project B, 2. project C]. You can also submit an application with a "mixed" ranking including projects from discrete and nonlinear optimization. If you are also interested in the Case Studies Life Science Mathematics (see also https://www-m6.ma.tum.de/Lehrstuhl/Fallstudien_LifeScience_2020), you can include projects from Life Science, too (in this case: please submit your application also to firstname.lastname@example.org). We will then assign you to one of these 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. 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 week, please resubmit your application.
After March 1st, 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.