@misc{OPUS4-6998, title = {Two Approximate Dynamic Programming Algorithms for Managing Complete SIS Networks}, editor = {COMPASS '18,}, publisher = {ACM New York, NY, USA}, isbn = {978-1-4503-5816-3}, doi = {10.1145/3209811.3209814}, year = {2018}, abstract = {Inspired by the problem of best managing the invasive mosquito Aedes albopictus across the 17 Torres Straits islands of Australia, we aim at solving a Markov decision process on large Susceptible-Infected-Susceptible (SIS) networks that are highly connected. While dynamic programming approaches can solve sequential decision-making problems on sparsely connected networks, these approaches are intractable for highly connected networks. Inspired by our case study, we focus on problems where the probability of nodes changing state is low and propose two approximate dynamic programming approaches. The first approach is a modified version of value iteration where only those future states that are similar to the current state are accounted for. The second approach models the state space as continuous instead of binary, with an on-line algorithm that takes advantage of Bellman's adapted equation. We evaluate the resulting policies through simulations and provide a priority order to manage the 17 infested Torres Strait islands. Both algorithms show promise, with the continuous state approach being able to scale up to high dimensionality (50 nodes). This work provides a successful example of how AI algorithms can be designed to tackle challenging computational sustainability problems.}, language = {en} } @inproceedings{GleixnerWeltge2013, author = {Gleixner, Ambros and Weltge, Stefan}, title = {Learning and Propagating Lagrangian Variable Bounds for Mixed-Integer Nonlinear Programming}, volume = {7874}, booktitle = {Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 10th International Conference, CPAIOR 2013, Yorktown Heights, NY, USA, May 18-22, 2013}, doi = {10.1007/978-3-642-38171-3_26}, pages = {355 -- 361}, year = {2013}, abstract = {Optimization-based bound tightening (OBBT) is a domain reduction technique commonly used in nonconvex mixed-integer nonlinear programming that solves a sequence of auxiliary linear programs. Each variable is minimized and maximized to obtain the tightest bounds valid for a global linear relaxation. This paper shows how the dual solutions of the auxiliary linear programs can be used to learn what we call Lagrangian variable bound constraints. These are linear inequalities that explain OBBT's domain reductions in terms of the bounds on other variables and the objective value of the incumbent solution. Within a spatial branch-and-bound algorithm, they can be learnt a priori (during OBBT at the root node) and propagated within the search tree at very low computational cost. Experiments with an implementation inside the MINLP solver SCIP show that this reduces the number of branch-and-bound nodes and speeds up solution times.}, language = {en} } @inproceedings{GleixnerSteffyWolter2012, author = {Gleixner, Ambros and Steffy, Daniel and Wolter, Kati}, title = {Improving the Accuracy of Linear Programming Solvers with Iterative Refinement}, booktitle = {ISSAC '12. Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation}, doi = {10.1145/2442829.2442858}, pages = {187 -- 194}, year = {2012}, language = {en} } @article{RaackKosterOrlowskietal.2011, author = {Raack, Christian and Koster, Arie M.C.A. and Orlowski, Sebastian and Wess{\"a}ly, Roland}, title = {On cut-based inequalities for capacitated network design polyhedra}, volume = {57}, journal = {Networks}, number = {2}, pages = {141 -- 156}, year = {2011}, language = {en} } @inproceedings{SofranacGleixnerPokutta2021, author = {Sofranac, Boro and Gleixner, Ambros and Pokutta, Sebastian}, title = {An Algorithm-Independent Measure of Progress for Linear Constraint Propagation}, volume = {210}, booktitle = {27th International Conference on Principles and Practice of Constraint Programming (CP 2021)}, doi = {10.4230/LIPIcs.CP.2021.52}, pages = {52:1 -- 52:17}, year = {2021}, abstract = {Propagation of linear constraints has become a crucial sub-routine in modern Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with tolerance-based stopping criteria are used to avoid problems with slow or infinite convergence. However, these heuristic stopping criteria can pose difficulties for fairly comparing the efficiency of different implementations of iterative propagation algorithms in a real-world setting. Most significantly, the presence of unbounded variable domains in the problem formulation