@misc{BertholdPfetsch2008, author = {Berthold, Timo and Pfetsch, Marc}, title = {Detecting Orbitopal Symmetries}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10842}, number = {08-33}, year = {2008}, abstract = {Orbitopes can be used to handle symmetries which arise in integer programming formulations with an inherent assignment structure. We investigate the detection of symmetries appearing in this approach. We show that detecting so-called orbitopal symmetries is graph-isomorphism hard in general, but can be performed in linear time if the assignment structure is known.}, language = {en} } @misc{BorndoerferNeumannPfetsch2008, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc}, title = {The Line Connectivity Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10820}, number = {08-31}, year = {2008}, abstract = {This paper introduces the "line connectivity problem", a generalization of the Steiner tree problem and a special case of the line planning problem. We study its complexity and give an IP formulation in terms of an exponential number of constraints associated with "line cut constraints". These inequalities can be separated in polynomial time. We also generalize the Steiner partition inequalities.}, language = {en} } @misc{BorndoerferNeumannPfetsch2008, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc}, title = {Models for Fare Planning in Public Transport}, issn = {1438-0064}, doi = {10.1016/j.dam.2012.02.027}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10708}, number = {08-16}, year = {2008}, abstract = {The optimization of fare systems in public transit allows to pursue objectives such as the maximization of demand, revenue, profit, or social welfare. We propose a non-linear optimization approach to fare planning that is based on a detailed discrete choice model of user behavior. The approach allows to analyze different fare structures, optimization objectives, and operational scenarios involving, e.g., subsidies. We use the resulting models to compute optimized fare systems for the city of Potsdam, Germany.}, language = {en} } @misc{BertholdHeinzPfetsch2008, author = {Berthold, Timo and Heinz, Stefan and Pfetsch, Marc}, title = {Solving Pseudo-Boolean Problems with SCIP}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10671}, number = {08-12}, year = {2008}, abstract = {Pseudo-Boolean problems generalize SAT problems by allowing linear constraints and a linear objective function. Different solvers, mainly having their roots in the SAT domain, have been proposed and compared,for instance, in Pseudo-Boolean evaluations. One can also formulate Pseudo-Boolean models as integer programming models. That is,Pseudo-Boolean problems lie on the border between the SAT domain and the integer programming field. In this paper, we approach Pseudo-Boolean problems from the integer programming side. We introduce the framework SCIP that implements constraint integer programming techniques. It integrates methods from constraint programming, integer programming, and SAT-solving: the solution of linear programming relaxations, propagation of linear as well as nonlinear constraints, and conflict analysis. We argue that this approach is suitable for Pseudo-Boolean instances containing general linear constraints, while it is less efficient for pure SAT problems. We present extensive computational experiments on the test set used for the Pseudo-Boolean evaluation 2007. We show that our approach is very efficient for optimization instances and competitive for feasibility problems. For the nonlinear parts, we also investigate the influence of linear programming relaxations and propagation methods on the performance. It turns out that both techniques are helpful for obtaining an efficient solution method.}, language = {en} } @misc{BorndoerferNeumannPfetsch2008, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc}, title = {Angebotsplanung im {\"o}ffentlichen Nahverkehr}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10555}, number = {08-04}, year = {2008}, abstract = {Die Angebotsplanung im {\"o}ffentlichen Nahverkehr umfasst die Aufgaben der Netz-, Linien-,Fahr- und Preisplanung. Wir stellen zwei mathematische Optimierungsmodelle zur Linien- und Preisplanung vor. Wir zeigen anhand von Berechnungen f{\"u}r die Verkehrsbetriebe in Potsdam(ViP), dass sich damit komplexe Zusammenh{\"a}nge quantitativ analysieren lassen. Auf diese Weise untersuchen wir die Auswirkungen von Freiheitsgraden auf die Konstruktion von Linien und die Wahl von Reisewegen der Passagiere, Abh{\"a}ngigkeiten zwischen Kosten und Reisezeiten sowie den Einfluss verschiedener Preissysteme auf Nachfrage und Kostendeckung.}, language = {de} } @misc{AncoBlumanWolf2008, author = {Anco, Stephen and Bluman, George and Wolf, Thomas}, title = {Invertible Mappings of Nonlinear PDEs to Linear PDEs Through Admitted Conservation Laws}, organization = {Department of Mathematics, Brock University, St. Catharines, ON Canada L2S 3A1}, issn = {1438-0064}, doi = {10.1007/s10440-008-9205-7}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10652}, number = {08-11}, year = {2008}, abstract = {An algorithmic method using conservation law multipliers is introduced that yields necessary and sufficient conditions to find invertible mappings of a given nonlinear PDE to some linear PDE and to construct such a mapping when it exists. Previous methods yielded such conditions from admitted point or contact symmetries of the nonlinear PDE. Through examples, these two linearization approaches are contrasted.}, language = {en} } @misc{Wolf2008, author = {Wolf, Thomas}, title = {On solving large systems of polynomial equations appearing in Discrete Differential Geometry}, issn = {1438-0064}, doi = {10.1134/S0361768808020047}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10646}, number = {08-10}, year = {2008}, abstract = {The paper describes a method for solution of very large overdetermined algebraic polynomial systems on an example that appears from a classification of all integrable 3-dimensional scalar discrete quasilinear equations \$Q_3=0\$ on an elementary cubic cell of the lattice \${\mathbb Z}^3\$. The overdetermined polynomial algebraic system that has to be solved is far too large to be formulated. A probing' technique which replaces independent variables by random integers or zero allows to formulate subsets of this system. An automatic alteration of equation formulating steps and equation solving steps leads to an iteration process that solves the computational problem.}, language = {en} } @misc{Stephan2008, author = {Stephan, R{\"u}diger}, title = {On the cardinality constrained matroid polytope}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10614}, number = {08-08}, year = {2008}, abstract = {Edmonds showed that the so-called rank inequalities and the nonnegativity constraints provide a complete linear description of the matroid polytope. By essentially adding Gr{\"o}tschel's cardinality forcing inequalities, we obtain a complete linear description of the cardinality constrained matroid polytope which is the convex hull of the incidence vectors of those independent sets that have a feasible cardinality. Moreover, we show how the separation problem for the cardinality forcing inequalities can be reduced to that for the rank inequalities. We also give necessary and sufficient conditions for a cardinality forcing inequality to be facet defining.}, language = {en} } @misc{Wolf2008, author = {Wolf, Thomas}, title = {The Parametric Solution of Underdetermined linear ODEs}, issn = {1438-0064}, doi = {10.1134/S0361768811020113}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10693}, number = {08-15}, year = {2008}, abstract = {The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are arbitrary analytic functions in the independent variable. A second conceptual aim is to present an algorithm that is in some sense dual to the fundamental Euclids algorithm, and thus an alternative to the special case of a Gr\"{o}bner basis algorithm as it is used for solving linear ODE-systems. In the paper Euclids algorithm and the new dual version' are compared and their complementary strengths are analysed on the task of solving underdetermined ODEs. An implementation of the described algorithm is interactively accessible at http://lie.math.brocku.ca/crack/uode.}, language = {en} } @misc{TsarevWolf2008, author = {Tsarev, Sergey and Wolf, Thomas}, title = {Classification of 3-dimensional integrable scalar discrete equations}, issn = {1438-0064}, arxiv = {http://arxiv.org/abs/0706.2464}, doi = {10.1007/s11005-008-0230-2}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10667}, number = {08-13}, year = {2008}, abstract = {We classify all integrable 3-dimensional scalar discrete affine linear equations \$Q_3=0\$ on an elementary cubic cell of the lattice \${\mathbb Z}^3\$. An equation \$Q_3=0\$ \%of such form is called integrable if it may be consistently imposed on all \$3\$-dimensional elementary faces of the lattice \${\mathbb Z}^4\$. Under the natural requirement of invariance of the equation under the action of the complete group of symmetries of the cube we prove that the only ontrivial(non-linearizable) integrable equation from this class is the well-known dBKP-system.}, language = {en} } @misc{AchterbergHeinzKoch2008, author = {Achterberg, Tobias and Heinz, Stefan and Koch, Thorsten}, title = {Counting solutions of integer programs using unrestricted subtree detection}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10632}, number = {08-09}, year = {2008}, abstract = {In the recent years there has been tremendous progress in the development of algorithms to find optimal solutions for integer programs. In many applications it is, however, desirable (or even necessary) to generate all feasible solutions. Examples arise in the areas of hardware and software verification and discrete geometry. In this paper, we investigate how to extend branch-and-cut integer programming frameworks to support the generation of all solutions. We propose a method to detect so-called unrestricted subtrees, which allows us to prune the integer program search tree and to collect several solutions simultaneously. We present computational results of this branch-and-count paradigm which show the potential of the unrestricted subtree detection.}, language = {en} } @phdthesis{Bley2007, author = {Bley, Andreas}, title = {Routing and Capacity Optimization for IP Networks}, isbn = {978-3-86727-281-0}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:83-opus-15530}, year = {2007}, abstract = {This thesis is concerned with dimensioning and routing optimization problems for communication networks that employ a shortest path routing protocol such as OSPF, IS-IS, or RIP. These protocols are widely used in the Internet. With these routing protocols, all end-to-end data streams are routed along shortest paths with respect to a metric of link lengths. The network administrator can configure the routing only by modifying this metric. In this thesis we consider the unsplittable shortest path routing variant, where each communication demand must be sent unsplit through the network. This requires that all shortest paths are uniquely determined. The major difficulties in planning such networks are that the routing can be controlled only indirectly via the routing metric and that all routing paths depend on the same routing metric. This leads to rather complicated and subtle interdependencies among the paths that comprise a valid routing. In contrast to most other routing schemes, the paths for different communication demands cannot be configured independent of each other. Part I of the thesis is dedicated to the relation between path sets and routing metrics and to the combinatorial properties of those path sets that comprise a valid unsplittable shortest path routing. Besides reviewing known approaches to find a compatible metric for a given path set (or to prove that none exists) and discussing some properties of valid path sets, we show that the problem of finding a compatible metric with integer lengths as small as possible and the problem of finding a smallest possible conflict in the given path set are both NP-hard to approximate within a constant factor. In Part II of the thesis we discuss the relation between unsplittable shortest path routing and several other routing schemes and we analyze the computational complexity of three basic unsplittable shortest path routing problems. We show that the lowest congestion that can be obtained with unsplittable shortest path routing may significantly exceed that achievable with other routing paradigms and we prove several non-approximability results for unsplittable shortest path routing problems that are stronger than those for the corresponding unsplittable flow problems. In addition, we derive various polynomial time approximation algorithms for general and special cases of these problems. In Part III of the thesis we finally develop an integer linear programming approach to solve these and more realistic unsplittable shortest path routing problems to optimality. We present alternative formulations for these problems, discuss their strength and computational complexity, and show how to derive strong valid inequalities. Eventually, we describe our implementation of this solution approach and report on the numerical results obtained for real-world problems that came up in the planning the German National Research and Education Networks G-WiN and X-WiN and for several benchmark instances.