Originally being a mathematician my interests are tending towards more abstract concepts like
Graph Theory
Algebra and Number Theory
Analytic Combinatorics
Representation Theory.
However, utilizing the abstract way of thinking to tackle more concrete problems enjoys me. For instance, I am also interested in
Complexity of Counting Problems
Game Theory
Random Graphs and Networks in different Geometries
Evolutionary Algorithms.
Miscellaneous
Fun Facts
The golden ratio is not always nice to have. The clock-scheme for the visualization of continuous fractions due to L.R. Ford gives for the golden ratio the result you can find on the left hand side. Taking the numbers mod 12 results in a clock, that might prevent you from calling it a day!
Kötzing, Timo; Lagodzinski, J. A. Gregor; Lengler, Johannes; Melnichenko, AnnaDestructiveness of Lexicographic Parsimony Pressure and Alleviation by a Concatenation Crossover in Genetic Programming. Parallel Problem Solving From Nature (PPSN) 2018
Friedrich, Tobias; Kötzing, Timo; Lagodzinski, J. A. Gregor; Neumann, Frank; Schirneck, MartinAnalysis of the (1+1) EA on Subclasses of Linear Functions under Uniform and Linear Constraints. Theoretical Computer Science 2018
Linear functions have gained great attention in the run time analysis of evolutionary computation methods. The corresponding investigations have provided many effective tools for analyzing more complex problems. So far, the runtime analysis of evolutionary algorithms has mainly focused on unconstrained problems, but problems occurring in applications frequently involve constraints. Therefore, there is a strong need to extend the methods for analyzing unconstrained problems to a setting involving constraints. In this paper, we consider the behavior of the classical (1+1) evolutionary algorithm on linear functions under linear constraint. We show tight bounds in the case where the constraint is given by the OneMax function and the objective function is given by either the OneMax or the BinVal function. For the general case we present upper and lower bounds.
Göbel, Andreas; Lagodzinski, J. A. Gregor; Seidel, KarenCounting Homomorphisms to Trees Modulo a Prime. arXiv 2018
While many optimization problems work with a fixed number of decision variables and thus a fixed-length representation of possible solutions, genetic programming (GP) works on variable-length representations. A naturally occurring problem is that of bloat (unnecessary growth of solutions) slowing down optimization. Theoretical analyses could so far not bound bloat and required explicit assumptions on the magnitude of bloat. In this paper we analyze bloat in mutation-based genetic programming for the two test functions ORDER and MAJORITY. We overcome previous assumptions on the magnitude of bloat and give matching or close-to-matching upper and lower bounds for the expected optimization time. In particular, we show that the \((1+1)\) GP takes (i) \(\Theta(T_\text{init + n\, \log n)\) iterations with bloat control on ORDER as well as MAJORITY; and (ii) \(O(T_{\text{init ,log \,T_{\text{init + n(\log n)^3)\) and \(\Omega(T_\text{init + n \,\log n)\) (and \(\Omega(T_\text{init \,\log \,T_{\text{init}})\) for \(n = 1\)) iterations without bloat control on MAJORITY.
Friedrich, Tobias; Kötzing, Timo; Lagodzinski, J. A. Gregor; Neumann, Frank; Schirneck, MartinAnalysis of the (1+1) EA on Subclasses of Linear Functions under Uniform and Linear Constraints. Foundations of Genetic Algorithms (FOGA) 2017: 45-54
Linear functions have gained a lot of attention in the area of run time analysis of evolutionary computation methods and the corresponding analyses have provided many effective tools for analyzing more complex problems. In this paper, we consider the behavior of the classical (1+1) Evolutionary Algorithm for linear functions under linear constraint. We show tight bounds in the case where both the objective function and the constraint is given by the OneMax function and present upper bounds as well as lower bounds for the general case. Furthermore, we also consider the LeadingOnes fitness function.
Randomisierte Algorithmen II, Winter 2016/17, HPI Potsdam
Short CV
Education
June 2008: German high school degree (Abitur) from Schadow Gymnasium Berlin, Germany
Oct. 2008 - Sept. 2012: Undergraduate studies in mathematics at FU Berlin, Germany
Feb. 2013: Bachelor of Science degree in mathematics
Oct. 2012 - Mar. 2016: Graduate studies in mathematics at FU Berlin, Germany
Oct. 2015: Master of Science degree in mathematics
Positions
Aug. 2011 - July 2013: Student Assistant in the ERC Advanced Grant Project SDModels at the chair for Discrete Geometry at FU Berlin, Germany.
Starting 2016: Ph.D. student and researcher at the chair for Algorithm Engineering at HPI Potsdam, Germany
Algorithm Engineering
Our research focus is on theoretical computer science and algorithm engineering. We are equally interested in the mathematical foundations of algorithms and developing efficient algorithms in practice. A special focus is on random structures and methods.