makes it difficult to quantify the relative size of reductions performed on them. In this work, we develop a method to measure -- independently of the algorithmic design -- the progress that a given iterative propagation procedure has made at a given point in time during its execution. Our measure makes it possible to study and better compare the behavior of bounds propagation algorithms for linear constraints. We apply the new measure to answer two questions of practical relevance: (i) We investigate to what extent heuristic stopping criteria can lead to premature termination on real-world MIP instances. (ii) We compare a GPU-parallel propagation algorithm against a sequential state-of-the-art implementation and show that the parallel version is even more competitive in a real-world setting than originally reported.}, language = {en} } @article{FrankChiLauSzabo2008, author = {Frank, A. and Chi Lau, L. and Szab{\´o}, J{\´a}cint}, title = {A note on degree-constrained subgraphs}, volume = {308}, journal = {Discrete Mathematics}, number = {12}, publisher = {Elsevier}, pages = {2647 -- 2648}, year = {2008}, language = {en} } @misc{Eifler2017, type = {Master Thesis}, author = {Eifler, Leon}, title = {Mixed-Integer Programming for Clustering in Non-reversible Markov Processes}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66486}, pages = {74}, year = {2017}, abstract = {The topic of this thesis is the examination of an optimization model which stems from the clustering process of non-reversible markov processes. We introduce the cycle clustering problem und formulate it as a mixed integer program (MIP). We prove that this problem is N P-hard and discuss polytopal aspects such as facets and dimension. The focus of this thesis is the development of solving methods for this clustering problem. We develop problem specific primal heuristics, as well as separation methods and an approximation algorithm. These techniques are implemented in practice as an application for the MIP solver SCIP. Our computational experiments show that these solving methods result in an average speedup of ×4 compared to generic solvers and that our application is able to solve more instances to optimality within the given time limit of one hour.}, language = {en} } @misc{EiflerGleixnerPulaj2018, author = {Eifler, Leon and Gleixner, Ambros and Pulaj, Jonad}, title = {Chv{\´a}tal's Conjecture Holds for Ground Sets of Seven Elements}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-70240}, year = {2018}, abstract = {We establish a general computational framework for Chv{\´a}tal's conjecture based on exact rational integer programming. As a result we prove Chv{\´a}tal's conjecture holds for all downsets whose union of sets contains seven elements or less. The computational proof relies on an exact branch-and-bound certificate that allows for elementary verification and is independent of the integer programming solver used.}, language = {en} } @incollection{Groetschel2005, author = {Gr{\"o}tschel, Martin}, title = {Der junge Albring und Schwelm}, booktitle = {Der Forscher und der Zweifler - Werner Albring zum 90. Geburtstag}, editor = {der Wissenschaften, Berlin-Brandenburgische}, publisher = {Berlin-Brandenburgische Akademie der Wissenschaften}, pages = {11 -- 35}, year = {2005}, language = {en} } @incollection{GroetschelHillerTuchscherer2009, author = {Gr{\"o}tschel, Martin and Hiller, Benjamin and Tuchscherer, Andreas}, title = {Structuring a Dynamic Environment}, booktitle = {Emergence, Analysis and Evolution of Structures. Concepts and Strategies Across Disciplines}, editor = {Lucas, Klaus and Roosen, Peter}, publisher = {Springer}, doi = {10.1007/978-3-642-00870-2}, pages = {199 -- 214}, year = {2009}, language = {en} } @incollection{GroetschelKochHoang2010, author = {Gr{\"o}tschel, Martin and Koch, Thorsten and Hoang, Nam-Dung}, title = {Lagenwechsel minimieren - oder das Bohren von L{\"o}chern in Leiterplatten}, booktitle = {Besser als Mathe}, editor = {Biermann, Katja and Gr{\"o}tschel, Martin and Lutz-Westphal, Brigitte}, publisher = {Vieweg+Teubner}, doi = {10.1007/978-3-658-01004-1_19}, pages = {161 -- 174}, year = {2010}, language = {en} } @incollection{Groetschel2008, author = {Gr{\"o}tschel, Martin}, title = {Tiefensuche}, volume = {58}, booktitle = {Kosmos und Zahl - Beitr{\"a}ge zur Mathematik- und Astronomiegeschichte, zu Alexander von Humboldt und Leibniz}, editor = {Hecht, Hartmut and Mikosch, Regina and Schwarz, Ingo and Siebert, Harald and Werther, Romy}, publisher = {Franz Steiner Verlag}, pages = {331 -- 346}, year = {2008}, language = {en} } @incollection{GroetschelLuegger2007, author = {Gr{\"o}tschel, Martin and L{\"u}gger, Joachim}, title = {Die Wissenschaftsgalaxis}, booktitle = {eUniversity - Update Bologna}, editor = {Keil, Reinhard and Kerres, Michael and Schulmeister, Rolf}, publisher = {Waxmann Verlag}, pages = {335 -- 354}, year = {2007}, language = {en} } @incollection{Groetschel2008, author = {Gr{\"o}tschel, Martin}, title = {Geistiges Eigentum - Eine Zusammenfassung der vorgetragenen Standpunkte}, volume = {Heft 7}, booktitle = {Geistiges Eigentum - Streitgespr{\"a}che in den Wissenschaftlichen Sitzungen der Versammlung der Berlin-Brandenburgischen Akademie der Wissenschaften}, editor = {der Wissenschaften, Berlin-Brandenburgische}, publisher = {Berlin-Brandenburgische Akademie der Wissenschaften}, pages = {89 -- 95}, year = {2008}, language = {en} } @incollection{Groetschel2008, author = {Gr{\"o}tschel, Martin}, title = {Geistiges Eigentum - Einf{\"u}hrung in das Thema}, volume = {Heft 7}, booktitle = {Geistiges Eigentum - Streitgespr{\"a}che in den Wissenschaftlichen Sitzungen der Versammlung der Berlin-Brandenburgischen Akademie der Wissenschaften}, editor = {der Wissenschaften, Berlin-Brandenburgische}, publisher = {Berlin-Brandenburgische Akademie der Wissenschaften}, pages = {9 -- 14}, year = {2008}, language = {en} } @incollection{Groetschel2007, author = {Gr{\"o}tschel, Martin}, title = {Schnelle Rundreisen}, booktitle = {Kombinatorische Optimierung erleben - In Studium und Unterricht}, editor = {Hußmann, Stephan and Lutz-Westphal, Brigitte}, publisher = {Vieweg}, address = {Wiesbaden}, pages = {95 -- 128}, year = {2007}, language = {en} } @misc{Groetschel2007, author = {Gr{\"o}tschel, Martin}, title = {Das Problem mit der Komplexit{\"a}t}, journal = {Kombinatorische Optimierung erleben - In Studium und Unterricht}, editor = {Hußmann, Stephan and Lutz-Westphal, Brigitte}, publisher = {Vieweg}, address = {Wiesbaden}, doi = {10.1007/978-3-8348-9120-4_9}, pages = {265 -- 274}, year = {2007}, language = {en} } @incollection{Groetschel2004, author = {Gr{\"o}tschel, Martin}, title = {Cardinality Homogeneous Set Systems, Cycles in Matroids, and Associated Polytopes}, booktitle = {The Sharpest Cut}, editor = {Gr{\"o}tschel, Martin}, publisher = {MPS-SIAM}, pages = {99 -- 120}, year = {2004}, language = {en} } @incollection{Groetschel2005, author = {Gr{\"o}tschel, Martin}, title = {In der Mathematik sind sich alle einig und die Gesellschaft hat von ihr nichts zu bef{\"u}rchten}, volume = {2}, booktitle = {Wissenschaft Kontrovers}, publisher = {Chronos, Edition Collegium Helveticum}, address = {Z{\"u}rich}, year = {2005}, language = {en} } @incollection{Groetschel2008, author = {Gr{\"o}tschel, Martin}, title = {Ohne x is nix}, volume = {14}, booktitle = {Berichte und Abhandlungen}, editor = {der Wissenschaften, Berlin-Brandenburgische}, publisher = {Akademie-Verlag}, address = {Berlin}, pages = {195 -- 219}, year = {2008}, language = {en} } @misc{Groetschel2008, author = {Gr{\"o}tschel, Martin}, title = {Tiefensuche: Bemerkungen zur Algorithmengeschichte}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9628}, number = {08-23}, year = {2008}, abstract = {Dieser kurze Aufsatz zur Algorithmengeschichte ist Eberhard Knobloch, meinem Lieblings-Mathematikhistoriker, zum 65. Geburtstag gewidmet. Eberhard Knobloch hat immer, wenn ich ihm eine historische Frage zur Mathematik stellte, eine Antwort gewusst - fast immer auch sofort. Erst als ich mich selbst ein wenig und dazu amateurhaft mit Mathematikgeschichte besch{\"a}ftigte, wurde mir bewusst, wie schwierig dieses „Gesch{\"a}ft" ist. Man muss nicht nur mehrere (alte) Sprachen beherrschen, sondern auch die wissenschaftliche Bedeutung von Begriffen und Symbolen in fr{\"u}heren Zeiten kennen. Man muss zus{\"a}tzlich herausfinden, was zur Zeit der Entstehung der Texte „allgemeines Wissen" war, insbesondere, was seinerzeit g{\"u}ltige Beweisideen und -schritte waren, und daher damals keiner pr{\"a}zisen Definition oder Einf{\"u}hrung bedurfte. Es gibt aber noch eine Steigerung des historischen Schwierigkeitsgrades: Algorithmengeschichte. Dies m{\"o}chte ich in diesem Artikel kurz darlegen in der Hoffnung, dass sich Wissenschaftshistoriker dieses Themas noch intensiver annehmen, als sie das bisher tun. Der Grund ist, dass heute Algorithmen viele Bereiche unserer Alltagswelt steuern und unser t{\"a}gliches Leben oft von funktionierenden Algorithmen abh{\"a}ngt. Daher w{\"a}re eine bessere Kenntnis der Algorithmengeschichte von großem Interesse.}, language = {de} }