@misc{FerreiraMartinWeismantel1993, author = {Ferreira, Carlos E. and Martin, Alexander and Weismantel, Robert}, title = {Facets for the Multiple Knapsack Problem.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1007}, number = {SC-93-04}, year = {1993}, abstract = {In this paper we consider the multiple knapsack problem which is defined as follows: given a set \$N\$ of items with weights \$f_i\$, \$i \in N\$, a set \$M\$ of knapsacks with capacities \$F_k\$, \$k \in M\$, and a profit function \$c_{ik}, i \in N, k \in M\$; find an assignment of a subset of the set of items to the set of knapsacks that yields maximum profit (or minimum cost). With every instance of this problem we associate a polyhedron whose vertices are in one to one correspondence to the feasible solutions of the instance. This polytope is the subject of our investigations. In particular, we present several new classes of inequalities and work out necessary and sufficient conditions under which the corresponding inequality defines a facet. Some of these conditions involve only properties of certain knapsack constraints, and hence, apply to the generalized assignment polytope as well. The results presented here serve as the theoretical basis for solving practical problems. The algorithmic side of our study, i.e., separation algorithms, implementation details and computational experience with a branch and cut algorithm are discussed in the companion paper SC 93-07.}, language = {en} } @misc{MartinWeismantel1998, author = {Martin, Alexander and Weismantel, Robert}, title = {Conjunctive Cuts for Integer Programs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3618}, number = {SC-98-18}, year = {1998}, abstract = {This paper deals with a family of conjunctive inequalities. Such inequalities are needed to describe the polyhedron associated with all the integer points that satisfy several knapsack constraints simultaneously. Here we demonstrate the strength and potential of conjunctive inequalities in connection with lifting from a computational point of view.}, language = {en} } @misc{BorndoerferEisenblaetterGroetscheletal.1997, author = {Bornd{\"o}rfer, Ralf and Eisenbl{\"a}tter, Andreas and Gr{\"o}tschel, Martin and Martin, Alexander}, title = {Frequency Assignment in Cellular Phone Networks}, doi = {10.1023/A:1018908907763}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3044}, number = {SC-97-35}, year = {1997}, abstract = {We present a graph-theoretic model for the \emph{frequency assignment problem} in Cellular Phone Networks: Obeying several technical and legal restrictions, frequencies have to be assigned to transceivers so that interference is as small as possible. This optimization problem is NP-hard. Good approximation cannot be guaranteed, unless P = NP. We describe several assignment heuristics. These heuristics are simple and not too hard to implement. We give an assessment of the heuristics' efficiency and practical usefulness. For this purpose, typical instances of frequency assignment problems with up to 4240 transceivers and 75 frequencies of a German cellular phone network operator are used. The results are satisfying from a practitioner's point of view. The best performing heuristics were integrated into a network planning system used in practice.}, language = {en} } @misc{MartinWeismantel1997, author = {Martin, Alexander and Weismantel, Robert}, title = {Contributions to General Mixed Integer Knapsack Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3075}, number = {SC-97-38}, year = {1997}, abstract = {This paper deals with a general mixed integer knapsack polyhedron for which we introduce and analyze a new family of inequalities. We discuss the value of this family both from a theoretic and a computational point of view.}, language = {en} } @misc{BrunsGubeladzeHenketal.1998, author = {Bruns, Winfried and Gubeladze, Joseph and Henk, Martin and Martin, Alexander and Weismantel, Robert}, title = {A counterexample to an integer analogue of Caratheodorys theorem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3718}, number = {SC-98-28}, year = {1998}, abstract = {For \$n\geq 6\$ we provide a counterexample to the conjecture that every integral vector of a \$n\$-dimensional integral polyhedral pointed cone \$C\$ can be written as a nonnegative integral combination of at most \$n\$ elements of the Hilbert basis of \$C\$. In fact, we show that in general at least \$\lfloor 7/6 \cdot n \rfloor\$ elements of the Hilbert basis are needed.}, language = {en} } @article{GamrathGleixnerKochetal.2019, author = {Gamrath, Gerald and Gleixner, Ambros and Koch, Thorsten and Miltenberger, Matthias and Kniasew, Dimitri and Schl{\"o}gel, Dominik and Martin, Alexander and Weninger, Dieter}, title = {Tackling Industrial-Scale Supply Chain Problems by Mixed-Integer Programming}, volume = {37}, journal = {Journal of Computational Mathematics}, doi = {10.4208/jcm.1905-m2019-0055}, pages = {866 -- 888}, year = {2019}, abstract = {The modeling flexibility and the optimality guarantees provided by mixed-integer programming greatly aid the design of robust and future-proof decision support systems. The complexity of industrial-scale supply chain optimization, however, often poses limits to the application of general mixed-integer programming solvers. In this paper we describe algorithmic innovations that help to ensure that MIP solver performance matches the complexity of the large supply chain problems and tight time limits encountered in practice. Our computational evaluation is based on a diverse set, modeling real-world scenarios supplied by our industry partner SAP.