}, language = {en} } @phdthesis{Weider2007, author = {Weider, Steffen}, title = {Integration of Vehicle and Duty Scheduling in Public Transport}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:83-opus-16240}, year = {2007}, abstract = {This thesis describes the algorithm IS-OPT that integrates scheduling of vehicles and duties in public bus transit. IS-OPT is the first algorithm which solves integrated vehicle and duty scheduling problems arising in medium sized carriers such that its solutions can be used in daily operations without further adaptions. This thesis is structured as follows: The first chapter highlights mathematical models of the planning process of public transit companies and examines their potential for integrating them with other planning steps. It also introduces descriptions of the vehicle and the duty scheduling problem. Chapter 2 motivates why it can be useful to integrate vehicle and duty scheduling, explains approaches of the literature, and gives an outline of our algorithm IS-OPT. The following chapters go into the details of the most important techniques and methods of IS-OPT: In Chapter 3 we describe how we use Lagrangean relaxation in a column generation framework. Next, in Chapter 4, we describe a variant of the proximal bundle method (PBM) that is used to approximate linear programs occurring in the solution process. We introduce here a new variant of the PBM which is able to utilize inexact function evaluation and the use of epsilon-subgradients. We also show the convergence of this method under certain assumptions. Chapter 5 treats the generation of duties for the duty scheduling problem. This problem is modeled as a resourceconstraint- shortest-path-problem with non-linear side constraints and nearly linear objective function. It is solved in a two-stage approach. At first we calculate lower bounds on the reduced costs of duties using certain nodes by a new inexact label-setting algorithm. Then we use these bounds to speed up a depth-first-search algorithm that finds feasible duties. In Chapter 6 we present the primal heuristic of IS-OPT that solves the integrated problem to integrality. We introduce a new branch-and-bound based heuristic which we call rapid branching. Rapid branching uses the proximal bundle method to compute lower bounds, it introduces a heuristic node selection scheme, and it utilizes a new branching rule that fixes sets of many variables at once. The common approach to solve the problems occurring in IS-OPT is to trade inexactness of the solutions for speed of the algorithms. This enables, as we show in Chapter 7, to solve large real world integrated problems by IS-OPT. The scheduled produced by IS-OPT save up to 5\% of the vehicle and duty cost of existing schedules of regional and urban public transport companies.}, language = {en} } @phdthesis{Harks2007, author = {Harks, Tobias}, title = {Multicommodity Routing Problems-Selfish Behavior and Online Aspects-}, isbn = {3867273596}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10426}, year = {2007}, abstract = {In this thesis, we study multicommodity routing problems in networks, in which commodities have to be routed from source to destination nodes. Such problems model for instance the traffic flows in street networks, data flows in the Internet, or production flows in factories. In most of these applications, the quality of a flow depends on load dependent cost functions on the edges of the given network. The total cost of a flow is usually defined as the sum of the arc cost of the network. An optimal flow minimizes this cost. A main focus of this thesis is to investigate online multicommodity routing problems in networks, in which commodities have to be routed sequentially. Arcs are equipped with load dependent price functions defining routing costs, which have to be minimized. We discuss a greedy online algorithm that routes (fractionally) each commodity by minimizing a convex cost function that depends on the previously routed flow. We present a competitive analysis of this algorithm and prove upper bounds of (d+1)^(d+1) for polynomial price functions with nonnegative coefficients and maximum degree d. For networks with two nodes and parallel arcs, we show that this algorithm returns an optimal solution. Without restrictions on the price functions and network, no algorithm is competitive. We also investigate a variant in which the demands have to be routed unsplittably. In this case, it is NP-hard to compute the offline optimum. Furthermore, we study selfish routing problems (network games). In a network game, players route demand in a network with minimum cost. In this setting, we study the quality of Nash equilibria compared to the the system optimum (price of anarchy) in network games with nonatomic and atomic players and spittable flow. As a main result, we prove upper bounds on the price of anarchy for polynomial latency functions with nonnegative coefficients and maximum degree d, which improve upon the previous best ones.}, language = {en} } @misc{AchterbergBertholdKochetal.2008, author = {Achterberg, Tobias and Berthold, Timo and Koch, Thorsten and Wolter, Kati}, title = {Constraint Integer Programming: a New Approach to Integrate CP and MIP}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10520}, number = {08-01}, year = {2008}, abstract = {This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques from SAT solving. SCIP is available in source code and free for non-commercial use. We demonstrate the usefulness of CIP on two tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we employ the CIP framework to solve chip design verification problems, which involve some highly non-linear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the non-linear constraints by employing constraint programming techniques.}, language = {en} } @misc{Berthold2007, author = {Berthold, Timo}, title = {RENS - Relaxation Enforced Neighborhood Search}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4264}, number = {07-28}, year = {2007}, abstract = {In the recent years, a couple of quite successful large neighborhood search heuristics for mixed integer programs has been published. Up to our knowledge, all of them are improvement heuristics. We present a new start heuristic for general MIPs working in the spirit of large neighborhood search. It constructs a sub-MIP which represents the space of all feasible roundings of some fractional point - normally the optimum of the LP-relaxation of the original MIP. Thereby, one is able to determine whether a point can be rounded to a feasible solution and which is the best possible rounding. Furthermore, a slightly modified version of RENS proves to be a well-performing heuristic inside the branch-cut-and-price-framework SCIP.}, language = {en} } @misc{AchterbergBrinkmannWedler2007, author = {Achterberg, Tobias and Brinkmann, Raik and Wedler, Markus}, title = {Property Checking with Constraint Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10376}, number = {07-37}, year = {2007}, abstract = {We address the property checking problem for SoC design verification at the register transfer level (RTL) by integrating techniques from integer programming, constraint programming, and SAT solving. Specialized domain propagation and preprocessing algorithms for individual RTL operations extend a general constraint integer programming framework. Conflict clauses are learned by analyzing infeasible LPs and deductions, and by employing reverse propagation. Experimental results show that our approach outperforms SAT techniques for proving the validity of properties on circuits containing arithmetics.}, language = {en} } @misc{Bley2007, author = {Bley, Andreas}, title = {Routing and Capacity Optimization for IP networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10323}, number = {07-33}, year = {2007}, abstract = {This article describes the main concepts and techniques that have been developed during the last year at ZIB to solve dimensioning and routing optimization problems for IP networks. We discuss the problem of deciding if a given path set corresponds to an unsplittable shortest path routing, the fundamental properties of such path sets, and the computational complexity of some basic network planning problems for this routing type. Then we describe an integer-linear programming approach to solve such problems in practice. This approach has been used successfully in the planning of the German national education and research network for several years.}, language = {en} } @misc{Berthold2007, author = {Berthold, Timo}, title = {Heuristics of the Branch-Cut-and-Price-Framework SCIP}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10280}, number = {07-30}, year = {2007}, abstract = {In this paper we give an overview of the heuristics which are integrated into the open source branch-cut-and-price-framework SCIP. We briefly describe the fundamental ideas of different categories of heuristics and present some computational results which demonstrate the impact of heuristics on the overall solving process of SCIP.}, language = {en} } @misc{BorndoerferLiebchen2007, author = {Bornd{\"o}rfer, Ralf and Liebchen, Christian}, title = {When Periodic Timetables are Suboptimal}, organization = {DFG Reseach Center Matheon "Mathematics for Key Technologies"}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9151}, number = {07-29}, year = {2007}, abstract = {The timetable is the essence of the service offered by any provider of public transport'' (Jonathan Tyler, CASPT 2006). Indeed, the timetable has a major impact on both operating costs and on passenger comfort. Most European agglomerations and railways use periodic timetables in which operation repeats in regular intervals. In contrast, many North and South American municipalities use trip timetables in which the vehicle trips are scheduled individually subject to frequency constraints. We compare these two strategies with respect to vehicle operation costs. It turns out that for short time horizons, periodic timetabling can be suboptimal; for sufficiently long time horizons, however, periodic timetabling can always be done in an optimal way'.