# Select projects

## Select Recent Ongoing Projects

#### MODAL Synlab [homepage]

Collaborators.
(see official homepage)
Abstract.

The Research Campus MODAL recently entered into its second funding phase (2020-2025) with a funding volume of more than €25 million. The SynLab, one of the labs in MODAL, researches on the mathematical generalization of application-specific advances achieved in the Gas-, Rail– and MedLab of the research campus MODAL. Its focus is on exact methods for solving a broad class of discrete-continuous optimization problems. This requires advanced techniques for structure recognition, consideration of nonlinear restrictions from practice, and the efficient implementation of mathematical algorithms on modern computer architectures. The results are bundled in a professional software package and complemented by a range of high-performance methods for specific applications with a high degree of innovation.

[MODAL Research Campus]
Funding.
[BMBF]

#### SCIP Platforms

Collaborators.
Ambros Gleixner
Abstract.

This projects aims to bringing SCIP to alternative architectures. This includes alternative hardware architectures such as ARM and RISC-V as well as highly parallel computing setups. The project goes beyond mere porting and aims for optimized versions for the target architectures. We will also consider embedded systems as well as hardware accelerator specific extensions.

[SCIP homepage] [Blog post about SCIP x Raspberry Pi]

#### COVID-19 spread prediction and tracing [homepage]

Collaborators.
Abstract.

COVID-19 caused by the novel virus SARS-CoV-2 (severe acute respiratory syndrome Coronavirus 2) is currently spreading across the globe. Our objective is to track and monitor confirmed and active cases for various locations and to forecast new infections for the country or region. We developed a simple model to monitor confirmed COVID-19 cases by country or region using the 2019 Novel Coronavirus COVID—19 (2019-nCoV) Data Repository by Johns Hopkins CSSE. We use the Facebook Prophet library among other tools, which is a really great forecasting toolbox. Generally, predictions are highly unreliable because data is currently quite sparse and reporting may not be accurate. Moreover, important factors may change quickly.

[Official Project Page (German)] [COVID-19 spread prediction] [Predictions specifically for Berlin] [Simulation-based Disease Spread Model (German)] [Pan-European Privacy-Preserving Proximity Tracing (PEPP-PT)]
Funding.
[MODUS-COVID / BMBF]

#### Positional Games and Reinforcement Learning

Collaborators.
Tibor Szabó
Abstract.

Erdős-Selfridge-Spencer games are uniquely suited environments for comparing different Reinforcement Learning methods. These games offer the advantage of having a fully characterized optimal behavior while still offering a sufficient amount of complexity, neatly controlled by a single parameter, for Neural Networks to learn. Erdős-Selfridge-Spencer games are part of the much larger study of Positional Games that has been the center of much attention in the world of Combinatorics due to their close connection to Ramsey-type problems. As a result, there is a myriad of environments in which optimal behavior has been well studied and that offer interesting features for an application to Machine Learning.

[Homepage of Tibor Szabó]

#### SFB Transregio 154: Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks [homepage]

Collaborators.
(see official homepage)
Abstract.

The “turnaround in energy policy” is currently in the main focus of public opinion. It concerns social, political and scientific aspects as the dependence on a reliable, efficient and affordable energy supply becomes increasingly dominant. On the other side, the desire for a clean, environmentally consistent and climate-friendly energy production is stronger than ever. To balance these tendencies while making a transition to nuclear-free energy supply, gas becomes more and more important in the decades to come. Natural gas is and will be sufficiently available, is storable and can be traded. On the other side focusing on an efficient handling of gas transportation induces a number of technical and regulatory problems, also in the context of coupling to other energy carriers. As an example, energy transporters are required by law to provide evidence that within the given capacities all contracts defining the market are physically and technically feasible. Given the amount of data and the potential of stochastic effects, this is a formidable task all by itself, regardless from the actual process of distributing the proper amount of gas with the required quality to the customer. It is the goal of the Transregio-CRC to provide certified novel answers to these grand challenges, based on mathematical modeling, simulation and optimization. In order to achieve this goal new paradigms in the integration of these disciplines and in particular in the interplay between integer and nonlinear programming in the context of stochastic data have to be established and brought to bear. Clearly, without a specified underlying structure of the problems to face, such a breakthrough is rather unlikely. Thus, the particular network structure, the given hierarchical hybrid modeling in terms of switching algebraic, ordinary and partial differential-algebraic equations of hyperbolic type that is present in gas network transportation systems gives rise to the confidence that the challenges can be met by the team of the proposed Transregio-CRC. Moreover, the fundamental research conducted here will also be applicable in the context of other energy networks such as fresh- and waste water networks. In this respect the proposed research goes beyond the exemplary problem chosen and will provide, besides a cutting edge in enabling technologies, new mathematics in the emerging area of discrete, respectively, integer and continuous problems.