}, language = {en} } @article{AignerClarnerLiersetal.2021, author = {Aigner, Kevin-Martin and Clarner, Jan-Patrick and Liers, Frauke and Martin, Alexander}, title = {Robust Approximation of Chance Constrained DC Optimal Power Flow under Decision-Dependent Uncertainty}, journal = {European Journal of Operational Research}, year = {2021}, abstract = {We propose a mathematical optimization model and its solution for joint chance constrained DC Optimal Power Flow. In this application, it is particularly important that there is a high probability of transmission limits being satisfied, even in the case of uncertain or fluctuating feed-in from renewable energy sources. In critical network situations where the network risks overload, renewable energy feed-in has to be curtailed by the transmission system operator (TSO). The TSO can reduce the feed-in in discrete steps at each network node. The proposed optimization model minimizes curtailment while ensuring that there is a high probability of transmission limits being maintained. The latter is modeled via (joint) chance constraints that are computationally challenging. Thus, we propose a solution approach based on the robust safe approximation of these constraints. Hereby, probabilistic constraints are replaced by robust constraints with suitably defined uncertainty sets constructed from historical data. The ability to discretely control the power feed-in then leads to a robust optimization problem with decision-dependent uncertainties, i.e. the uncertainty sets depend on decision variables. We propose an equivalent mixed-integer linear reformulation for box uncertainties with the exact linearization of bilinear terms. Finally, we present numerical results for different test cases from the Nesta archive, as well as for a real network. We consider the discrete curtailment of solar feed-in, for which we use real-world weather and network data. The experimental tests demonstrate the effectiveness of this method and run times are very fast. Moreover, on average the calculated robust solutions only lead to a small increase in curtailment, when compared to nominal solutions.}, language = {en} } @article{KochSchmidtHilleretal.2020, author = {Koch, Thorsten and Schmidt, Martin and Hiller, Benjamin and Pfetsch, Marc and Geißler, Bj{\"o}rn and Henrion, Ren{\´e} and Joormann, Imke and Martin, Alexander and Morsi, Antonio and R{\"o}misch, Werner and Schewe, Lars and Schultz, R{\"u}diger}, title = {Capacity Evaluation for Large-Scale Gas Networks}, volume = {35}, journal = {German Success Stories in Industrial Mathematics}, isbn = {978-3-030-81454-0}, doi = {10.1007/978-3-030-81455-7}, pages = {23 -- 28}, year = {2020}, language = {en} } @misc{GamrathKochMartinetal.2013, author = {Gamrath, Gerald and Koch, Thorsten and Martin, Alexander and Miltenberger, Matthias and Weninger, Dieter}, title = {Progress in Presolving for Mixed Integer Programming}, issn = {1438-0064}, doi = {10.1007/s12532-015-0083-5}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42530}, year = {2013}, abstract = {Presolving attempts to eliminate redundant information from the problem formulation and simultaneously tries to strengthen the formulation. It can be very effective and is often essential for solving instances. Especially for mixed integer programming problems, fast and effective presolving algorithms are very important. In this paper, we report on three new presolving techniques. The first method searches for singleton continuous columns and tries to fix the corresponding variables. Then we present a presolving technique which exploits a partial order of the variables to induce fixings. Finally, we show an approach based on connected components in graphs. Our computational results confirm the profitable use of the algorithms in practice.}, language = {en} } @misc{KochMartinVoss2000, author = {Koch, Thorsten and Martin, Alexander and Voß, Stefan}, title = {SteinLib: An Updated Library on Steiner Tree Problems in Graphs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6056}, number = {00-37}, year = {2000}, abstract = {In this paper we present the {\em SteinLib}, a library of data sets for the Steiner tree problem in graphs. This library extends former libraries on Steiner tree problems by many new interesting and difficult instances, most of them arising from real-world applications. We give a survey on the difficulty of these problem instances by giving references to state-of-the-art software packages that were the first or are currently among the best to solve these instances.}, language = {en} } @misc{EisenblaetterFuegenschuhKochetal.2002, author = {Eisenbl{\"a}tter, Andreas and F{\"u}genschuh, Armin and Koch, Thorsten and Koster, Arie M.C.A. and Martin, Alexander and Pfender, Tobias and Wegel, Oliver and Wess{\"a}ly, Roland}, title = {Modelling Feasible Network Configurations for UMTS}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6837}, number = {02-16}, year = {2002}, abstract = {A model for the optimisation of the location and configuration of base stations in a UMTS network is described. The focus is primarily on modelling the configuration problem sufficiently accurate using mixed-integer variables and (essentially) linear constraints. These constraints reflect the limited downlink code capacity in each cell, the interference limitations for successful up- and downlink transmissions, the need for sufficiently strong (cell) pilot signals, and the potential gain for mobiles from being in soft(er) hand-over. It is also explained how to use the model as a basis for rating network configurations.}, language = {en} } @misc{AchterbergKochMartin2002, author = {Achterberg, Tobias and Koch, Thorsten and Martin, Alexander}, title = {Branching on History Information}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6990}, number = {02-32}, year = {2002}, abstract = {Mixed integer programs (\$MIPs\$) are commonly solved with branch and bound algorithms based on linear programming. The success and the speed of the algorithm strongly depends on the strategy used to select the branching variables. Today's state-of-the-art strategy is called \emph{pseudocost branching} and uses information of previous branchings to determine the current branching. We propose a modification of \emph{pseudocost branching} which we call \emph{history branching}. This strategy has been implemented in \$SIP\$, a state-of-the-art \$MIP\$ solver. We give computational results that show the superiority of the new strategy.}, language = {en} } @misc{EisenblaetterFuegenschuhGeerdesetal.2003, author = {Eisenbl{\"a}tter, Andreas and F{\"u}genschuh, Armin and Geerdes, Hans-Florian and Junglas, Daniel and Koch, Thorsten and Martin, Alexander}, title = {Optimization Methods for UMTS Radio Network Planning}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7637}, number = {03-41}, year = {2003}, abstract = {The UMTS radio network planning problem poses the challenge of designing a cost-effective network that provides users with sufficient coverage and capacity. We describe an optimization model for this problem that is based on comprehensive planning data of the EU project MOMENTUM. We present heuristic mathematical methods for this realistic model, including computational results.}, language = {en} } @phdthesis{Martin1992, author = {Martin, Alexander}, title = {Packen von Steinerb{\"a}umen: Polyedrische Studien und Anwendung.