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Faculty 3 - Mathematics and Computer Science: Combinatorial Optimization and Logistics

Summer 2024

Approximation Algorithms

Bachelor/Master Course in Summer 2024
03-ME-602.99a (03-IMAT-APX), 6 CP (+ 3 CP possible)

A large number of problems arising in practical scenarios like communication, transportation, planning, logistics etc. can be modeled as combinatorial optimization problems. In most cases, these problems are computationally intractable and one often resorts to heuristics that provide sufficiently good solutions in reasonable amount of runtime. However, in most cases, such heuristics do not provide a worst case guarantee on the performance in comparison to the optimum solution. In this course, we shall study algorithms for combinatorial optimization problems which can provide strong mathematical guarantees on performance. The course aims at developing a toolkit for solving such problems. The lectures will consist of designing polynomial-time algorithms and proving rigorous bounds on their worst case performances.

We review many classical results in the field of approximation algorithms, highlighting different techniques commonly used for the design of such algorithms. Among others, we will treat the following topics:

  • Greedy algorithms and Local Search
  • Rounding Data and Dynamic Programming 
  • Deterministic Rounding of Linear Programs (LPs)
  • Random Sampling and Randomized Rounding of LPs
  • Primal-Dual Methods
  • Hardness of Approximation
  • Problem Solving under Uncertainty 

Lecturer: Dr. Felix Hommelsheim

Time & Format:

We will teach the course with 4 hours per week, where roughly every other week one class will be an interactive exercise session. The course takes place:

  • Tue 10-12 MZH 3150 and Thu 14-16 MZH 5500
  • The Course starts on Tuesday, April 9, at 10:15. Further information on StudIP.

There is the possibility to further extend the content of the course as well as the credits (+3 CP) by participating in a seminar. This participation consists of individually studying a recent research article and presenting the main results to the rest of the class.  

Examination:

The examination will be by individual oral exam. 

Literature: The course is based on parts of the literature below and recent research articles that will be provided later.

  • [WS] The Design of Approximation Algorithms, David P. Williamson and David B. Shmoys online version
  • [V] Approximation Algorithms, Vijay V. Vazirani
  • [GM] Approximation Algorithms and Semidefinite Programming, Bernd Gärtner and Jiří Matoušek, Springer, 2012

Operations Research

Sommersemester 2024, 6CP
03-BB-699.01 (03-IBAT-OR)

Moderne betriebliche Informationssysteme nutzen verschiedene quantitative Verfahren aus der Informatik und Mathematik um Planungs- und Entscheidungsprozesse zu unterstützen. So lassen sich viele praktische Fragestellungen als (ganzzahlige) lineare Optimierungsprobleme formulieren: z.B. Warenfluss und Planung von Produktionsprozessen in der Logistik, Portfoliotheorie und Risikomanagement in der Finanzwelt sowie Netzwerkdesign und Routing in der Telekommunikation.

Die Vorlesung gibt eine Einführung in die Modellierung betrieblicher Entscheidungsprobleme und grundlegende Methoden der linearen und ganzzahligen linearen Optimierung. Themen sind: Mathematische Modellierung praktischer Fragestellungen (Entscheidungs-, Planungs- und Optimierungsprobleme), Struktur und Geometrie linearer Programme, Simplexverfahren, Komplexität, Dualität, Sensitivitätsanalyse; Methoden zum Lösen ganzzahliger linearer Probleme: Branch-and Bound Methode, Schnittebenen-Verfahren, Dynamische Programmierung und Greedy Verfahren; Scheduling- und zeitliches Ressourcenmanagement; Anwendung grundlegender kombinatorische Algorithmen für Graphen- und Netzwerkflussprobleme.