}, language = {en} } @misc{Raack2005, type = {Master Thesis}, author = {Raack, Christian}, title = {Employing Mixed-Integer Rounding in Telecommunication Network Design}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10023}, school = {Zuse Institute Berlin (ZIB)}, year = {2005}, abstract = {In dieser Diplomarbeit werden grundlegende Probleme der kostenoptimalen Dimensionierung von Telekommunikationsnetzwerken untersucht. Diese werden als lineare gemischt ganzzahlige Programme formuliert, wobei sich in der Modellierung auf die Konzepte Routing und Kapazit{\"a}tszuweisung beschr{\"a}nkt wird. Es werden parallel drei {\"u}bliche, aus der Praxis motivierte M{\"o}glichkeiten behandelt, die auf gerichteten oder ungerichteten Kanten eines Netzwerkes installierte Kapazit{\"a}t zu nutzen. Diese unterscheiden wir als DIrected, BIdirected und UNdirected. Die studierten Probleme treten als Relaxierungen vieler realistischer Fragestellungen der Netzwerkoptimierung auf. Sie enthalten elementare Strukturen, deren Studium ausschlaggebend ist f{\"u}r das Verst{\"a}ndnis komplexerer Modelle. Letztere k{\"o}nnen zus{\"a}tzliche Erfordernisse ber{\"u}cksichtigen, wie zum Beispiel die Ausfallsicherheit von Netzwerken. Zur L{\"o}sung solcher NP-schweren Optimierungsprobleme werden erfolgreich Branch \& Bound und Schnittebenenverfahren kombiniert (Branch \& Cut). F{\"u}r die Wirksamkeit dieser Algorithmen ist es sehr n{\"u}tzlich, m{\"o}glichst genaue Kenntnisse der Struktur der Seitenfl{\"a}chen der zugrundeliegenden Polyeder zu haben, welche die konvexe H{\"u}lle der L{\"o}sungsmenge beschreiben. Es sind starke g{\"u}ltige Ungleichungen zu finden, welche hochdimensionale Seitenfl{\"a}chen oder sogar Facetten definieren. Diese sollten zudem schnell separiert werden k{\"o}nnen und die numerische Stabilit{\"a}t der Algorithmen m{\"o}glichst nicht beeinflussen. Diese Arbeit besch{\"a}ftigt sich im Wesentlichen mit der sehr allgemeinen Rundungstechnik Mixed- Integer Rounding (MIR) zur Verst{\"a}rkung g{\"u}ltiger Ungleichungen unter Verwendung der Ganzzahligkeitsnebenbedingungen. Es wird eine MIR-Prozedur motiviert, bestehend aus den Schritten Aggregieren, Substituieren, Komplementieren und Skalieren, welche durch Ausnutzung der Struktur der gegebenen Parameter zu einer g{\"u}ltigen Basisungleichung f{\"u}hrt, die dann durch MIR eine starke und oft facetten-induzierende Ungleichung gibt. Es werden verschieden Klassen solcher Ungleichungen untersucht und auf ihre Praxistauglichkeit beim Einsatz in Branch \& Cut-Verfahren getestet. Nach einer kurzen Einf{\"u}hrung werden in Kapitel 2 die f{\"u}r uns in dieser Diplomarbeit relevanten Probleme definiert. Kapitel 3 gibt eine ausf{\"u}hrliche {\"U}bersicht {\"u}ber die Technik MIR.Wir besch{\"a}ftigen uns vor allen Dingen mit den Begriffen Superadditivit{\"a}t und Lifting und behandeln Aspekte wie Numerik und beschr{\"a}nkte Variablen. Kapitel 4 und Kapitel 5 umfassen Untersuchungen zu so genannten cut sets. Diese Polyeder werden durch Schnitte in Netzwerken definiert und relaxieren die von uns behandelten Probleme. Haupts{\"a}chlich durch MIR entwickeln wir sowohl neue als auch bekannte Klassen von facetten-definierenden Ungleichungen f{\"u}r cut sets, wobei strukturelle Unterschiede herausgearbeitet werden, die durch die drei verschiedenen Typen der Kapzit{\"a}tsbereitstellung und durch beschr{\"a}nkte Variablen entstehen. Als ein zentrales Resultat wird bewiesen unter welchen Bedingungen facetten-induzierende Ungleichungen f{\"u}r cut sets auch Facetten der zugeh{\"o}rigen relaxierten Polyeder sind. Im Kapitel 6 geben wir weitere Typen von MIR-Ungleichungen an, die auf anderen Netzwerkstrukturen basieren und weisen ferner auf offene Fragen sowie interessante Ideen hin. Das Kapitel 7 widmet sich schließlich der Entwicklung und Implementation von Separationsalgorithmen. Wir testen einige der entwickelten Ungleichungsklassen mit Hinblick auf Ihre Wirksamkeit zur L{\"o}sung von realistischen Problemen der Netzwerkdimensionierung aus der Telekommunikation und diskutieren die Ergebnisse.}, language = {de} } @phdthesis{LutzWestphal2006, author = {Lutz-Westphal, Brigitte}, title = {Kombinatorische Optimierung -Inhalte und Methoden f{\"u}r einen authentischen Mathematikunterricht}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10608}, year = {2006}, abstract = {wird nachgereicht}, language = {en} } @misc{Berthold2006, type = {Master Thesis}, author = {Berthold, Timo}, title = {Primal Heuristics for Mixed Integer Programs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10293}, school = {Zuse Institute Berlin (ZIB)}, year = {2006}, abstract = {A lot of problems arising in Combinatorial Optimization and Operations Research can be formulated as Mixed Integer Programs (MIP). Although MIP-solving is an NP-hard optimization problem, many practically relevant instances can be solved in reasonable time. In modern MIP-solvers like the branch-cut-and-price-framework SCIP, primal heuristics play a major role in finding and improving feasible solutions at the early steps of the solution process. This helps to reduce the overall computational effort, guides the remaining search process, and proves the feasibility of the MIP model. Furthermore, a heuristic solution with a small gap to optimality often is sufficient in practice. We investigate 16 different heuristics, all of which are available in SCIP. Four of them arise from the literature of the last decade, nine are specific implementations of general heuristic ideas, three have been newly developed. We present an improved version of the feasibility pump heuristic by Fischetti et al., which in experiments produced solutions with only a third of the optimality gap compared to the original version. Furthermore, we introduce two new Large Neighborhood Search (LNS) heuristics. Crossover is an LNS improvement heuristic making use of similarities of diverse MIP solutions to generate new incumbent solutions. RENS is an LNS rounding heuristic which evaluates the space of all possible roundings of a fractional LP-solution. This heuristic makes it possible to determine whether a point can be rounded to an integer solution and which is the best possible rounding. We conclude with a computational comparison of all described heuristics. It points out that a single heuristic on its own has only a slight impact on the overall performance of SCIP, but the combination of all of them reduces the running time by a factor of two compared to a version without any heuristics.}, language = {en} } @misc{Heinz2005, type = {Master Thesis}, author = {Heinz, Stefan}, title = {Policies for Online Target Date Assignment Problems: Competitive Analysis versus Expected Performance}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9933}, school = {Zuse Institute Berlin (ZIB)}, year = {2005}, language = {en} } @misc{Menne2003, type = {Master Thesis}, author = {Menne, Ulrich}, title = {LP approaches to survivable networks with single path routing}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9989}, school = {Zuse Institute Berlin (ZIB)}, year = {2003}, language = {en} } @misc{Hiller2004, type = {Master Thesis}, author = {Hiller, Benjamin}, title = {Bad Guys are Rare: Probabilistic Analysis of an Elementary Dial-a-Ride Problem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10114}, school = {Zuse Institute Berlin (ZIB)}, year = {2004}, abstract = {This thesis deals with a Dial-a-Ride problem on trees and considers both offline and online versions of this problem. We study the behavior of certain algorithms on random instances, i.e. we do probabilistic analysis. The focus is on results describing the typical behavior of the algorithms, i.e. results holding with (asymptotically) high probability. For the offline version, we present a simplified proof of a result of Coja-Oghlan, Krumke und Nierhoff. The results states that some heuristic using a minimum spanning tree to approximate a Steiner tree gives optimal results with high probability. This explains why this heuristic produces optimal solutions quite often. In the second part, probabilistic online versions of the problem are introduced. We study the online strategies REPLAN and IGNORE. Regarding the IGNORE strategy we can show that it works almost optimal under high load with high probability.}, language = {en} } @misc{BorndoerferGroetschelLukacetal.2005, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Lukac, Sascha and Mitusch, Kay and Schlechte, Thomas and Schultz, S{\"o}ren and Tanner, Andreas}, title = {An Auctioning Approach to Railway Slot Allocation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8786}, number = {05-45}, year = {2005}, abstract = {We present an approach to implement an auction of railway slots. Railway network, train driving characteristics, and safety requirements are described by a simplified, but still complex macroscopic model. In this environment, slots are modelled as combinations of scheduled track segments. The auction design builds on the iterative combinatorial auction. However, combinatorial bids are restricted to some types of slot bundles that realize positive synergies between slots. We present a bidding language that allows bidding for these slot bundles. An integer programming approach is proposed to solve the winner determination problem of our auction. Computational results for auction simulations in the Hannover-Fulda-Kassel area of the German railway network give evidence that auction approaches can induce a more efficient use of railway capacity.}, language = {en} } @misc{BorndoerferNeumannPfetsch2005, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc}, title = {Fare Planning for Public Transport}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8541}, number = {05-20}, year = {2005}, abstract = {In this paper we introduce the fare planning problem for public transport which consists in designing a system of fares maximizing revenue. We propose a new simple general model for this problem. It i s based on a demand function and constraints for the different fares. The constraints define the structure of the fare system, e.g., distance dependent fares or zone fares. We discuss a simple example with a quadratic demand function and distance dependent fares. Then we introduce a more realistic discrete choice model in which passengers choose between different alternatives depending on the numb er of trips per month. We demonstrate the examples by computational experiments.}, language = {en} } @phdthesis{Achterberg2007, author = {Achterberg, Tobias}, title = {Constraint Integer Programming}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:83-opus-16117}, year = {2007}, abstract = {This thesis introduces the novel paradigm of constraint integer programming (CIP), which integrates constraint programming (CP) and mixed integer programming (MIP) modeling and solving techniques. It is supplemented by the software SCIP, which is a solver and framework for constraint integer programming that also features SAT solving techniques. SCIP is freely available in source code for academic and non-commercial purposes. Our constraint integer programming approach is a generalization of MIP that allows for the inclusion of arbitrary constraints, as long as they turn into linear constraints on the continuous variables after all integer variables have been fixed. The constraints, may they be linear or more complex, are treated by any combination of CP and MIP techniques: the propagation of the domains by constraint specific algorithms, the generation of a linear relaxation and its solving by LP methods, and the strengthening of the LP by cutting plane separation. The current version of SCIP comes with all of the necessary components to solve mixed integer programs. In the thesis, we cover most of these ingredients and present extensive computational results to compare different variants for the individual building blocks of a MIP solver. We focus on the algorithms and their impact on the overall performance of the solver. In addition to mixed integer programming, the thesis deals with chip design verification, which is an important topic of electronic design automation. Chip manufacturers have to make sure that the logic design of a circuit conforms to the specification of the chip. Otherwise, the chip would show an erroneous behavior that may cause failures in the device where it is employed. An important subproblem of chip design verification is the property checking problem, which is to verify whether a circuit satisfies a specified property. We show how this problem can be modeled as constraint integer program and provide a number of problem-specific algorithms that exploit the structure of the individual constraints and the circuit as a whole. Another set of extensive computational benchmarks compares our CIP approach to the current state-of-the-art SAT methodology and documents the success of our method.