Funding.
[DFG SFB/TRR 154]

## Select Past Projects

### Foundational Research and Methodology

#### SDP Extended Formulations

Abstract.

This Faculty Early Career Development (CAREER) Program grant will explore the power of Semidefinite Optimization problems. This broad class of optimization problems is fundamental to solving many real-world problems in engineering and computer science as well as pivotal in analyzing the theoretical performance of algorithms. Approaches based on semidefinite optimization often provide superior algorithms yet at the same time the power of semidefinite optimization problems is only partially understood. The leitmotif of this grant is: How best to exploit the power of semidefinite optimization problems? This grant will relate the structure of optimization problems to their representability as semidefinite optimization problems and explore new ways of solving large semidefinite programs efficiently. Moreover, it will relate semidefinite optimization to the weaker but more easily solvable class of so called linear optimization problems. Understanding the power of semidefinite optimization problems will advance both our understanding of theoretical computational complexity as well as practical feasibility of solving semidefinite optimization problems. As such the results will positively impact both society and the U.S. economy. The tightly integrated educational program will broaden the involvement of under-represented groups and enhance engineering education.

Funding.
[NSF CMMI-1452463]

#### Almost Symmetric Integer Programs

Collaborators.
Jim Ostrowski (U Tennessee)
Abstract.

The objective of this collaborative research award is to develop techniques that exploit almost symmetry in integer programming. In the past decade, the exploitation of regular symmetries has led to a dramatic decrease in computation time for many classes of integer programming problems. Unfortunately, many of these problems, perhaps due to measurement or modeling error, are only close to being symmetric; minuscule differences in coefficients can hide exact symmetries. These almost symmetries are permutations that can become exact symmetries when the problem instance is modified slightly. This project seeks to expand the concept of symmetry to include almost symmetries and will develop a framework to treat almost symmetries as if they are actual symmetries. This will significantly broaden the class of optimization problem that can benefit from symmetry-exploiting techniques, resulting in improved computational times for a wider class of problems. This project will develop software that identifies almost symmetries and used to identify the prevalence of almost symmetries and assess how the existence of almost symmetries affect the difficulty of an integer programming instance. Algorithms designed to exploit almost symmetries will be developed and tested.

[Jim Ostrowski]
Funding.
[NSF CMMI-133789]

#### Physical Flow and other Industrial Challenges

Collaborators.
Prasad Tetali (Georgia Tech), Henrik Christensen (UC San Diego), George Nemhauser (Georgia Tech)
Abstract.

At the core of many societal challenges, particularly in view of sustainability and efficiency, there are hard optimization problems. While these underlying problems can be solved for smaller setups using optimization methods, realistic problem sizes are still prohibitive. Apart from the immediate challenges arising from sheer size, in today’s fast-paced and intertwined economies we additionally face the challenge of addressing real-time aspects; otherwise, the obtained solutions might not apply anymore: the problem changed faster than it was solved. This EAGER addresses specific optimization problems arising from societal challenges and will motivate the study of the underlying optimization problems. For this, new methods at the intersection of continuous and discrete optimization as well as machine learning and randomization will be developed.

[Prasad Tetali] [Henrik Christensen] [George Nemhauser]
Funding.
[NSF CCF-1415496]

### Engineering

#### DAPRA SC2 Spectrum Challenge

Collaborators.
Matthieu Bloch (Georgia Tech)
Abstract.