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4894}, number = {TR-92-04}, year = {1992}, abstract = {Gegeben sei ein Graph \$G=(V,E)\$ mit positiven Kantenkapazit{\"a}ten \$c_e\$ und Knotenmengen \$T_1,\ldots,T_N\$. Das Steinerbaumpackungs-Problem besteht darin, Kantenmengen \$S_1,\ldots,S_N\$ zu finden, so da\ss\ jedes \$S_k\$ die Knoten aus \$T_k\$ verbindet und jede Kante \$e\$ in h{\"o}chstens \$c_e\$ Kantenmengen aus \$S_1,\ldots,S_N\$ vorkommt. Eine zul{\"a}ssige L{\"o}sung dieses Problems nennen wir eine Steinerbaumpackung. Ist zus{\"a}tzlich eine Gewichtung der Kanten gegeben und nach einer bez{\"u}glich dieser Gewichtung minimalen Steinerbaumpackung gesucht, so sprechen wir vom gewichteten Steinerbaumpackungs-Problem. Die Motivation zum Studium dieses Problems kommt aus dem Entwurf elektronischer Schaltungen. Ein dort auftretendes Teilproblem ist das sogenannte Verdrahtungsproblem, das im wesentlichen darin besteht, gegebene Punktmengen unter bestimmten Nebenbedingungen und Optimalit{\"a}tskriterien auf einer Grundfl{\"a}che zu verbinden. Wir studieren das Steinerbaumpackungs-Problem aus polyedrischer Sicht und definieren ein Polyeder, dessen Ecken genau den Steinerbaumpackungen entsprechen. Anschlie\ss end versuchen wir, dieses Polyeder durch gute'' beziehungsweise facetten-definierenden Ungleichungen zu beschreiben. Basierend auf diesen Ungleichungen entwickeln wir ein Schnittebenenverfahren. Die L{\"o}sung des Schnittebenenverfahrens liefert eine untere Schranke f{\"u}r die Optimall{\"o}sung und dient als Grundlage f{\"u}r die Entwicklung guter Primalheuristiken. Wir haben das von uns implementierte Schnittebenenverfahren an einem Spezialfall des Verdrahtungsproblems, dem sogenannten Switchbox-Verdrahtungsproblem, getestet und vielversprechende Ergebnisse erzielt.}, language = {de} } @misc{BorndoerferEisenblaetterGroetscheletal.1998, author = {Bornd{\"o}rfer, Ralf and Eisenbl{\"a}tter, Andreas and Gr{\"o}tschel, Martin and Martin, Alexander}, title = {The Orientation Model for Frequency Assignment Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5627}, number = {TR-98-01}, year = {1998}, abstract = {Mobile telecommunication systems establish a large number of communication links with a limited number of available frequencies; reuse of the same or adjacent frequencies on neighboring links causes interference. The task to find an assignment of frequencies to channels with minimal interference is the frequency assignment problem. The frequency assignment problem is usually treated as a graph coloring problem where the number of colors is minimized, but this approach does not model interference minimization correctly. We give in this paper a new integer programming formulation of the frequency assignment problem, the orientation model, and develop a heuristic two-stage method to solve it. The algorithm iteratively solves an outer and an inner optimization problem. The outer problem decides for each pair of communication links which link gets the higher frequency and leads to an acyclic subdigraph problem with additional longest path restrictions. The inner problem to find an optimal assignment respecting an orientation leads to a min-cost flow problem.}, language = {en} } @misc{MarchandMartinWeismanteletal.1999, author = {Marchand, Hugues and Martin, Alexander and Weismantel, Robert and Wolsey, Laurence}, title = {Cutting Planes in Integer and Mixed Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4339}, number = {SC-99-44}, year = {1999}, abstract = {This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs. Valid inequalities for i) general integer programs, ii) problems with local structure such as knapsack constraints, and iii) problems with 0-1 coefficient matrices, such as set packing, are examined in turn. Finally the use of valid inequalities for classes of problems with structure, such as network design, is explored.}, language = {en} } @misc{MartinWeismantel1997, author = {Martin, Alexander and Weismantel, Robert}, title = {The Intersection of Knapsack Polyhedra and Extensions}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3300}, number = {SC-97-61}, year = {1997}, abstract = {This paper introduces a scheme of deriving strong cutting planes for a general integer programming problem. The scheme is related to Chvatal-Gomory cutting planes and important special cases such as odd hole and clique inequalities for the stable set polyhedron or families of inequalities for the knapsack polyhedron. We analyze how relations between covering and incomparability numbers associated with the matrix can be used to bound coefficients in these inequalities. For the intersection of several knapsack polyhedra, incomparabilities between the column vectors of the associated matrix will be shown to transfer into inequalities of the associated polyhedron. Our scheme has been incorporated into the mixed integer programming code SIP. About experimental results will be reported.}, language = {en} } @misc{AchterbergKochMartin2004, author = {Achterberg, Tobias and Koch, Thorsten and Martin, Alexander}, title = {Branching rules revisited}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7886}, number = {04-13}, year = {2004}, abstract = {Mixed integer programs are commonly solved with linear programming based branch-and-bound algorithms. The success of the algorithm strongly depends on the strategy used to select the variable to branch on. We present a new generalization called {\sl reliability branching} of today's state-of-the-art {\sl strong branching} and {\sl pseudocost branching} strategies for linear programming based branch-and-bound algorithms. After reviewing commonly used branching strategies and performing extensive computational studies we compare different parameter settings and show the superiority of our proposed newstrategy.