}, language = {en} } @misc{HillerKochScheweetal.2018, author = {Hiller, Benjamin and Koch, Thorsten and Schewe, Lars and Schwarz, Robert and Schweiger, Jonas}, title = {A System to Evaluate Gas Network Capacities: Concepts and Implementation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-67438}, year = {2018}, abstract = {In 2005 the European Union liberalized the gas market with a disruptive change and decoupled trading of natural gas from its transport. The gas is now transported by independent so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer the maximum possible capacities at each entry and exit such that any resulting gas flow can be realized by the network. The revenue from selling these capacities more than one billion Euro in Germany alone, but overestimating the capacity might compromise the security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs. This is a report on a large project in mathematical optimization, set out to develop a new toolset for evaluating gas network capacities. The goals and the challenges as they occurred in the project are described, as well as the developments and design decisions taken to meet the requirements.}, language = {en} } @misc{BennerGrundelHimpeetal.2017, author = {Benner, Peter and Grundel, Sara and Himpe, Christian and Huck, Christoph and Streubel, Tom and Tischendorf, Caren}, title = {Gas Network Benchmark Models}, issn = {1438-0064}, doi = {10.1007/11221_2018_5}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66274}, year = {2017}, abstract = {The simulation of gas transportation networks becomes increasingly more important as its use-cases broadens to more complex applications. Classically, the purpose of the gas network was the transportation of predominantly natural gas from a supplier to the consumer for long-term scheduled volumes. With the rise of renewable energy sources, gas-fired power plants are often chosen to compensate for the fluctuating nature of the renewables, due to their on-demand power generation capability. Such an only short-term plannable supply and demand setting requires sophisticated simulations of the gas network prior to the dispatch to ensure the supply of all customers for a range of possible scenarios and to prevent damages to the gas network. In this work we describe the modelling of gas networks and present benchmark systems to test implementations and compare new or extended models.}, language = {en} } @misc{GamrathSchubert2017, author = {Gamrath, Gerald and Schubert, Christoph}, title = {Measuring the impact of branching rules for mixed-integer programming}, issn = {1438-0064}, doi = {10.1007/978-3-319-89920-6_23}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64722}, year = {2017}, abstract = {Branching rules are an integral component of the branch-and-bound algorithm typically used to solve mixed-integer programs and subject to intense research. Different approaches for branching are typically compared based on the solving time as well as the size of the branch-and-bound tree needed to prove optimality. The latter, however, has some flaws when it comes to sophisticated branching rules that do not only try to take a good branching decision, but have additional side-effects. We propose a new measure for the quality of a branching rule that distinguishes tree size reductions obtained by better branching decisions from those obtained by such side-effects. It is evaluated for common branching rules providing new insights in the importance of strong branching.}, language = {en} } @misc{BeckenbachPeisSchaudtetal.2017, author = {Beckenbach, Isabel and Peis, Britta and Schaudt, Oliver and Scheidweiler, Robert}, title = {A Combinatorial Proof of a K{\"o}nig-type Theorem for Unimodular Hypergraphs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64017}, year = {2017}, abstract = {We state purely combinatorial proofs for K{\"o}nig- and Hall-type theorems for a wide class of combinatorial optimization problems. Our methods rely on relaxations of the matching and vertex cover problem and, moreover, on the strong coloring properties admitted by bipartite graphs and their generalizations.}, language = {en} } @misc{GrimmBorndoerferReutheretal.2017, author = {Grimm, Boris and Bornd{\"o}rfer, Ralf and Reuther, Markus and Schade, Stanley and Schlechte, Thomas}, title = {A Propagation Approach to Acyclic Rolling Stock Rotation Optimization}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63930}, year = {2017}, abstract = {The rolling stock, i.e., railway vehicles, are one of the key ingredients of a running railway system. As it is well known, the offer of a railway company to their customers, i.e., the railway timetable, changes from time to time. Typical reasons for that are different timetables associated with different seasons, maintenance periods or holidays. Therefore, the regular lifetime of a timetable is split into (more or less) irregular periods where parts of the timetable are changed. In order to operate a railway timetable most railway companies set up sequences that define the operation of timetabled trips by a single physical railway vehicle called (rolling stock) rotations. Not surprisingly, the individual parts of a timetable also affect the rotations. More precisely, each of the parts brings up an acyclic rolling stock rotation problem with start and end conditions associated with the beginning and ending of the corresponding period. In this paper, we propose a propagation approach to deal with large planning horizons that are composed of many timetables with shorter individual lifetimes. The approach is based on an integer linear programming formulation that propagates rolling stock rotations through the irregular parts of the timetable while taking a large variety of operational requirements into account. This approach is implemented within the rolling stock rotation optimization framework ROTOR used by DB Fernverkehr AG, one of the leading railway operators in Europe. Computational results for real world scenarios are presented to evaluate the approach.}, language = {en} } @misc{BorndoerferBuwayaSagnoletal.2012, author = {Bornd{\"o}rfer, Ralf and Buwaya, Julia and Sagnol, Guillaume and Swarat, Elmar}, title = {Optimizing Toll Enforcement in Transportation Networks: a Game-Theoretic Approach}, issn = {1438-0064}, doi = {/10.1016/j.endm.2013.05.100}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17401}, year = {2012}, abstract = {We present a game-theoretic approach to optimize the strategies of toll enforcement on a motorway network. In contrast to previous approaches, we consider a network with an arbitrary topology, and we handle the fact that users may choose their Origin-Destination path; in particular they may take a detour to avoid sections with a high control rate. We show that a Nash equilibrium can be computed with an LP (although the game is not zero-sum), and we give a MIP for the computation of a Stackelberg equilibrium. Experimental results based on an application to the enforcement of a truck toll on German motorways are presented.}, language = {en} } @misc{BorndoerferSagnolSwarat2011, author = {Bornd{\"o}rfer, Ralf and Sagnol, Guillaume and Swarat, Elmar}, title = {An IP Approach to Toll Enforcement Optimization on German Motorways}, issn = {1438-0064}, doi = {10.1007/978-3-642-29210-1_51}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14299}, number = {11-42}, year = {2011}, abstract = {This paper proposes the first model for toll enforcement optimization on German motorways. The enforcement is done by mobile control teams and our goal is to produce a schedule achieving network-wide control, proportional to spatial and time-dependent traffic distributions. Our model consists of two parts. The first plans control tours using a vehicle routing approach with profits and some side constraints. The second plans feasible rosters for the control teams. Both problems can be modeled as Multi-Commodity Flow Problems. Adding additional coupling constraints produces a large-scale integrated integer programming formulation. We show that this model can be solved to optimality for real world instances associated with a control area in East Germany.}, language = {en} } @misc{SagnolBorndoerferSchlechteetal.2014, author = {Sagnol, Guillaume and Bornd{\"o}rfer, Ralf and Schlechte, Thomas and Swarat, Elmar}, title = {The Price of Spite in Spot-checking games}, issn = {1438-0064}, doi = {10.1007/978-3-662-44803-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-52775}, year = {2014}, abstract = {We introduce the class of spot-checking games (SC games). These games model problems where the goal is to distribute fare inspectors over a toll network. Although SC games are not zero-sum, we show that a Nash equilibrium can be computed by linear programming. The computation of a strong Stackelberg equilibrium is more relevant for this problem, but we show that this is NP-hard. However, we give some bounds on the \emph{price of spite}, which measures how the payoff of the inspector degrades when committing to a Nash equilibrium. Finally, we demonstrate the quality of these bounds for a real-world application, namely the enforcement of a truck toll on German motorways.}, language = {en} } @inproceedings{GilgKlugMartienssenetal.2017, author = {Gilg, Brady and Klug, Torsten and Martienssen, Rosemarie and Paat, Joseph and Schlechte, Thomas and Schulz, Christof and Seymen, Sinan and Tesch, Alexander}, title = {Conflict-Free Railway Track Assignment at Depots}, booktitle = {Proceedings of the IAROR conference RailLille}, year = {2017}, abstract = {Managing rolling stock with no passengers aboard is a critical component of railway operations. In particular, one problem is to park the rolling stock on a given set of tracks at the end of a day or service. Depending on the parking assignment, shunting may be required in order for a parked train to depart or for an incoming train to park. Given a collection of tracks M and a collection of trains T with fixed arrival-departure timetable, the train assignment problem (TAP) is to determine the maximum number of trains from T that can be parked on M according to the timetable and without the use of shunting. Hence, efficiently solving the TAP allows to quickly compute feasible parking schedules that do not require further shunting adjustments. In this paper, we present two integer programming models for solving the TAP. To our knowledge, this is the first integrated approach that considers track lengths along with the three most common types of parking tracks. We compare these models on a theoretical level. We also prove that a decision version of the TAP is NP-complete, justifying the use of integer programming techniques. Using stochastic and robust modelling techniques, both models produce parking assignments that are optimized and robust according to random train delays. We conclude with computational results for both models, observing that they perform well on real timetables.}, language = {en} } @inproceedings{BorndoerferSagnolSchwartz2016, author = {Bornd{\"o}rfer, Ralf and Sagnol, Guillaume and Schwartz, Stephan}, title = {An Extended Network Interdiction Problem for Optimal Toll Control}, volume = {52}, booktitle = {INOC 2015 - 7th International Network Optimization Conference}, doi = {10.1016/j.endm.2016.03.040}, pages = {301 -- 308}, year = {2016}, abstract = {We study an extension of the shortest path network interdiction problem and present a novel real-world application in this area. We consider the problem of determining optimal locations for toll control stations on the arcs of a transportation network. We handle the fact that drivers can avoid control stations on parallel secondary roads. The problem is formulated as a mixed integer program and solved using Benders decomposition. We present experimental results for the application of our models to German motorways.