# SCoNDO 2022

## Students' Conference on Nonlinear and Discrete Optimization

SCoNDO, the TUM students' conference for nonlinear and discrete optimization, is taking place on a yearly basis. The conference is the final meeting for the courses Case Studies Nonlinear / Discrete Optimization. Course participants present their projects and their results in a scientific talk and get a chance to discuss their project's specific challenges, relevant mathematical theory and applications.

Everyone interested in mathematical optimization and its applications in real-world projects is invited to join the conference, listen to the presentations, and discuss possible questions with the teams.

### Date and Venue

SCoNDO 13 is taking place on **Monday and Tuesday, 25. and 26. July 2022 between 16:00 and 20:00** at "Hörsaal 1" (Room BC2 0.01.16) at the Garching-Hochbrück campus Garching Parkring 35-39.

Parking in the area is very limited, so please use public transportation if possible. The conference venue is about a five minute walk from the underground station "Garching-Hochbrück (U6)".

### Program

Monday Sessions | 16:00 - 19:20 |

Coffee break | 17:30 - 18:00 |

Tuesday Sessions | 16:00 - 19:30 |

Coffee Break | 17:30 - 18:00 |

Conference Dinner | Tuesday, starting at 19:45 |

### Presentations

**16:00 – Welcome**

The Organizers

**16:10 – Automated Visual Quality Inspection for High Precision Gearwheels**

Fault inspection of mass-produced high precision machine components is in many cases a critical task, which often must be performed by hand. This project aims, in cooperation with the manufacturer VOITH Turbo, to create a method to automatically detect faulty gear wheels. To this end, VOITH provided images of the gear wheels’ teeth, photographed in a deliberate camera setting. The team attempted to create a high precision method to decide whether each image contains a fault, using simple image operations for data initialization, various computer vision operations as image preprocessing, and three artificial intelligence models in comparison for classification. Our task is intentionally limited to binary classification of single images at the best possible rate.

**16:50 – Robot Cell Optimization**

In today’s industry, production lines are becoming more autonomous and flexible. The workspace is no longer fixed and should be adapted to the given tasks. Our goal is to find the optimal location of the materials such that the energy needed by the robot arm, to perform the assembly task, is minimized. We consider a two-dimensional workspace that includes materials, fixtures and two robot arms. The robot arm consists of two links and it is modeled using the angles at the base and joint of the robot. We control the movement of the robot by specifying the acceleration of the angles. In particular, focus is placed on modeling collision avoidance between the robot arm and the materials. This project is in cooperation with Siemens.

**18:00 – Facility Layout**

In our project, we investigated the question of how to arrange given departments within a facility. The desired layout has a high efficiency for some production processes. The present problem focuses on the aspect of minimizing transportation costs between the departments. This can be mathematically modeled as a mixed integer optimization problem. As solving it at once using the standard solver for MIPs Gurobi has a very long running time, we implemented an algorithm that solves the optimization problem in two stages. In the first step, relative positions are determined for the departments. This is done by solving a nonlinear minimization problem. With these relative positions the MIP can be simplified enough to be solvable with Gurobi within a short time.

**18:40 – Source term estimation with remote sensing**

A crucial step in closing gas leaks is locating the source. Data about the gas can be gathered rapidly by sending out drones that can measure the concentration between each other with laser signals.

Knowing the wind, we can estimate the source from these data by parametrizing its shape, and then minimizing the error between hypothetical and real measurements.

First, we fix the shape of the source to a Gaussian. This parametrization achieves good results even for a small number of measurements, and the location is simply obtained by the two estimated positional coordinates. However, the source has a nonlinear dependence on the parameters, leading to high computational costs for the objective gradient.

Second, we approximate the source as FE function, which allows for arbitrary source shapes and fast computation of the objective gradient but requires further work to locate the source from the result.

**16:00 – Welcome**

The Organizers

**16:10 – Scheduling for the math exam phase: Supervision & Correction**

In the previous workaround, assigning 170 staff members to 500 supervision and correction tasks caused some major issues. Date preferences of staff members like absence due to conferences or holidays were ignored and the correction schedule were split in a tremendous number of correction units with 1 or 2 units per corrector at multiple different exams. Until now these problems were solved manually by the responsible person and private agreements between the staff members.

We describe how this process has been optimized via answering the following questions:

- What exactly is a good and fair schedule?
- Which new data should be used and collected in a new process?
- How can we collect, store and use this data?
- How can we model and solve the problem then?

**16:50 – **Deformable Shape Correspondence with Coupled Functional Maps

The similarity and correspondence of shapes is a key problem in computer vision. Especially Partial correspondence problems appear in numerous applications of computer vision as Shape Reconstruction, Object Detection and also in Computational Biology.

In our project, we consider, for 3D partial shapes M and full shape N, the point wise mapping T : N → M. We use the spectral functional map based frameworks, which have proven to be ﬂexible and robust, with the coupled functional map approach.

Existing literature have mostly explored in optimizing functional maps with hand-crafted descriptors, and by combining with deep learning framework, we can then learn the descriptors through the deep neural networks, which brings more ﬂexibility and variability into the topic. But unfortunately those works have mostly been developed with functional maps instead of coupled functional maps. We thus would like to take a further step in this direction and explore how coupled functional maps works incorporated with deep learning frameworks.

In addition, since partial shape correspondence is comparatively a harder task to learn for loss of information, we further evaluate correspondence on partial shapes with the coupled functional map approach.

**18:00 – **Point Cloud Registration for Non-Rigid Deformation

We find correspondences between point clouds of the same object after non-rigid deformation. In RIGA [Hao Yu et al.(2022)] correspondences for the rigid case are found using angles and Euclidean distances. However, in the non-rigid setting a bending invariant quantity is needed. We use the geodesic distance which is the shortest distance between two points along the surface of the object. For that we adapted the current framework of RIGA by computing shortest paths in a graph constructed out of the point cloud. Correspondences between the two point clouds are then learned via a neural network. The main issue is the long run-time of the all pair geodesic distance computations. With the diffusion distance, another bending invariant quantity is investigated, that is computed only from Euclidean distances.

You are welcome to attend SCoNDO, listen to the talks and discuss with students and advisors without registration and free of charge. To make sure we will have plenty of fresh coffee and snacks for all participants and guests, a quick message by email to michael.ritter (at) tum.de would be helpful, though.