}, language = {en} } @misc{EisenblaetterGeerdesKochetal.2004, author = {Eisenbl{\"a}tter, Andreas and Geerdes, Hans-Florian and Koch, Thorsten and Martin, Alexander and Wess{\"a}ly, Roland}, title = {UMTS Radio Network Evaluation and Optimization beyond Snapshots}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7903}, number = {04-15}, year = {2004}, abstract = {This paper is concerned with UMTS radio network design. Our task is to reconfigure antennas and the related cells as to improve network quality. In contrast to second generation GSM networks, \emph{interference} plays a paramount role when designing third generation radio networks. A known compact formulation for assessing the interference characteristics of a radio network as coupling relations between cells based on user snapshots is generalized to statistical average load. This enables us to overcome the notorious difficulties of snapshot-based network optimization approaches. We recall a mixed-integer programming model for the network design problem that is based on user snapshots and contrast it with a new network design model based on the average coupling formulation. Exemplarily focusing on the important problem of optimizing antenna tilts, we give computational results for a fast local search algorithm and the application of a MIP solver to both models. These results demonstrate that our new average-based approaches outperform state-of-the-art snapshot models for UMTS radio network optimization.}, language = {en} } @article{BaermannMartinPokuttaetal.2018, author = {B{\"a}rmann, Andreas and Martin, Alexander and Pokutta, Sebastian and Schneider, Oskar}, title = {An Online-Learning Approach to Inverse Optimization}, year = {2018}, language = {en} } @article{EisenblaetterGeerdesKochetal.2005, author = {Eisenbl{\"a}tter, Andreas and Geerdes, Hans-Florian and Koch, Thorsten and Martin, Alexander and Wess{\"a}ly, Roland}, title = {UMTS Radio Network Evaluation and Optimization beyond Snapshots}, volume = {63}, journal = {Mathematical Methods of Operations Research}, number = {1}, doi = {10.1007/s00186-005-0002-z}, pages = {1 -- 29}, year = {2005}, language = {en} } @article{GroetschelMartinWeismantel1996, author = {Gr{\"o}tschel, Martin and Martin, Alexander and Weismantel, Robert}, title = {Packing Steiner trees: Polyhedral Investigations}, volume = {72}, journal = {Mathematical Programming, Series A}, number = {2}, doi = {10.1007/BF02592085}, pages = {101 -- 123}, year = {1996}, language = {en} } @article{GroetschelMartinWeismantel1996, author = {Gr{\"o}tschel, Martin and Martin, Alexander and Weismantel, Robert}, title = {Optimum Path Packing on Wheels}, volume = {31}, journal = {Computers and Mathematics with Applications}, number = {11}, publisher = {Elsevier}, pages = {23 -- 35}, year = {1996}, language = {en} } @article{BorndoerferEisenblaetterGroetscheletal.1998, author = {Bornd{\"o}rfer, Ralf and Eisenbl{\"a}tter, Andreas and Gr{\"o}tschel, Martin and Martin, Alexander}, title = {Frequency assignment in cellular phone networks}, volume = {76}, journal = {Annals of Operations Research}, publisher = {J. C. Baltzer AG, Science Publishers}, doi = {10.1023/A:1018908907763}, pages = {73 -- 93}, year = {1998}, language = {en} } @article{GroetschelMartinWeismantel1996, author = {Gr{\"o}tschel, Martin and Martin, Alexander and Weismantel, Robert}, title = {Packing Steiner trees: a cutting plane algorithm and computational results}, volume = {72}, journal = {Mathematical Programming, Series A}, number = {2}, doi = {10.1007/BF02592086}, pages = {125 -- 145}, year = {1996}, language = {en} } @article{GroetschelMartinWeismantel1997, author = {Gr{\"o}tschel, Martin and Martin, Alexander and Weismantel, Robert}, title = {The Steiner tree packing problem in VLSI design}, volume = {78}, journal = {Mathematical Programming}, number = {2}, pages = {265 -- 281}, year = {1997}, language = {en} } @inproceedings{BirkhoferFuegenschuhGuentheretal.2006, author = {Birkhofer, Herbert and F{\"u}genschuh, Armin and G{\"u}nther, Ute and Junglas, Daniel and Martin, Alexander and Sauer, Thorsten and Ulbrich, Stefan and W{\"a}ldele, Martin and Walter, Stephan}, title = {Topology- and shape-optimization of branched sheet metal products}, booktitle = {Operations Research Proceedings}, editor = {Haasis, Hans-Dietrich and Kopfer, Herbert and Sch{\"o}nberger, J{\"o}rn}, pages = {327 -- 336}, year = {2006}, language = {en} } @inproceedings{FuegenschuhHessMartinetal.2007, author = {F{\"u}genschuh, Armin and Hess, Wolfgang and Martin, Alexander and Ulbrich, Stefan}, title = {Diskrete und kontinuierliche Modelle zur Topologie- und Geometrie-Optimierung von Blechprofilen}, booktitle = {Sonderforschungsbereich 666}, editor = {Groche, P.}, pages = {37 -- 47}, year = {2007}, language = {en} } @inproceedings{GroetschelMartinWeismantel1993, author = {Gr{\"o}tschel, Martin and Martin, Alexander and Weismantel, Robert}, title = {Routing in grid graphs by cutting planes}, booktitle = {Integer Programming and Combinatorial Optimization. Proceedings of a Conference held at Centro Ettore Majorana, Erice, Italy, April 29 - May 1, 1993}, editor = {Rinaldi, Giovanni and Wolsey, Laurence}, publisher = {Librarian CORE}, address = {Louvain-la-Neuve}, pages = {447 -- 461}, year = {1993}, language = {en} } @incollection{EisenblaetterFuegenschuhKochetal.2002, author = {Eisenbl{\"a}tter, Andreas and F{\"u}genschuh, Armin and Koch, Thorsten and Koster, Arie M.C.A. and Martin, Alexander and Pfender, Tobias and Wegel, Oliver and Wess{\"a}ly, Roland}, title = {Mathematical Model of Feasible Network Configurations for UMTS}, booktitle = {Telecommunications network design and management}, editor = {G. Anandalingam, S.}, publisher = {Kluwer}, pages = {1 -- 24}, year = {2002}, language = {en} } @inproceedings{FuegenschuhMartinStoeveken2004, author = {F{\"u}genschuh, Armin and Martin, Alexander and St{\"o}veken, Peter}, title = {Integrated Optimization of School Starting Times and Public Bus Services}, booktitle = {Mathematics in the Supply Chain}, editor = {Bixby, Robert E. and Simchi-Levi, D. and Martin, Alexander and Zimmermann, U.}, year = {2004}, language = {en} } @inproceedings{EisenblaetterFuegenschuhGeerdesetal.2004, author = {Eisenbl{\"a}tter, Andreas and F{\"u}genschuh, Armin and Geerdes, Hans-Florian and Junglas, Daniel and Koch, Thorsten and Martin, Alexander}, title = {Integer Programming Methods for UMTS Radio Network Planning}, booktitle = {Proceedings of the WiOpt'04, Cambridge, UK}, year = {2004}, language = {en} } @incollection{FuegenschuhMartin2005, author = {F{\"u}genschuh, Armin and Martin, Alexander}, title = {Computational Integer Programming and Cutting Planes}, booktitle = {Handbooks in Operations Research and Management Science, Vol. 12}, editor = {Aardal, Karen I. and Nemhauser, George and Weismantel, R.}, publisher = {North-Holland}, pages = {69 -- 122}, year = {2005}, language = {en} } @inproceedings{FuegenschuhHomfeldHucketal.2006, author = {F{\"u}genschuh, Armin and Homfeld, Henning and Huck, Andreas and Martin, Alexander}, title = {Locomotive and Wagon Scheduling in Freight Transport}, booktitle = {Proceedings of the ATMOS06}, editor = {Jacob, R. and M{\"u}ller-Hannemann, Matthias}, year = {2006}, language = {en} } @inproceedings{FuegenschuhMartinMehlertetal.2005, author = {F{\"u}genschuh, Armin and Martin, Alexander and Mehlert, Christian and St{\"o}veken, Peter}, title = {Ein Planungstool zur Schulzeitstaffelung}, booktitle = {Supply Chain Management und Logistik}, editor = {G{\"u}nther, H.