}, language = {en} } @misc{FischerSchlechte2017, author = {Fischer, Frank and Schlechte, Thomas}, title = {Strong Relaxations for the Train Timetabling Problem using Connected Configurations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64743}, year = {2017}, abstract = {The task of the train timetabling problem or track allocation problem is to find conflict free schedules for a set of trains with predefined routes in a railway network. Especially for non-periodic instances models based on time expanded networks are often used. Unfortunately, the linear programming relaxation of these models is often extremely weak because these models do not describe combinatorial relations like overtaking possibilities very well. In this paper we extend the model by so called connected configuration subproblems. These subproblems perfectly describe feasible schedules of a small subset of trains (2-3) on consecutive track segments. In a Lagrangian relaxation approach we solve several of these subproblems together in order to produce solutions which consist of combinatorially compatible schedules along the track segments. The computational results on a mostly single track corridor taken from the INFORMS RAS Problem Solving Competition 2012 data indicate that our new solution approach is rather strong. Indeed, for this instance the solution of the Lagrangian relaxation is already integral.}, language = {en} } @misc{GriewankHasenfelderRadonsetal.2017, author = {Griewank, Andreas and Hasenfelder, Richard and Radons, Manuel and Lehmann, Lutz and Streubel, Tom}, title = {Integrating Lipschitzian Dynamical Systems using Piecewise Algorithmic Differentiation}, issn = {1438-0064}, doi = {10.1080/10556788.2017.1378653}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64639}, year = {2017}, abstract = {In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side \(F:R^n \to R^n\) based on a generalization of algorithmic differentiation. When applied to such a problem, the classical trapezoidal rule suffers from a loss of accuracy if the solution trajectory intersects a nondifferentiability of \(F\). The advantage of the proposed generalized trapezoidal rule is threefold: Firstly, we can achieve a higher convergence order than with the classical method. Moreover, the method is energy preserving for piecewise linear Hamiltonian systems. Finally, in analogy to the classical case we derive a third order interpolation polynomial for the numerical trajectory. In the smooth case the generalized rule reduces to the classical one. Hence, it is a proper extension of the classical theory. An error estimator is given and numerical results are presented.}, language = {en} } @misc{RehfeldtKoch2017, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {Generalized preprocessing techniques for Steiner tree and maximum-weight connected subgraph problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65439}, year = {2017}, abstract = {This article introduces new preprocessing techniques for the Steiner tree problem in graphs and one of its most popular relatives, the maximum-weight connected subgraph problem. Several of the techniques generalize previous results from the literature. The correctness of the new methods is shown, but also their NP-hardness is demonstrated. Despite this pessimistic worst-case complexity, several relaxations are discussed that are expected to allow for a strong practical efficiency of these techniques in strengthening both exact and heuristic solving approaches.}, language = {en} } @misc{BertholdPerregaardMeszaros2017, author = {Berthold, Timo and Perregaard, Michael and M{\´e}sz{\´a}ros, Csaba}, title = {Four good reasons to use an Interior Point solver within a MIP solver}, issn = {1438-0064}, doi = {10.1007/978-3-319-89920-6_22}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64599}, year = {2017}, abstract = {"Interior point algorithms are a good choice for solving pure LPs or QPs, but when you solve MIPs, all you need is a dual simplex." This is the common conception which disregards that an interior point solution provides some unique structural insight into the problem at hand. In this paper, we will discuss some of the benefits that an interior point solver brings to the solution of difficult MIPs within FICO Xpress. This includes many different components of the MIP solver such as branching variable selection, primal heuristics, preprocessing, and of course the solution of the LP relaxation.}, language = {en} } @misc{MiltenbergerRalphsSteffy2017, author = {Miltenberger, Matthias and Ralphs, Ted and Steffy, Daniel}, title = {Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization}, journal = {Operations Research Proceedings 2017}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64645}, year = {2017}, abstract = {We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the numerical conditioning of the LP relaxations resulting from the branching and cutting operations can be effectively predicted and whether such predictions can be used to make better algorithmic choices. In a first step towards this goal, we discuss here the numerical behavior of an existing solver in order to determine whether our intuitive understanding of this behavior is correct.}, language = {en} } @misc{SchadeSchlechteWitzig2017, author = {Schade, Stanley and Schlechte, Thomas and Witzig, Jakob}, title = {Structure-based Decomposition for Pattern-Detection for Railway Timetables}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64525}, year = {2017}, abstract = {We consider the problem of pattern detection in large scale railway timetables. This problem arises in rolling stock optimization planning in order to identify invariant sections of the timetable for which a cyclic rotation plan is adequate. We propose a dual reduction technique which leads to an decomposition and enumeration method. Computational results for real world instances demonstrate that the method is able to produce optimal solutions as fast as standard MIP solvers.}, language = {en} } @misc{RenkenAhmadiBorndoerferetal.2017, author = {Renken, Malte and Ahmadi, Amin and Bornd{\"o}rfer, Ralf and Sahin, Guvenc and Schlechte, Thomas}, title = {Demand-Driven Line Planning with Selfish Routing}, issn = {1438-0064}, doi = {10.1007/978-3-319-89920-6_91}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64547}, year = {2017}, abstract = {Bus rapid transit systems in developing and newly industrialized countries are often operated at the limits of passenger capacity. In particular, demand during morning and afternoon peaks is hardly or even not covered with available line plans. In order to develop demand-driven line plans, we use two mathematical models in the form of integer programming problem formulations. While the actual demand data is specified with origin-destination pairs, the arc-based model considers the demand over the arcs derived from the origin-destination demand. In order to test the accuracy of the models in terms of demand satisfaction, we simulate the optimal solutions and compare number of transfers and travel times. We also question the effect of a selfish route choice behavior which in theory results in a Braess-like paradox by increasing the number of transfers when system capacity is increased with additional lines.}, language = {en} } @misc{Hennings2017, author = {Hennings, Felix}, title = {Benefits and Limitations of Simplified Transient Gas Flow Formulations}, issn = {1438-0064}, doi = {10.1007/978-3-319-89920-6_32}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64570}, year = {2017}, abstract = {Although intensively studied in recent years, the optimization of the transient (time-dependent) control of large real-world gas networks is still out of reach for current state-of-the-art approaches. For this reason, we present further simplifications of the commonly used model, which lead to a linear description of the gas flow on pipelines. In an empirical analysis of real-world data, we investigate the properties of the involved quantities and evaluate the errors made by our simplification.}, language = {en} } @misc{StreubelStrohmTrunschkeetal.2017, author = {Streubel, Tom and Strohm, Christian and Trunschke, Philipp and Tischendorf, Caren}, title = {Generic Construction and Efficient Evaluation of Network DAEs and Their Derivatives in the Context of Gas Networks}, issn = {1438-0064}, doi = {10.1007/978-3-319-89920-6_83}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64582}, year = {2017}, abstract = {We present a concept that provides an efficient description of differential-algebraic equations (DAEs) describing flow networks which provides the DAE function f and their Jacobians in an automatized way such that the sparsity pattern of the Jacobians is determined before their evaluation and previously determined values of f can be exploited. The user only has to provide the network topology and local function descriptions for each network element. The approach uses automatic differentiation (AD) and is adapted to switching element functions via the abs-normal-form (ANF).}, language = {en} } @inproceedings{MiltenbergerRalphsSteffy2018, author = {Miltenberger, Matthias and Ralphs, Ted and Steffy, Daniel}, title = {Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization}, booktitle = {Operations Research Proceedings 2017}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-89920-6}, pages = {151 -- 157}, year = {2018}, abstract = {We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the numerical conditioning of the LP relaxations resulting from the branching and cutting operations can be effectively predicted and whether such predictions can be used to make better algorithmic choices. In a first step towards this goal, we discuss here the numerical behavior of an existing solver in order to determine whether our intuitive understanding of this behavior is correct.}, language = {en} } @inproceedings{D'AndreagiovanniMettPulaj2016, author = {D'Andreagiovanni, Fabio and Mett, Fabian and Pulaj, Jonad}, title = {An (MI)LP-based Primal Heuristic for 3-Architecture Connected Facility Location in Urban Access Network Design}, volume = {9597}, booktitle = {EvoApplications: European Conference on the Applications of Evolutionary Computation. Applications of Evolutionary Computation. 19th European Conference, EvoApplications 2016, Porto, Portugal, March 30 -- April 1, 2016, Proceedings, Part I}, doi = {10.1007/978-3-319-31204-0_19}, pages = {283 -- 298}, year = {2016}, abstract = {We investigate the 3-architecture Connected Facility Location Problem arising in the design of urban telecommunication access networks integrating wired and wireless technologies. We propose an original optimization model for the problem that includes additional variables and constraints to take into account wireless signal coverage represented through signal-to-interference ratios. Since the problem can prove very challenging even for modern state-of-the art optimization solvers, we propose to solve it by an original primal heuristic that combines a probabilistic fixing procedure, guided by peculiar Linear Programming relaxations, with an exact MIP heuristic, based on a very large neighborhood search. Computational experiments on a set of realistic instances show that our heuristic can find solutions associated with much lower optimality gaps than a state-of-the-art solver.}, language = {en} } @inproceedings{YokoyamaShinanoTaniguchietal.2015, author = {Yokoyama, Ryohei and Shinano, Yuji and Taniguchi, Syusuke and Ohkura, Masashi and Wakui, Tetsuya}, title = {Generation of multiple best solutions in multiobjective optimal design of energy supply systems}, booktitle = {Proceedings of the 15th International Conference on Power Engineering. ICOPE 2015}, doi = {10.1299/jsmeicope.2015.12._ICOPE-15-_56}, year = {2015}, abstract = {Optimization approaches based on the mixed-integer linear programming (MILP) have been utilized to design energy supply systems. In this paper, an MILP method utilizing the hierarchical relationship between design and operation is extended to search not only the optimal solution but also suboptimal ones which follow the optimal one without any omissions, what are called K-best solutions, efficiently in a multiobjective optimal design problem. At the upper level, the values of design variables for the K-best solutions are searched by the branch and bound method. At the lower level, the values of operation variables are optimized independently at each period by the branch and bound method under the values of design variables given tentatively. Incumbents for the K-best solutions and an upper bound for all the values of the objective function for the K-best solutions are renewed if necessary between both the levels. This method is implemented into a commercial MILP solver. A practical case study on the multiobjective optimal design of a cogeneration system is conducted, and the validity and effectiveness of the method are clarified.