Students' Conference on Nonlinear and Discrete Optimization
SCoNDO, die Konferenz für Nichtlineare und Diskrete Optimierung, findet einmal im Jahr an der TUM statt. Die Konferenz bietet den Teilnehmern unserer Fallstudien in Diskreter und Nichtlinearer Optimierung die Chance, ihre Projekte und Ergebnisse einem breiteren Publikum zu präsentieren. Zudem können sie sich über die spezifischen Herausforderungen, die mathematische Theorie und die praktischen Ergebnisse austauschen.
Alle, die sich für mathematische Optimierung und ihre Anwendungen in realen Projekten interessieren, laden wir herzlich ein. Hören Sie die Vorträge und unterhalten Sie sich mit den Teams.
Datum und Ort
Da die Parkmöglichkeiten in der Umgebung eingeschränkt sind, nutzen Sie bitte möglichst die öffentlichen Verkehrsmittel. Der Tagungsort ist von der U-Bahnstation Garching-Hochbrück (U6) in 5 Minuten zu Fuß erreichbar
|Morning Session 1||09:00 - 11:10|
|Coffee break||11:10 - 11:40|
|Morning Session 2||11:40 - 13:00|
|Lunch break||13:00 - 14:00|
14:00 - 16:10
09:00 – Welcome
9:10 – Topology Optimization - Light & Stable
In the field of Topology Optimization, the optimization variable is the distribution of material in a given domain of available free space. Our project partner BMW wants to find the optimal design of a mounting connecting engine and body of a car. The goal of our project was to find a combination of model and efficient solver where constraints on the deformation could be applied in a meaningful way. Objective functions describe the volume or deformability. In each case, suitable constraints are considered. The corresponding deformation field is computed by discretizing the linear elasticity equation with bilinear Finite Elements. The density distribution is discretized by elementwise constants. The different approaches were compared on a simplified 2D geometry.
9:50 – Portfolio Optimization using Conditional Value-at-Risk
In asset management, different financial instruments are combined into a portfolio to reduce the risk of a failed investment. There are different measures to quantify risk in such a portfolio which can be minimized to find the safest investment strategy. We investigate the Conditional Value-at-Risk measure and compare different methods to minimize it in terms of solution quality, runtime and robustness.
10:30 – Time-optimal Nonlinear Model Predictive Control of Autonomous Vehicles
In the hot topic of autonomous driving, motion planning plays an important role. We tackled this task using an optimal control strategy called Model Predictive Control (MPC), in order to have an autonomous vehicle clear a race track autonomously while adapting to possible disturbances. To this end, one has to solve several subproblems such as track generation, choosing a suitable vehicle model and incorporating both into the optimal control problems. Another crucial issue is the notion of time-optimality, that has to be defined. Since the car has to be controlled in real time, the ultimate goal is to find a good trade-off between computation time and accuracy.
11:40 – Constrained Global Optimization of Power Trains
We aim to find a global minimum of a non-convex, non-smooth objective function on a linearly bounded feasible set. It models the fuel consumption of a car with given speed and torque. The variable corresponds to the way of shifting gears. Since, due to the non-smoothness no gradient based method can be applied, we implemented several heuristic approaches to obtain a global solution. Namely, Particle Swarm Method (PSO), Genetic Algorithm (GA) and the Covariance Matrix Adaption Evolution Strategy (CMAES). To include the constraints we tested several (non-differentiable) penalty functions. All methods were implemented and tested in Python and it became clear that the latter one (CMAES) produced the best results and was able to find the feasible set effectively. CMAES also converges faster compared to the PSO and Genetic.
12:20 – Optimal Camera Placement in a Warehouse
Autonomous guided vehicles (AGVs) gain more popularity in the field of logistics. To use such AGVs in a warehouse, the floor needs to be fully covered by cameras for guidance and supervision. Our goal was to find an optimal camera placement to have the minimum number of cameras to cover the whole floor of the warehouse. This problem can be modeled as a Set Cover Problem with varying constraints. Since this problem is NP-hard, we tried to find a good approximation of the solution. For this, we considered different versions of greedy-type algorithms. Additionally, we compare the results of our algorithm to the optimal solution of the corresponding integer linear program. This allows us to determine how good our approximate solution is.
14:00 – Photovoltaic Power Plant Optimization
The layout of photovoltaic (PV) power plants which contribute significantly to green energy has to be customized with respect to the area where it should be built. The goal of our project was to develop a tool which determines the optimal layout of a PV powerplant with only the coordinates of the area and the resulting topological information as an input. A suitable simplification is to maximize the number of PV tables fitting in the given area and minimize the length of cables connecting the tables and inverters. For the first subproblem we developed a discretization. For the second one we adjusted Lloyds k-mean algorithm such that all the electro-physical constraints are satisfied. Within the resulting clusters the cabling is represented by a minimum spanning tree.
14:40 – Distributing School Meals
We live in a century where still every ninth person suffers from malnutrition. The School Meals Programme by the World Food Programme (WFP) aims to cut down this number by delivering nutrient rich meals to the schools of students in need. To achieve that, the WFP builds kitchens from where they use vehicles to distribute the meals efficiently to schools nearby. The main part of our task is to develop a suitable model to decide where to place these kitchens and which vehicles are needed to deliver all meals in time. When we plan the distribution network, complexity is greatly increased by taking constraints such as freshness of food into account. A combinatorial optimization problem is formed when representing the network with a complete graph. We find good solutions to our model by covering the resulting graph with suitable tours of food delivering vehicles. In order to visualize the outcome of our well-working approach we created an user-friendly interface.
15:20 – Just-In-Time Delivery in Car Production
Our project is realized in cooperation with AUDI and is about planning efficient transportation routes for their car production. In the automotive production nowadays car parts exist in many different variations. Considering that each variant of a part is stored in a container, it is obvious that this leads to a storage problem at the production line. Therefore trains driven by workers pick up the needed car parts from a storage area and bring them to their target location at the production line. Furthermore, the trains only have a certain time span to fulfill these tasks. Our task was to minimize the amount of workers while still being able to deliver every part "just-in-time" and to allocate the workload equally. Our solution approach is made out of different steps and optimization problems. The main part of our talk will be covered by the presentation of the solution procedure, in which we want to explain the general functionality of our algorithm.
16:00 – Closing
Wir freuen uns, wenn Sie die SCoNDO besuchen, sich die Vorträge anhören und sich mit den Studierenden über ihre Projekte austauschen. Bitte melden Sie sich vorab an, wenn Sie teilnehmen möchten, damit wir Sie mit ausreichend Kaffee, Keksen und Obst versorgen können. Senden Sie dazu einfach eine E-Mail an pfefferer (at) ma.tum.de.