-O. and Mattfeld, D. and Suhl, L.}, pages = {419 -- 436}, year = {2005}, language = {en} } @inproceedings{FuegenschuhMartinStoeveken2005, author = {F{\"u}genschuh, Armin and Martin, Alexander and St{\"o}veken, Peter}, title = {Integrated Optimization of School Starting Times and Public Bus Services}, booktitle = {Operations Research Proceedings}, editor = {Fleuren, Hein and den Hertog, Dick and Kort, Peter}, pages = {150 -- 157}, year = {2005}, language = {en} } @inproceedings{FuegenschuhMartin2007, author = {F{\"u}genschuh, Armin and Martin, Alexander}, title = {Mixed-integer models for topology optimization in sheet metal design}, booktitle = {Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Z{\"u}rich 2007}, pages = {2060049 -- 2060050}, year = {2007}, language = {en} } @inproceedings{BirkhoferFuegenschuhMartinetal.2007, author = {Birkhofer, Herbert and F{\"u}genschuh, Armin and Martin, Alexander and W{\"a}ldele, Martin}, title = {Algorithmenbasierte Produktentwicklung f{\"u}r integrale Blechbauweisen h{\"o}herer Verzweigungsordnung}, booktitle = {Optimierung in der Produktentwicklung, 5. Geimeinsames Kolloquium Konstruktionstechnik}, year = {2007}, language = {en} } @inproceedings{FuegenschuhlerMartinetal.2009, author = {F{\"u}genschuh, Armin and ler, Bj{\"o}rn and Martin, Alexander and Morsi, Antonio}, title = {The Transport PDE and Mixed-Integer Linear Programming}, booktitle = {Dagstuhl Seminar Proceedings 09261, Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik, Deutschland}, editor = {Barnhart, Cynthia and Clausen, Uwe and Lauther, Ulrich and M{\"o}hring, Rolf}, year = {2009}, language = {en} } @inproceedings{FuegenschuhHessScheweetal.2008, author = {F{\"u}genschuh, Armin and Hess, Wolfgang and Schewe, Lars and Martin, Alexander and Ulbrich, Stefan}, title = {Verfeinerte Modelle zur Topologie- und Geometrie-Optimierung von Blechprofilen mit Kammern}, booktitle = {Sonderforschungsbereich 666}, editor = {Groche, P.}, pages = {17 -- 28}, year = {2008}, language = {en} } @article{PfetschFuegenschuhGeissleretal.2014, author = {Pfetsch, Marc and F{\"u}genschuh, Armin and Geißler, Bj{\"o}rn and Geißler, Nina and Gollmer, Ralf and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Martin, Alexander and Morsi, Antonio and R{\"o}vekamp, Jessica and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Steinbach, Marc and Vigerske, Stefan and Willert, Bernhard}, title = {Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions}, journal = {Optimization Methods and Software}, publisher = {Taylor \& Francis}, doi = {10.1080/10556788.2014.888426}, year = {2014}, abstract = {In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult feasibility problem. The first phase consists of four distinct algorithms applying linear, and methods for complementarity constraints to compute possible settings for the discrete decisions. The second phase employs a precise continuous programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances that are significantly larger than networks that have appeared in the mathematical programming literature before.}, language = {en} } @article{FuegenschuhGeisslerGollmeretal.2013, author = {F{\"u}genschuh, Armin and Geißler, Bj{\"o}rn and Gollmer, Ralf and Hayn, Christine and Henrion, Ren{\´e} and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Martin, Alexander and Mirkov, Radoslava and Morsi, Antonio and R{\"o}misch, Werner and R{\"o}vekamp, Jessica and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Steinbach, Marc and Willert, Bernhard}, title = {Mathematical optimization for challenging network planning problems in unbundled liberalized gas markets}, volume = {5}, journal = {Energy Systems}, number = {3}, publisher = {Springer Berlin Heidelberg}, address = {Berlin}, doi = {10.1007/s12667-013-0099-8}, pages = {449 -- 473}, year = {2013}, abstract = {The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor were united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We discuss how these changing paradigms lead to new and challenging mathematical optimization problems. This includes the validation of nominations, that asks for the decision if the network's capacity is sufficient to transport a specific amount of flow, the verification of booked capacities and the detection of available freely allocable capacities, and the topological extension of the network with new pipelines or compressors in order to increase its capacity. In order to solve each of these problems and to provide meaningful results for the practice, a mixture of different mathematical aspects have to be addressed, such as combinatorics, stochasticity, uncertainty, and nonlinearity. Currently, no numerical solver is available that can deal with such blended problems out-of-the-box. The main goal of our research is to develop such a solver, that moreover is able to solve instances of realistic size. In this article, we describe the main ingredients of our prototypical software implementations.}, language = {en} } @incollection{BorndoerferHoangKarbsteinetal.2013, author = {Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung and Karbstein, Marika and Koch, Thorsten and Martin, Alexander}, title = {How many Steiner terminals can you connect in 20 years?}, booktitle = {Facets of Combinatorial Optimization; Festschrift for Martin Gr{\"o}tschel}, editor = {J{\"u}nger, Michael and Reinelt, Gerhard}, publisher = {Springer}, doi = {10.1007/978-3-642-38189-8_10}, pages = {215 -- 244}, year = {2013}, language = {en} } @article{BorndoerferFerreiraMartin1998, author = {Bornd{\"o}rfer, Ralf and Ferreira, Carlos and Martin, Alexander}, title = {Decomposing Matrices into Blocks}, volume = {9}, journal = {SIAM J. Optim.}, number = {1}, pages = {236 -- 269}, year = {1998}, language = {en} } @misc{BorndoerferHoangKarbsteinetal.2013, author = {Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung and Karbstein, Marika and Koch, Thorsten and Martin, Alexander}, title = {How Many Steiner Terminals Can You Connect in 20 Years?