}, language = {en} } @article{GleixnerSteffyWolter2016, author = {Gleixner, Ambros and Steffy, Daniel and Wolter, Kati}, title = {Iterative Refinement for Linear Programming}, volume = {28}, journal = {INFORMS Journal on Computing}, number = {3}, doi = {10.1287/ijoc.2016.0692}, pages = {449 -- 464}, year = {2016}, abstract = {We describe an iterative refinement procedure for computing extended precision or exact solutions to linear programming problems (LPs). Arbitrarily precise solutions can be computed by solving a sequence of closely related LPs with limited precision arithmetic. The LPs solved share the same constraint matrix as the original problem instance and are transformed only by modification of the objective function, right-hand side, and variable bounds. Exact computation is used to compute and store the exact representation of the transformed problems, while numeric computation is used for solving LPs. At all steps of the algorithm the LP bases encountered in the transformed problems correspond directly to LP bases in the original problem description. We show that this algorithm is effective in practice for computing extended precision solutions and that it leads to a direct improvement of the best known methods for solving LPs exactly over the rational numbers. Our implementation is publically available as an extension of the academic LP solver SoPlex.}, language = {en} } @inproceedings{Hendel2016, author = {Hendel, Gregor}, title = {Exploiting Solving Phases for Mixed-Integer Programs}, booktitle = {Operations Research Proceedings 2015}, doi = {10.1007/978-3-319-42902-1_1}, pages = {3 -- 9}, year = {2016}, abstract = {Modern MIP solving software incorporates dozens of auxiliary algorithmic components for supporting the branch-and-bound search in finding and improving solutions and in strengthening the relaxation. Intuitively, a dynamic solving strategy with an appropriate emphasis on different solving components and strategies is desirable during the search process. We propose an adaptive solver behavior that dynamically reacts on transitions between the three typical phases of a MIP solving process: The first phase objective is to find a feasible solution. During the second phase, a sequence of incumbent solutions gets constructed until the incumbent is eventually optimal. Proving optimality is the central objective of the remaining third phase. Based on the MIP-solver SCIP, we demonstrate the usefulness of the phase concept both with an exact recognition of the optimality of a solution, and provide heuristic alternatives to make use of the concept in practice.}, language = {en} } @inproceedings{ShinanoAchterbergBertholdetal.2016, author = {Shinano, Yuji and Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Winkler, Michael}, title = {Solving Open MIP Instances with ParaSCIP on Supercomputers using up to 80,000 Cores}, booktitle = {Proc. of 30th IEEE International Parallel \& Distributed Processing Symposium}, doi = {10.1109/IPDPS.2016.56}, year = {2016}, abstract = {This paper describes how we solved 12 previously unsolved mixed-integer program- ming (MIP) instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper we describe the basic parallelization mechanism of ParaSCIP, improvements of the dynamic load balancing and novel techniques to exploit the power of parallelization for MIP solving. We give a detailed overview of computing times and statistics for solving open MIPLIB instances.}, language = {en} } @incollection{BargmannEbbersHeineckeetal.2015, author = {Bargmann, Dagmar and Ebbers, Mirko and Heinecke, Nina and Koch, Thorsten and K{\"u}hl, Veronika and Pelzer, Antje and Pfetsch, Marc and R{\"o}vekamp, Jessica and Spreckelsen, Klaus}, title = {State-of-the-art in evaluating gas network capacities}, booktitle = {Evaluating Gas Network Capacities}, publisher = {Society for Industrial and Applied Mathematics}, isbn = {9781611973686}, pages = {65 -- 84}, year = {2015}, language = {en} } @article{LeitnerLjubicSinnletal.2016, author = {Leitner, Markus and Ljubic, Ivana and Sinnl, Markus and Werner, Axel}, title = {ILP heuristics and a new exact method for bi-objective 0/1 ILPs: Application to FTTx-network design}, journal = {Computers \& Operations Research}, doi = {10.1016/j.cor.2016.02.006}, year = {2016}, language = {en} } @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} } @misc{Humpola2015, author = {Humpola, Jesco}, title = {Sufficient Pruning Conditions for MINLP in Gas Network Design}, doi = {10.1007/s13675-016-0077-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53489}, year = {2015}, abstract = {One quarter of Europe's energy demand is provided by natural gas distributed through a vast pipeline network covering the whole of Europe. At a cost of 1 million Euros per kilometer the extension of the European pipeline network is already a multi billion Euro business. Therefore, automatic planning tools that support the decision process are desired. We model the topology extension problem in gas networks by a mixed-integer nonlinear program (MINLP). This gives rise to a so-called active transmission problem, a continuous nonlinear non-convex feasibility problem which emerges from the MINLP model by fixing all integral variables. In this article we offer novel sufficient conditions for proving the infeasibility of this active transmission problem. These conditions can be expressed in the form of a mixed-integer program (MILP), i.e., the infeasibility of a non-convex NLP can be certified by solving an MILP. These results provide an efficient bounding procedure in a branch-and-bound algorithm. Our computational results demonstrate a substantial speed-up for the necessary computations.}, language = {en} } @misc{D'AndreagiovanniKrolikowskiPulaj2014, author = {D'Andreagiovanni, Fabio and Krolikowski, Jonatan and Pulaj, Jonad}, title = {A Fast Hybrid Primal Heuristic for Multiband Robust Capacitated Network Design with Multiple Time Periods}, issn = {1438-0064}, doi = {10.1016/j.asoc.2014.10.016}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-52862}, year = {2014}, abstract = {We investigate the Robust Multiperiod Network Design Problem, a generalization of the Capacitated Network Design Problem (CNDP) that, besides establishing flow routing and network capacity installation as in a canonical CNDP, also considers a planning horizon made up of multiple time periods and protection against fluctuations in traffic volumes. As a remedy against traffic volume uncertainty, we propose a Robust Optimization model based on Multiband Robustness (B{\"u}sing and D'Andreagiovanni, 2012), a refinement of classical Gamma-Robustness by Bertsimas and Sim (2004) that uses a system of multiple deviation bands. Since the resulting optimization problem may prove very challenging even for instances of moderate size solved by a state-of-the-art optimization solver, we propose a hybrid primal heuristic that combines a randomized fixing strategy inspired by ant colony optimization and an exact large neighbourhood search. Computational experiments on a set of realistic instances from the SNDlib (2010) show that our original heuristic can run fast and produce solutions of extremely high quality associated with low optimality gaps.}, language = {en} } @misc{BrettHobergPachecoetal.2015, author = {Brett, Charles and Hoberg, Rebecca and Pacheco, Meritxell and Smith, Kyle and Bornd{\"o}rfer, Ralf and Euler, Ricardo and Gamrath, Gerwin and Grimm, Boris and Heismann, Olga and Reuther, Markus and Schlechte, Thomas and Tesch, Alexander}, title = {G-RIPS 2014 RailLab - Towards robust rolling stock rotations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53475}, year = {2015}, abstract = {The Graduate-Level Research in Industrial Projects (G-RIPS) Program provides an opportunity for high-achieving graduate-level students to work in teams on a real-world research project proposed by a sponsor from industry or the public sector. Each G-RIPS team consists of four international students (two from the US and two from European universities), an academic mentor, and an industrial sponsor. This is the report of the Rail-Lab project on the definition and integration of robustness aspects into optimizing rolling stock schedules. In general, there is a trade-off for complex systems between robustness and efficiency. The ambitious goal was to explore this trade-off by implementing numerical simulations and developing analytic models. In rolling stock planning a very large set of industrial railway requirements, such as vehicle composition, maintenance constraints, infrastructure capacity, and regularity aspects, have to be considered in an integrated model. General hypergraphs provide the modeling power to tackle those requirements. Furthermore, integer programming approaches are able to produce high quality solutions for the deterministic problem. When stochastic time delays are considered, the mathematical programming problem is much more complex and presents additional challenges. Thus, we started with a basic variant of the deterministic case, i.e., we are only considering hypergraphs representing vehicle composition and regularity. We transfered solution approaches for robust optimization from the airline industry to the setting of railways and attained a reasonable measure of robustness. Finally, we present and discuss different methods to optimize this robustness measure.}, language = {en} } @phdthesis{Humpola2014, author = {Humpola, Jesco}, title = {Gas Network Optimization by MINLP}, school = {Technische Universit{\"a}t Berlin}, year = {2014}, abstract = {One quarter of Europe's energy demand is provided by natural gas distributed through a vast pipeline network covering the whole of Europe. At a cost of 1 million Euros per kilometer the extension of the European pipeline network is already a multi billion Euro business. The challenging question is how to expand and operate the network in order to facilitate the transportation of specified gas quantities at minimum cost. This task can be formulated as a mathematical optimization problem that reflects to real-world instances of enormous size and complexity. The aim of this thesis is the development of novel theory and optimization algorithms which make it possible to solve these problems. Gas network topology optimization problems can be modeled as nonlinear mixed-integer programs (MINLPs). Such an MINLP gives rise to a so-called active transmission problem (ATP), a continuous nonlinear non-convex feasibility problem which emerges from the MINLP model by fixing all integral variables. The key to solving the ATP as well as the overall gas network topology optimization problem and the main contribution of this thesis is a novel domain relaxation of the variable bounds and constraints in combination with a penalization in the objective function. In case the domain relaxation does not yield a primal feasible solution for the ATP we offer novel sufficient conditions for proving the infeasibility of the ATP. These conditions can be expressed in the form of an MILP, i.e., the infeasibility of a non-convex NLP can be certified by solving an MILP. These results provide an efficient bounding procedure in a branch-and-bound algorithm. If the gas network consists only of pipes and valves, the ATP turns into a passive transmission problem (PTP). Although its constraints are non-convex, its domain relaxation can be proven to be convex. Consequently, the feasibility of the PTP can be checked directly in an efficient way. Another advantage of the passive case is that the solution of the domain relaxation gives rise to a cutting plane for the overall topology optimization problem that expresses the infeasibility of the PTP. This cut is obtained by a Benders argument from the Lagrange function of the domain relaxation augmented by a specially tailored pc-regularization. These cuts provide tight lower bounds for the passive gas network topology optimization problem. The domain relaxation does not only provide certificates of infeasibility and cutting planes, it can also be used to construct feasible primal solutions. We make use of parametric sensitivity analysis in order to identify binary variables to be switched based on dual information. This approach allows for the first time to compute directly MINLP solutions for large-scale gas network topology optimization problems. All the research in this thesis has been realized within the collaborative research project "Forschungskooperation Netzoptimierung (ForNe)". The developed software is in use by the cooperation partner Open Grid Europe GmbH. Parts of this thesis have been published in book chapters, journal articles and technical reports. An overview of the topics and solution approaches within the research project is given by Martin et al. (2011) and F{\"u}genschuh et al. (2013). Gas network operation approaches and solution methods are described in detail by Pfetsch et al. (2014) and with a special focus on topology optimization in F{\"u}genschuh et al. (2011). The primal heuristic presented in this thesis is published by Humpola et al. (2014b). The method for pruning nodes of the branch-and-bound tree for an approximation of the original problem is described in F{\"u}genschuh and Humpola (2013) and Humpola et al. (2014a). The Benders like inequality is introduced by Humpola and F{\"u}genschuh (2013).