The approach envisions a paradigm shift in radio design, by which intelligence and agility are pushed closer to the physical (PHY) layer than ever before. Specifically, the approach comprises three key elements: (1) a multi-carrier modulation format at the PHY layer that provides the required agility to react to interfering signals; (2) a high-performing modulation recognition software that exploits the latest advances in deep learning and Convolutional Neural Networks (CNNs) to accurately classify the RF signals in the environment; and (3) a decision module exploiting the latest advances in regret minimization online algorithms to achieve high exploration versus exploitation performance in the wireless environment.

Funding.
[NSF CNS-1737842]

#### Rope Tension Measurement

Collaborators.
Matthieu Bloch (Georgia Tech) and Justin Romberg (Georgia Tech)
Abstract.

An approach based on the combination of digital signal processing and machine learning to reliably identify the base frequency of a vibration signal in a data sample obtained from elevator maintenance equipment.

Funding.
[ThyssenKrupp Elevators]

#### Algebraic Oil Research Project [homepage]

Collaborators.
Kreuzer Lab (now: University of Passau)
Abstract.

The research project addresses several topics at the heart of oil recovery and oil exploration: production optimization, production allocation, improvement of the ultimate recovery, development of production strategies, and discovery of new oil reservoirs. The basic idea was to introduce methods of of symbolic computation (computer algebra) to solve problems in these areas. More precisely, the new techniques were part of an emerging area called Approximate Computational Commutative Algebra (or hybrid computation or symbolic-numeric computation).

[patent] [Kreuzer Lab @ University of Passau]
Funding.
[Shell]

#### Detecting lymphedema onset

Collaborators.
Dixon Lab (Georgia Tech) and Gleason Lab (Georgia Tech)
Abstract.

Nearly every breast cancer patient undergoes some type of surgical intervention, chemotherapy, or radiation as part of their therapy process, and while these procedures have proven to be very effective for cancer removal, they can create an unintended side-effect of severe, permanent arm swelling. This severe limb swelling condition is known as lymphedema and there are approximately 4 million lymphedema patients in the United States. A treatment for lymphedema exists in the form of compression garments and manual lymph massage, but the major limitation of this treatment is that there is an extremely narrow therapeutic window in which it can effectively reverse the disease. Current diagnostics cannot be implemented in a way to reliably detect lymphedema within this window. We will provide an affordable home-based diagnostic that can track limb volumes over time for early detection of lymphedema.

[patent] [Dixon Lab] [Gleason Lab]

#### Predicting obstructed labor in low-resource settings

Collaborators.
Dixon Lab (Georgia Tech) and Gleason Lab (Georgia Tech)
Abstract.

Cephalopelvic disproportion (CPD) is one of the most common preventable causes of unfavorable pregnancy outcomes and one of the major contributors to high infant and maternal mortality rates in the developing world. According to the WHO report 8% of the maternal deaths worldwide are still attributable to CPD. A reliable, low-cost screening tool to identify at-risk women is of paramount importance especially in resource-limited areas where ultrasound screening is not available and cesarean sections are not a feasible delivery option. In such cases, early detection of CPD could allow for high-risk patients to be referred to urban clinics for medically observed labor or a cesarean procedure. The technology will present an economical and easy-to-use diagnostic alternative to more sophisticated imaging methods unavailable in the rural developing world.

[Georgia Tech News] [Dixon Lab] [Gleason Lab]
Funding.
[George Family Foundation Seed Grant] [Saving Lives @ Birth]

#### Just a perfect day? Developing a happiness optimised day schedule

Collaborators.
Christian Kroll (Harvard)
Abstract.

With the Day Reconstruction Method (DRM), Kahneman et al. (2004) introduced an important approach in subjective well-being (SWB) research to explore how people experience daily activities. A major unresolved question for laypeople and scholars alike resulting from this research, however, is the neglect of saturation and scarcity effects in this area of study. To fill this gap, we apply methods from optimisation research to the field of SWB. Combining utility functions with DRM data allows us to generate an optimal day schedule: It differs considerably from how people usually spend their time, whereby the distribution of activities is remarkably even. The results show how a paradigm shift away from a focus on increasing Gross Domestic Product towards greater well-being at the macro level could play out at the micro level with potential consequences for how we might live our day-to-day lives.