}, issn = {1438-0064}, doi = {10.1007/978-3-642-38189-8_10}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42524}, year = {2013}, abstract = {Steiner trees are constructed to connect a set of terminal nodes in a graph. This basic version of the Steiner tree problem is idealized, but it can effectively guide the search for successful approaches to many relevant variants, from both a theoretical and a computational point of view. This article illustrates the theoretical and algorithmic progress on Steiner tree type problems on two examples, the Steiner connectivity and the Steiner tree packing problem.}, language = {en} } @article{DuerFuegenschuhMartinetal.2010, author = {D{\"u}r, Mirjam and F{\"u}genschuh, Armin and Martin, Alexander and Schabel, Samuel and Sch{\"o}nberger, Christine and Villforth, Klaus}, title = {Steuerung einer Sortieranlage, z.B. f{\"u}r Altpapier}, volume = {EP 09 718 564.9}, journal = {Europ{\"a}ische Patentanmeldung}, year = {2010}, language = {en} } @article{FuegenschuhHertyKlaretal.2006, author = {F{\"u}genschuh, Armin and Herty, Michael and Klar, Axel and Martin, Alexander}, title = {Combinatorial and Continuous Models and Optimization for Traffic Flow on Networks}, volume = {16}, journal = {SIAM Journal on Optimization}, number = {4}, pages = {1155 -- 1176}, year = {2006}, language = {en} } @article{FuegenschuhMartin2006, author = {F{\"u}genschuh, Armin and Martin, Alexander}, title = {Welche Gemeinsamkeiten haben Jugendliche und Groß banken?}, volume = {129}, journal = {mathematiklehren}, pages = {50 -- 54}, year = {2006}, language = {en} } @article{DuerFuegenschuhMartinetal.2008, author = {D{\"u}r, Mirjam and F{\"u}genschuh, Armin and Martin, Alexander and Schabel, Samuel and Sch{\"o}nberger, Christine and Villforth, Klaus}, title = {Verfahren zum Einstellen und/oder Optimieren einer einen Gutstoff von einem Schlechtstoff trennenden Sortieranlage und Sortieranlage}, volume = {DE 10 2008 013 034}, journal = {Deutsches Patent}, year = {2008}, language = {en} } @article{FuegenschuhMartin2004, author = {F{\"u}genschuh, Armin and Martin, Alexander}, title = {Verfahren und Vorrichtung zur automatischen Optimierung von Schulanfangszeiten und des {\"o}ffentlichen Personenverkehrs und entsprechendes Computerprogramm}, volume = {DE 10 2004 020 786.0}, journal = {Deutsche Patentanmeldung}, year = {2004}, language = {en} } @article{DuerFuegenschuhMartinetal.2006, author = {D{\"u}r, Mirjam and F{\"u}genschuh, Armin and Martin, Alexander and Ulbrich, Stefan}, title = {Verfahren und Vorrichtung zum Auswuchten von wellenelastischen Rotoren}, volume = {DE 10 2006 060 583.7}, journal = {Deutsche Patentanmeldung}, year = {2006}, language = {en} } @article{FuegenschuhGoettlichKirchneretal.2009, author = {F{\"u}genschuh, Armin and G{\"o}ttlich, Simone and Kirchner, Claus and Herty, Michael and Martin, Alexander}, title = {Efficient Reformulation and Solution of a Nonlinear PDE-Controlled Flow Network Model}, volume = {85}, journal = {Computing}, number = {3}, pages = {245 -- 265}, year = {2009}, language = {en} } @article{FuegenschuhGoettlichHertyetal.2008, author = {F{\"u}genschuh, Armin and G{\"o}ttlich, Simone and Herty, Michael and Klar, Alexander and Martin, Alexander}, title = {A Discrete Optimization Approach to Large Scale Supply Networks Based on Partial Differential Equations}, volume = {30}, journal = {SIAM Journal on Scientific Computing}, number = {3}, pages = {1490 -- 1507}, year = {2008}, language = {en} } @article{FuegenschuhHomfeldHucketal.2008, author = {F{\"u}genschuh, Armin and Homfeld, Henning and Huck, Andreas and Martin, Alexander and Yuan, Zhi}, title = {Scheduling Locomotives and Car Transfers in Freight Transport}, volume = {42}, journal = {Transportation Science}, number = {4}, pages = {1 -- 14}, year = {2008}, language = {en} } @article{FuegenschuhMartin2006, author = {F{\"u}genschuh, Armin and Martin, Alexander}, title = {A Multicriterial Approach for Optimizing Bus Schedules and School Starting Times}, volume = {147}, journal = {Annals of Operations Research}, number = {1}, pages = {199 -- 216}, year = {2006}, language = {en} } @article{FerreiraGroetschelMartinetal.1993, author = {Ferreira, Carlos and Gr{\"o}tschel, Martin and Martin, Alexander and Weismantel, Robert and Kiefl, Stefan and Krispenz, Ludwig}, title = {Some Integer Programs Arising in the Design of Main Frame Computers}, volume = {38}, journal = {ZOR - Methods and Models of Operations Research}, number = {1}, pages = {77 -- 100}, year = {1993}, language = {en} } @article{EisenblaetterFuegenschuhFledderusetal.2003, author = {Eisenbl{\"a}tter, Andreas and F{\"u}genschuh, Armin and Fledderus, E. and Geerdes, Hans-Florian and Heideck, B. and Junglas, Daniel and Koch, Thorsten and K{\"u}rner, T. and Martin, Alexander}, title = {Mathematical Methods for Automatic Optimization of UMTS Radio Networks}, number = {D4.3}, editor = {Martin, Alexander}, publisher = {IST-2000-28088 MOMENTUM}, year = {2003}, language = {en} } @article{EisenblaetterGeerdesJunglasetal.2003, author = {Eisenbl{\"a}tter, Andreas and Geerdes, Hans-Florian and Junglas, Daniel and Koch, Thorsten and K{\"u}rner, T. and Martin, Alexander}, title = {Final Report on Automatic Planning and Optimisation}, number = {D4.7}, publisher = {IST-2000-28088 MOMENTUM}, year = {2003}, language = {en} } @article{GroetschelMartinWeismantel1995, author = {Gr{\"o}tschel, Martin and Martin, Alexander and Weismantel, Robert}, title = {Routing in Grid Graphs by Cutting Planes}, volume = {41}, journal = {ZOR - Mathematical Methods of Operations Research}, number = {3}, pages = {255 -- 275}, year = {1995}, language = {en} } @article{GroetschelMartinWeismantel1996, author = {Gr{\"o}tschel, Martin and Martin, Alexander and Weismantel, Robert}, title = {Packing Steiner Trees: Separation Algorithms}, volume = {9}, journal = {SIAM Journal on Discrete Mathematics}, number = {2}, doi = {10.1137/S0895480193258716}, pages = {233 -- 257}, year = {1996}, language = {en} } @inproceedings{MartinGeisslerHeynetal.2011, author = {Martin, Alexander and Geißler, Bj{\"o}rn and Heyn, Christine and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Morsi, Antonio and Pfetsch, Marc and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Steinbach, Marc and Willert, Bernhard}, title = {Optimierung Technischer Kapazit{\"a}ten in Gasnetzen}, booktitle = {Optimierung in der Energiewirtschaft}, publisher = {VDI-Verlag, D{\"u}sseldorf}, pages = {105 -- 114}, year = {2011}, language = {en} } @article{GroetschelMartinWeismantel1996, author = {Gr{\"o}tschel, Martin and Martin, Alexander and Weismantel, Robert}, title = {Packing Steiner Trees: Further Facets}, volume = {17}, journal = {European Journal of