}, language = {en} } @phdthesis{Dovica2014, author = {Dovica, Ivan}, title = {Robust tail assignment}, year = {2014}, abstract = {The first part of this thesis is devoted to the general problem of stochastic shortest path problem. It is about searching for the shortest path in a graph in which arc lengths are uncertain and specified by continuous random variables. This problem is at the core of various applications, especially in robust transportation planning where paths correspond to aircraft, train, or bus rotations, crew duties or rosters, etc. We propose a novel solution method based on a discretisation of random variables which is applicable to any class of continuous random variables. We also give bounds on the approximation error of the discretised path lengths compared to the continuous path lengths. In addition, we provide theoretical results for the computational complexity of this method. In the second part we apply this method to a real world airline transportation problem: the so-called tail assignment problem. The goal of the tail assignment problem is to construct aircraft rotations, routes consisting of flight segments, for a set of individual aircraft in order to cover a set of flight segments (legs) while considering operational constraints of each individual aircraft as well as short- to long-term individual maintenance requirements. We state a stochastic programming formulation of this problem and we show how to solve it efficiently by using our method within a column generation framework. We show the gain of our stochastic approach in comparison to standard KPI in terms of less propagated delay and thus less operational costs without growth of computational complexity. A key point of our complex approach to robust optimisation problem is the fit of the underlying stochastic model with reality. We propose a delay propagation model that is realistic, not overfitted, and can therefore be used for forecasting purposes. We benchmark our results using extensive simulation. We show a significant decrease of arrival delays and thus monetary savings on average as well as in the majority of our disruption scenarios. We confirm these benefits in even more life-like benchmarks as simulation where recovery actions are taken and in scenarios which use historical delays directly instead of the stochastic model.}, language = {en} } @incollection{HillerHumpolaLehmannetal.2015, author = {Hiller, Benjamin and Humpola, Jesco and Lehmann, Thomas and Lenz, Ralf and Morsi, Antonio and Pfetsch, Marc and Schewe, Lars and Schmidt, Martin and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Willert, Bernhard}, title = {Computational results for validation of nominations}, volume = {SIAM-MOS series on Optimization}, booktitle = {Evaluating Gas Network Capacities}, isbn = {9781611973686}, year = {2015}, abstract = {The different approaches to solve the validation of nomination problem presented in the previous chapters are evaluated computationally in this chapter. Each approach is analyzed individually, as well as the complete solvers for these problems. We demonstrate that the presented approaches can successfully solve large-scale real-world instances.}, language = {en} } @incollection{HumpolaFuegenschuhHilleretal.2015, author = {Humpola, Jesco and F{\"u}genschuh, Armin and Hiller, Benjamin and Koch, Thorsten and Lehmann, Thomas and Lenz, Ralf and Schwarz, Robert and Schweiger, Jonas}, title = {The Specialized MINLP Approach}, volume = {SIAM-MOS series on Optimization}, booktitle = {Evaluating Gas Network Capacities}, isbn = {9781611973686}, year = {2015}, abstract = {We propose an approach to solve the validation of nominations problem using mixed-integer nonlinear programming (MINLP) methods. Our approach handles both the discrete settings and the nonlinear aspects of gas physics. Our main contribution is an innovative coupling of mixed-integer (linear) programming (MILP) methods with nonlinear programming (NLP) that exploits the special structure of a suitable approximation of gas physics, resulting in a global optimization method for this type of problem.}, language = {en} } @article{BorndoerferDittbrennerLangenhanetal.2014, author = {Bornd{\"o}rfer, Ralf and Dittbrenner, Bastian and Langenhan, Andreas and Seidl, Stephan and Weider, Steffen}, title = {Integrierte Dienst- und Dienstreihenfolgeplanung zur Erh{\"o}hung der Fahrerzufriedenheit}, journal = {Straßenverkehrstechnik}, number = {9}, pages = {583 -- 591}, year = {2014}, language = {de} } @book{KochHillerPfetschetal.2015, author = {Koch, Thorsten and Hiller, Benjamin and Pfetsch, Marc and Schewe, Lars}, title = {Evaluating Gas Network Capacities}, publisher = {SIAM}, isbn = {978-1-611973-68-6}, pages = {xvi + 376 pages}, year = {2015}, language = {en} } @misc{Witzig2017, author = {Witzig, Jakob}, title = {Conflict Driven Diving for Mixed Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66116}, year = {2017}, abstract = {The analysis of infeasibility plays an important role in solving satisfiability problems (SAT) and mixed integer programs (MIPs). In mixed integer programming, this procedure is called conflict analysis. So far, modern MIP solvers use conflict analysis only for propagation and improving the dual bound, i.e., fathoming nodes that cannot contain feasible solutions. In this short paper, we present a new approach which uses conflict information to improve the primal bound during a MIP solve. To derive new improving primal solutions we use a conflict driven diving heuristic called conflict diving that uses the information obtained by conflict analysis. Conflict diving pursues a twofold strategy. By using conflict information the new diving approach is guided into parts of the search space that are usually not explored by other diving heuristics. At the same time, conflict diving has a fail-fast-strategy to reduce the time spent if it cannot find a new primal solution. As a byproduct, additional valid conflict constraints can be derived, from which a MIP solver can gain benefit to improve the dual bound as well. To show the added-value of conflict diving within a MIP solver, conflict diving has been implemented within the non-commercial MIP solver SCIP. Experiments are carried out on general MIP instances from standard public test sets, like MIPLIB2010 or Cor@l.}, language = {en} } @misc{AchterbergBixbyGuetal.2016, author = {Achterberg, Tobias and Bixby, Robert E. and Gu, Zonghao and Rothberg, Edward and Weninger, Dieter}, title = {Presolve Reductions in Mixed Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60370}, year = {2016}, abstract = {Mixed integer programming has become a very powerful tool for modeling and solving real-world planning and scheduling problems, with the breadth of applications appearing to be almost unlimited. A critical component in the solution of these mixed-integer programs is a set of routines commonly referred to as presolve. Presolve can be viewed as a collection of preprocessing techniques that reduce the size of and, more importantly, improve the ``strength'' of the given model formulation, that is, the degree to which the constraints of the formulation accurately describe the underlying polyhedron of integer-feasible solutions. As our computational results will show, presolve is a key factor in the speed with which we can solve mixed-integer programs, and is often the difference between a model being intractable and solvable, in some cases easily solvable. In this paper we describe the presolve functionality in the Gurobi commercial mixed-integer programming code. This includes an overview, or taxonomy of the different methods that are employed, as well as more-detailed descriptions of several of the techniques, with some of them appearing, to our knowledge, for the first time in the literature.}, language = {en} } @misc{RehfeldtKochMaher2016, author = {Rehfeldt, Daniel and Koch, Thorsten and Maher, Stephen J.}, title = {Reduction Techniques for the Prize-Collecting Steiner Tree Problem and the Maximum-Weight Connected Subgraph Problem}, issn = {1438-0064}, doi = {10.1002/net.21857}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60420}, year = {2016}, abstract = {The concept of reduction has frequently distinguished itself as a pivotal ingredient of exact solving approaches for the Steiner tree problem in graphs. In this paper we broaden the focus and consider reduction techniques for three Steiner problem variants that have been extensively discussed in the literature and entail various practical applications: The prize-collecting Steiner tree problem, the rooted prize-collecting Steiner tree problem and the maximum-weight connected subgraph problem. By introducing and subsequently deploying numerous new reduction methods, we are able to drastically decrease the size of a large number of benchmark instances, already solving more than 90 percent of them to optimality. Furthermore, we demonstrate the impact of these techniques on exact solving, using the example of the state-of-the-art Steiner problem solver SCIP-Jack.}, language = {en} } @misc{Pulaj2016, author = {Pulaj, Jonad}, title = {Cutting Planes for Families Implying Frankl's Conjecture}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60626}, year = {2016}, abstract = {We find previously unknown families which imply Frankl's conjecture using an algorithmic framework. The conjecture states that for any non-empty union-closed (or Frankl) family there exists an element in at least half of the sets. Poonen's Theorem characterizes the existence of weights which determine whether a given Frankl family implies the conjecture for all Frankl families which contain it. A Frankl family is Non-Frankl-Complete (Non-FC), if it does not imply the conjecture in its elements for some Frankl family that contains it. We design a cutting-plane method that computes the explicit weights which imply the existence conditions of Poonen's Theorem. This method allows us to find a counterexample to a ten-year-old conjecture by R. Morris about the structure of generators for Non-FC-families.}, language = {en} } @misc{WitzigBeckenbachEifleretal.2016, author = {Witzig, Jakob and Beckenbach, Isabel and Eifler, Leon and Fackeldey, Konstantin and Gleixner, Ambros and Grever, Andreas and Weber, Marcus}, title = {Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes}, issn = {1438-0064}, doi = {10.1137/16M1091162}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60353}, year = {2016}, abstract = {In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst.}, language = {en} } @misc{FischerGrimmKlugetal.2016, author = {Fischer, Frank and Grimm, Boris and Klug, Torsten and Schlechte, Thomas}, title = {A Re-optimization Approach for Train Dispatching}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60493}, year = {2016}, abstract = {The Train Dispatching Problem (TDP) is to schedule trains through a network in a cost optimal way. Due to disturbances during operation existing track allocations often have to be re-scheduled and integrated into the timetable. This has to be done in seconds and with minimal timetable changes to guarantee smooth and conflict free operation. We present an integrated modeling approach for the re-optimization task using Mixed Integer Programming. Finally, we provide computational results for scenarios provided by the INFORMS RAS Problem Soling Competition 2012.