### Logistics and Transportation

#### Pre-packaging of fast-moving inventory

Abstract.

Pre-packaging of fast-moving inventory can be a powerful inventory management strategy to reduce turnaround time and warehousing cost while simultaneously increasing service levels.

In this project we explore together with Macy’s Systems and Technology, the efficiency and efficacy of various pre-packaging strategies combining real-world requirements, both in terms of flexibility and speed with data-driven decision making approaches. Based on historical customer demand and expected future demand for a specific product the optimal quantity of stock to be pre-packaged is to be determined. Pre-packaged items can be shipped significantly faster, requiring often only the application of an address label. At the same time, pre-packaging items that are out of demand can be very costly due to inventory holding costs and space restrictions. Determining the optimal tradeoff is a hard problem as product life can be short, so that historic demand data is effectively not available. To overcome this we will be using auxiliary product data and various machine-learning strategies to more accurately determine the optimal pre-packaging strategy. The final goal of this project is a big data inventory management and pre-packaging framework, which leverages state-of-the-art analytics on real-time order data as well as hundreds of millions of historical and auxiliary data points, going beyond traditional, static inventory policies.

Funding.
[Macy’s Systems and Technology]

#### Center for Next Generation Logistics (C4NGL) [homepage]

Collaborators.
Chelsea ‘Chip’ White III (GT lead), Alan Erera (GT), Alejandro Toriello (GT), Lee Loo Hay (NUS), and Ek Peng Chew (NUS)
Abstract.

The intent of the GT-NUS Singapore Initiative is to establish a multi-disciplinary Center on Next Generation Logistics. The Center’s objective is to identify and carry out key pre-competitive research in supply chain and logistics systems having potential for significant economic and societal impact and to reduce the cost, time, and risk of moving from knowledge discovery to innovation and commercialization.

[Press Release GT] [Summary for Industry Partners]

### Risk, Banking, and Finance

#### Market Clearing and Opening Auctions for Electricty and Future Markets

Collaborators.
Alexander Martin (FAU) and Johannes Müller (FAU)
Abstract.

We employ various mechanisms to clear non-convex markets by means of mixed-integer linear programming. Our approach is used for clearing both electricity markets with indivisibilities in an opening auction as well as for clearing future markets with linked contracts.

[patent]
Funding.
[Deutsche Börse AG]

#### Optimizing for Basel III banking regulation

Collaborators.
Christian Schmaltz (Aarhus University)
Abstract.

In addition to the Basel II capital ratio, Basel III requires banks to respect additional ratios, such as leverage ratio, liquidity coverage ratio and net stable funding ratio. Banks are required to be compliant with all four constraints simultaneously. We provide a framework for banks to help their search for an optimal transition from Basel II to Basel III. Recognizing that banks’ return and the four constraints are of linear type, this search can be formulated as a linear program and solved by standard software. Incorporating uncertainty on future defaults, risk weights and withdrawals and formulating the problem as a Chance constrained model does not only yield optimal transition strategies but also determines the internal thresholds for the Basel III-ratios.

#### Optimal Liquidity Management

Collaborators.
Christian Schmaltz (Aarhus University)
Abstract.

Large banking groups face the question of how to optimally allocate and generate liquidity: in a central liquidity hub or in many decentralized branches. We translate this question into a facility-location problem under uncertainty and show that volatility is the key driver behind (de-)centralization. We provide an analytical solution for the 2-branch model and show that a liquidity center can be interpreted as an option on immediate liquidity. Its value can be interpreted as the price of information, i.e., the price of knowing the exact demand. Furthermore, we derive the threshold above which it is advantageous to open a liquidity center and show that it is a function of the volatility and the characteristic of the bank network. Finally, we develop an approach to solve the general $n$-branch model for real-world banking groups (10 to 60 branches) with state-of-the-art solves.