Combinatorics}, number = {1}, doi = {10.1006/eujc.1996.0004}, pages = {39 -- 52}, year = {1996}, language = {en} } @misc{DittelFuegenschuhMartin2011, author = {Dittel, Agnes and F{\"u}genschuh, Armin and Martin, Alexander}, title = {Polyhedral Aspects of Self-Avoiding Walks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12576}, number = {11-11}, year = {2011}, abstract = {In this paper, we study self-avoiding walks of a given length on a graph. We consider a formulation of this problem as a binary linear program. We analyze the polyhedral structure of the underlying polytope and describe valid inequalities. Proofs for their facial properties for certain special cases are given. In a variation of this problem one is interested in optimal configurations, where an energy function measures the benefit if certain path elements are placed on adjacent vertices of the graph. The most prominent application of this problem is the protein folding problem in biochemistry. On a set of selected instances, we demonstrate the computational merits of our approach.}, language = {en} } @phdthesis{Martin1999, author = {Martin, Alexander}, title = {Integer Programs with Block Structure}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3911}, number = {SC-99-03}, year = {1999}, abstract = {In this thesis we study and solve integer programs with block structure, i.\,e., problems that after the removal of certain rows (or columns) of the constraint matrix decompose into independent subproblems. The matrices associated with each subproblem are called blocks and the rows (columns) to be removed linking constraints (columns). Integer programs with block structure come up in a natural way in many real-world applications. The methods that are widely used to tackle integer programs with block structure are decomposition methods. The idea is to decouple the linking constraints (variables) from the problem and treat them at a superordinate level, often called master problem. The resulting residual subordinate problem then decomposes into independent subproblems that often can be solved more efficiently. Decomposition methods now work alternately on the master and subordinate problem and iteratively exchange information to solve the original problem to optimality. In Part I we follow a different approach. We treat the integer programming problem as a whole and keep the linking constraints in the formulation. We consider the associated polyhedra and investigate the polyhedral consequences of the involved linking constraints. The variety and complexity of the new inequalities that come into play is illustrated on three different types of real-world problems. The applications arise in the design of electronic circuits, in telecommunication and production planning. We develop a branch-and-cut algorithm for each of these problems, and our computational results show the benefits and limits of the polyhedral approach to solve these real-world models with block structure. Part II of the thesis deals with general mixed integer programming problems, that is integer programs with no apparent structure in the constraint matrix. We will discuss in Chapter 5 the main ingredients of an LP based branch-and-bound algorithm for the solution of general integer programs. Chapter 6 then asks the question whether general integer programs decompose into certain block structures and investigate whether it is possible to recognize such a structure. The remaining two chapters exploit information about the block structure of an integer program. In Chapter 7 we parallelize parts of the dual simplex algorithm, the method that is commonly used for the solution of the underlying linear programs within a branch-and-cut algorithm. In Chapter 8 we try to detect small blocks in the constraint matrix and to derive new cutting planes that strengthen the integer programming formulation. These inequalities may be associated with the intersection of several knapsack problems. We will see that they significantly improve the quality of the general integer programming solver introduced in Chapter 5.}, language = {en} } @misc{GamrathGleixnerKochetal.2016, author = {Gamrath, Gerald and Gleixner, Ambros and Koch, Thorsten and Miltenberger, Matthias and Kniasew, Dimitri and Schl{\"o}gel, Dominik and Martin, Alexander and Weninger, Dieter}, title = {Tackling Industrial-Scale Supply Chain Problems by Mixed-Integer Programming}, issn = {1438-0064}, doi = {10.4208/jcm.1905-m2019-0055}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61107}, year = {2016}, abstract = {SAP's decision support systems for optimized supply network planning rely on mixed-integer programming as the core engine to compute optimal or near-optimal solutions. The modeling flexibility and the optimality guarantees provided by mixed-integer programming greatly aid the design of a robust and future-proof decision support system for a large and diverse customer base. In this paper we describe our coordinated efforts to ensure that the performance of the underlying solution algorithms matches the complexity of the large supply chain problems and tight time limits encountered in practice.}, language = {en} } @misc{MartinGeisslerHaynetal.2012, author = {Martin, Alexander and Geißler, Bj{\"o}rn and Hayn, Christine and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Morsi, Antonio and Pfetsch, Marc and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Steinbach, Marc and Willert, Bernhard}, title = {Optimierung Technischer Kapazit{\"a}ten in Gasnetzen}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15121}, year = {2012}, abstract = {Die mittel- und l{\"a}ngerfristige Planung f{\"u}r den Gastransport hat sich durch {\"A}nderungen in den regulatorischen Rahmenbedingungen stark verkompliziert. Kernpunkt ist die Trennung von Gashandel und -transport. Dieser Artikel diskutiert die hieraus resultierenden mathematischen Planungsprobleme, welche als Validierung von Nominierungen und Buchungen, Bestimmung der technischen Kapazit{\"a}t und Topologieplanung bezeichnet werden. Diese mathematischen Optimierungsprobleme werden vorgestellt und L{\"o}sungsans{\"a}tze skizziert.