Dozentin:  Dr. Felix Hommelsheim, Dr. Jens Schlöter

Zeit und Format: 

Die Veranstaltung findet statt:

  • Vorlesungen Montag 14-16 Uhr MZH 1380/1400, Übungen Dienstag 08-10 Uhr und Mittwoch 14-16 Uhr MZH 6200.
  • Erste Veranstaltung: Montag, dem 08.04.2023, um 14:15 Uhr.
  • Alle weiteren Informationen über StudIP.

Es gibt wöchentliche feste virtuelle Termine für Übung und Diskussion. Nach Ankündigung findet alle zwei Wochen eine betreute Rechnerübung statt.

Leistungsnachweis:

Es ist eine Klausur geplant. Durch Erreichen einer Mindestpunktzahl bei den wöchentlichen Übungsblättern kann ein Notenbonus erzielt werden.

Literatur:

  • [W] Winston, A.: Operations Research, Algorithms and Applications, Whiley & Sons, Duxbury Press, 2003.
  • [NSW] Nickel, Stein, Waldmann: Operations Research, Springer Gabler, 2. Auflage, 2014.
  • [DDKS] Domschke, W.; Drexl, A.; Klein, R.; Scholl, A.: Einführung in Operations Research, 5. Auflage, Springer, 2015.
  • [BT] Bertsimas, Tsitsiklis: Introduction to Linear Optimization, Athena Scientific, 1997.
  • [GKT] Guenin, Könemann, Tuncel: A Gentle Introduction to Optimization, Cambridge University Press, 2014.

Seminar: Combinatorial Optimization and Machine Learning

Sommersemester 2024, 3 or 6 CP
03-IMS-COML

This seminar focusses on recent research at the interplay of combinatorial optimization and machine learning. Both fields provide important methods for solving various real-world problems. On the one hand, we study how machine learning techniques can improve well-established solution methods for NP-hard discrete optimization problems. How can untrusted prediction, e.g., machine-learned, be used to derived provable guarantees for the performance of online algorithms? How can machine learning accelerate existing optimization methods? On the other hand, combinatorial optimization problems are increasingly important in machine learning. We will study particular relevant problems such as clustering, feature selection and submodular function optimization.

Lecturer: Dr. Felix Hommelsheim

Format: 

Students are expected to read and thoroughly understand original research papers, and to deliver an oral presentation and a write up.

Most likely the seminar will be virtual via Zoom.

  • Organizational meeting: Tuesday, April 10, at 10:15 pm MZH 3150

We will discuss the organization and allocate the research articles in the first meeting. Please register with StudIP. The seminar is planned as a block seminar, meaning that all talks will be at two days in the end of the semester. We will discuss this in the first zoom meeting.

Hands-on Tutorial on Optimization (engl./dt.)

Block course, 2024
03-BE-699.12, 3 CP

A large number of problems arising in practical scenarios like communication, transportation, planning, logistics etc. can be formulated as discrete linear optimization problems. This course briefly introduces the theory of such problems. We develop a toolkit to model real-world problems as (discrete) linear programs. We also explore several ways to find integer solutions such as cutting planes, branch & bound, and column generation.

Throughout the course, we learn these skills by modeling and solving, for example, scheduling, packing, matching, routing, and network-design problems. We focus on translating practical examples into mixed-integer linear programs. We learn how to use solvers (such as CPLEX, XPress, Gurobi and others) via python and tailor the solution process to certain properties of the problem.

We will have special guests from industry on Wednesday: Industry Process Consultants from DELMIA Quintiq, Düsseldorf, will talk about Solving Optimization Problems in Practice. 

Lecturers: Prof. Dr. Nicole Megow and group

This course consists of two phases:

  • One week of lectures and practical labs: MZH 5500, September 23-27, 2024, Mon-Fri (9 am till 5 pm with breaks inbetween)
  • An individual project period: One project has to be modeled, implemented, and solved individually or in a group of at most two students. The topic will be either developed with or provided by the lecturers. The project including the implementation has to be presented in the beginning of the winter semester.

There are no prerequisites needed except some basic programming skills.


Please register via StudIP.

Updated by: Lukas Barning
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