}, language = {de} } @incollection{ScheweKochMartinetal.2015, author = {Schewe, Lars and Koch, Thorsten and Martin, Alexander and Pfetsch, Marc}, title = {Mathematical optimization for evaluating gas network capacities}, booktitle = {Evaluating Gas Network Capacities}, publisher = {Society for Industrial and Applied Mathematics}, isbn = {9781611973686}, pages = {87 -- 102}, year = {2015}, language = {en} } @inproceedings{FuegenschuhHomfeldMartin2007, author = {F{\"u}genschuh, Armin and Homfeld, Henning and Martin, Alexander}, title = {Leitwegeplanung}, booktitle = {Mathematik f{\"u}r Innovationen in Industrie und Dienstleistungen}, year = {2007}, language = {en} } @inproceedings{BorndoerferEisenblaetterGroetscheletal.1996, author = {Bornd{\"o}rfer, Ralf and Eisenbl{\"a}tter, Andreas and Gr{\"o}tschel, Martin and Martin, Alexander}, title = {Stable-Set and Other Techniques for Frequency Assignment Problems}, booktitle = {Anais da I Oficina Nacional em Problemas de Corte \& Empacotamento}, publisher = {Universidade de S{\~a}o Paulo, Instituto de Matem{\´a}tica e Estat{\´i}stica}, pages = {17 -- 21}, year = {1996}, language = {en} } @misc{FuegenschuhGeisslerGollmeretal.2013, author = {F{\"u}genschuh, Armin and Geißler, Bj{\"o}rn and Gollmer, Ralf and Hayn, Christine and Henrion, Rene and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Martin, Alexander and Mirkov, Radoslava and Morsi, Antonio and R{\"o}misch, Werner and R{\"o}vekamp, Jessica and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Steinbach, Marc and Willert, Bernhard}, title = {Mathematical Optimization for Challenging Network Planning Problems in Unbundled Liberalized Gas Markets}, issn = {1438-0064}, doi = {10.1007/s12667-013-0099-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17821}, year = {2013}, abstract = {The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor where united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We show that these new paradigms lead to new and challenging mathematical optimization problems. In order to solve them and to provide meaningful results for practice, all aspects of the underlying problems, such as combinatorics, stochasticity, uncertainty, and nonlinearity, have to be addressed. With such special-tailored solvers, free network capacities and topological network extensions can, for instance, be determined.}, language = {en} } @misc{PfetschFuegenschuhGeissleretal.2012, author = {Pfetsch, Marc and F{\"u}genschuh, Armin and Geißler, Bj{\"o}rn and Geißler, Nina and Gollmer, Ralf and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Martin, Alexander and Morsi, Antonio and R{\"o}vekamp, Jessica and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Steinbach, Marc and Vigerske, Stefan and Willert, Bernhard}, title = {Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions}, issn = {1438-0064}, doi = {10.1080/10556788.2014.888426}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-16531}, year = {2012}, abstract = {In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult mixed-integer non-convex nonlinear feasibility problem. The first phase consists of four distinct algorithms facilitating mixed-integer linear, mixed-integer nonlinear, reduced nonlinear, and complementarity constrained methods to compute possible settings for the discrete decisions. The second phase employs a precise continuous nonlinear programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances whose size is significantly larger than networks that have appeared in the literature previously.}, language = {en} } @misc{KochMartinPfetsch2013, author = {Koch, Thorsten and Martin, Alexander and Pfetsch, Marc}, title = {Progress in Academic Computational Integer Programming}, journal = {Facets of Combinatorial Optimization}, editor = {J{\"u}nger, Michael and Reinelt, Gerhard}, publisher = {Springer}, doi = {10.1007/978-3-642-38189-8_19}, pages = {483 -- 506}, year = {2013}, language = {en} } @article{GamrathKochMartinetal.2015, author = {Gamrath, Gerald and Koch, Thorsten and Martin, Alexander and Miltenberger, Matthias and Weninger, Dieter}, title = {Progress in presolving for mixed integer programming}, volume = {7}, journal = {Mathematical Programming Computation}, number = {4}, doi = {10.1007/s12532-015-0083-5}, pages = {367 -- 398}, year = {2015}, abstract = {This paper describes three presolving techniques for solving mixed integer programming problems (MIPs) that were implemented in the academic MIP solver SCIP. The task of presolving is to reduce the problem size and strengthen the formulation, mainly by eliminating redundant information and exploiting problem structures. The first method fixes continuous singleton columns and extends results known from duality fixing. The second analyzes and exploits pairwise dominance relations between variables, whereas the third detects isolated subproblems and solves them independently. The performance of the presented techniques is demonstrated on two MIP test sets. One contains all benchmark instances from the last three MIPLIB versions, while the other consists of real-world supply chain management problems. The computational results show that the combination of all three presolving techniques almost halves the solving time for the considered supply chain management problems. For the MIPLIB instances we obtain a speedup of 20 \% on affected instances while not degrading the performance on the remaining problems.}, language = {en} } @misc{BorndoerferFerreiraMartin1997, author = {Bornd{\"o}rfer, Ralf and Ferreira, Carlos E. and Martin, Alexander}, title = {Decomposing Matrices into Blocks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2849}, number = {SC-97-15}, year = {1997}, abstract = {In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so-called {\em bordered block diagonal form}. More precisely, given some matrix \$A\$, we try to assign as many rows as possible to some number of blocks of limited size such that no two rows assigned to different blocks intersect in a common column. Bordered block diagonal form is desirable because it can guide and speed up the solution process for linear and integer programming problems. We show that various matrices from the LP- and MIP-libraries NETLIB and MITLIB can indeed be decomposed into this form by computing optimal decompositions or decompositions with proven quality. These computations are done with a branch-and-cut algorithm based on polyhedral investigations of the matrix decomposition problem. In practice, however, one would use heuristics to find a good decomposition. We present several heuristic ideas and test their performance. Finally, we investigate the usefulness of optimal matrix decompositions into bordered block diagonal form for integer programming by using such decompositions to guide the branching process in a branch-and-cut code for general mixed integer programs.}, language = {en} }