}, language = {en} } @misc{BorndoerferHoppmannKarbsteinetal.2016, author = {Bornd{\"o}rfer, Ralf and Hoppmann, Heide and Karbstein, Marika and L{\"o}bel, Fabian}, title = {The Modulo Network Simplex with Integrated Passenger Routing}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60319}, year = {2016}, abstract = {Periodic timetabling is an important strategic planning problem in public transport. The task is to determine periodic arrival and departure times of the lines in a given network, minimizing the travel time of the passengers. We extend the modulo network simplex method, a well-established heuristic for the periodic timetabling problem, by integrating a passenger (re)routing step into the pivot operations. Computations on real-world networks show that we can indeed find timetables with much shorter total travel time, when we take the passengers' travel paths into consideration.}, language = {en} } @article{WitzigBeckenbachEifleretal.2018, author = {Witzig, Jakob and Beckenbach, Isabel and Eifler, Leon and Fackeldey, Konstantin and Gleixner, Ambros and Grever, Andreas and Weber, Marcus}, title = {Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes}, volume = {16}, journal = {Multiscale Modeling and Simulation}, number = {1}, issn = {1438-0064}, doi = {10.1137/16M1091162}, pages = {248 -- 265}, year = {2018}, abstract = {In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst.}, language = {en} } @inproceedings{SchadeStrehler2016, author = {Schade, Stanley and Strehler, Martin}, title = {The Maximum Flow Problem for Oriented Flows}, volume = {54}, booktitle = {16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016)}, editor = {Goerigk, Marc and Werneck, Renato}, publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik}, address = {Dagstuhl, Germany}, isbn = {978-3-95977-021-7}, issn = {2190-6807}, doi = {10.4230/OASIcs.ATMOS.2016.7}, url = {http://nbn-resolving.de/urn:nbn:de:0030-drops-65318}, pages = {1 -- 13}, year = {2016}, abstract = {In several applications of network flows, additional constraints have to be considered. In this paper, we study flows, where the flow particles have an orientation. For example, cargo containers with doors only on one side and train coaches with 1st and 2nd class compartments have such an orientation. If the end position has a mandatory orientation, not every path from source to sink is feasible for routing or additional transposition maneuvers have to be made. As a result, a source-sink path may visit a certain vertex several times. We describe structural properties of optimal solutions, determine the computational complexity, and present an approach for approximating such flows.}, language = {en} } @inproceedings{MaherMiltenbergerPedrosoetal.2016, author = {Maher, Stephen J. and Miltenberger, Matthias and Pedroso, Jo{\~a}o Pedro and Rehfeldt, Daniel and Schwarz, Robert and Serrano, Felipe}, title = {PySCIPOpt: Mathematical Programming in Python with the SCIP Optimization Suite}, volume = {9725}, booktitle = {Mathematical Software - ICMS 2016}, publisher = {Springer}, doi = {10.1007/978-3-319-42432-3_37}, pages = {301 -- 307}, year = {2016}, abstract = {SCIP is a solver for a wide variety of mathematical optimization problems. It is written in C and extendable due to its plug-in based design. However, dealing with all C specifics when extending SCIP can be detrimental to development and testing of new ideas. This paper attempts to provide a remedy by introducing PySCIPOpt, a Python interface to SCIP that enables users to write new SCIP code entirely in Python. We demonstrate how to intuitively model mixed-integer linear and quadratic optimization problems and moreover provide examples on how new Python plug-ins can be added to SCIP.}, language = {en} } @misc{BorndoerferKlugLamorgeseetal.2015, author = {Bornd{\"o}rfer, Ralf and Klug, Torsten and Lamorgese, Leonardo and Mannino, Carlo and Reuther, Markus and Schlechte, Thomas}, title = {Recent Success Stories on Optimization of Railway Systems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53726}, year = {2015}, abstract = {Planning and operating railway transportation systems is an extremely hard task due to the combinatorial complexity of the underlying discrete optimization problems, the technical intricacies, and the immense size of the problem instances. Because of that, however, mathematical models and optimization techniques can result in large gains for both railway cus- tomers and operators, e.g., in terms of cost reductions or service quality improvements. In the last years a large and growing group of researchers in the OR community have devoted their attention to this domain devel- oping mathematical models and optimization approaches to tackle many of the relevant problems in the railway planning process. However, there is still a gap to bridge between theory and practice, with a few notable exceptions. In this paper we address three success stories, namely, long-term freight train routing (part I), mid-term rolling stock rotation planning (part II), and real-time train dispatching (part III). In each case, we describe real-life, successful implementations. We will dis- cuss the individual problem setting, survey the optimization literature, and focus on particular aspects addressed by the mathematical models. We demonstrate on concrete applications how mathematical optimization can support railway planning and operations. This gives proof that math- ematical optimization can support the planning of rolling stock resources. Thus, mathematical models and optimization can lead to a greater effi- ciency of railway operations and will serve as a powerful and innovative tool to meet recent challenges of the railway industry.}, language = {en} } @misc{BorndoerferKarbstein2015, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika}, title = {Metric Inequalities for Routings on Direct Connections with Application in Line Planning}, issn = {1438-0064}, doi = {10.1016/j.disopt.2015.07.004}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53507}, year = {2015}, abstract = {We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the feasibility condition for arc capacities in ordinary multi-commodity flows. The concept allows to solve large-scale real-world line planning problems in public transport including a novel passenger routing model that favors direct connections over connections with transfers.}, language = {en} } @misc{DraegertEisenblaetterGamrathetal.2015, author = {Draegert, Andreas and Eisenbl{\"a}tter, Andreas and Gamrath, Inken and Werner, Axel}, title = {Optimal Battery Controlling for Smart Grid Nodes}, issn = {1438-0064}, doi = {10.1007/978-4-431-55420-2_6}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53550}, year = {2015}, abstract = {Energy storages can be of great value when added to power grids. They introduce the possibility to store and release energy whenever this is favorable. This is particularly relevant, for example, if power supply is volatile (as is the case with renewable energy) and the network is small (so that there are few other nodes that might balance fluctuations in consumption or production). We present models and methods from mathematical optimization for computing an optimized storage schedule for this purpose. We look at alternative optimization objectives, such as smallest possible peak load, low energy costs, or the close approximation of a prescribed load curve. The optimization needs to respect general operational and economic constraints as well as limitations in the use of storage, which are imposed by the chosen storage technology. We therefore introduce alternative approaches for modeling the non-linear properties of energy storages and study their impact on the efficiency of the optimization process. Finally, we present a computational study with batteries as storage devices. We use this to highlight the trade-off between solution quality and computational tractability. A version of the model for the purpose of leveling peaks and instabilities has been implemented into a control system for an office-building smart grid scenario.}, language = {en} } @misc{FuegenschuhJunoszaSzaniawskiKlugetal.2015, author = {F{\"u}genschuh, Armin and Junosza-Szaniawski, Konstanty and Klug, Torsten and Kwasiborski, Slawomir and Schlechte, Thomas}, title = {Fastest, average and quantile schedule}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53592}, year = {2015}, abstract = {We consider problems concerning the scheduling of a set of trains on a single track. For every pair of trains there is a minimum headway, which every train must wait before it enters the track after another train. The speed of each train is also given. Hence for every schedule - a sequence of trains - we may compute the time that is at least needed for all trains to travel along the track in the given order. We give the solution to three problems: the fastest schedule, the average schedule, and the problem of quantile schedules. The last problem is a question about the smallest upper bound on the time of a given fraction of all possible schedules. We show how these problems are related to the travelling salesman problem. We prove NP-completeness of the fastest schedule problem, NP-hardness of quantile of schedules problem, and polynomiality of the average schedule problem. We also describe some algorithms for all three problems. In the solution of the quantile problem we give an algorithm, based on a reverse search method, generating with polynomial delay all Eulerian multigraphs with the given degree sequence and a bound on the number of such multigraphs. A better bound is left as an open question.}, language = {en} } @misc{HarmanSagnol2015, author = {Harman, Radoslav and Sagnol, Guillaume}, title = {Computing D-optimal experimental designs for estimating treatment contrasts under the presence of a nuisance time trend}, issn = {1438-0064}, doi = {10.1007/978-3-319-13881-7_10}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53640}, year = {2015}, abstract = {We prove a mathematical programming characterisation of approximate partial D-optimality under general linear constraints. We use this characterisation with a branch-and-bound method to compute a list of all exact D-optimal designs for estimating a pair of treatment contrasts in the presence of a nuisance time trend up to the size of 24 consecutive trials.}, language = {en} } @article{Maher2015, author = {Maher, Stephen J.}, title = {A novel passenger recovery approach for the integrated airline recovery problem}, volume = {57}, journal = {Computers \& Operations Research}, doi = {10.1016/j.cor.2014.11.005}, pages = {123 -- 137}, year = {2015}, abstract = {Schedule disruptions require airlines to intervene through the process of recovery; this involves modifications to the planned schedule, aircraft routings, crew pairings and passenger itineraries. Passenger recovery is generally considered as the final stage in this process, and hence passengers experience unnecessarily large impacts resulting from flight delays and cancellations. Most recovery approaches considering passengers involve a separately defined module within the problem formulation. However, this approach may be overly complex for recovery in many aviation and general transportation applications. This paper presents a unique description of the cancellation variables that models passenger recovery by prescribing the alternative travel arrangements for passengers in the event of flight cancellations. The results will demonstrate that this simple, but effective, passenger recovery approach significantly reduces the operational costs of the airline and increases passenger flow through the network. The integrated airline recovery problem with passenger reallocation is solved using column-and-row generation to achieve high quality solutions in short runtimes. An analysis of the column-and-row generation solution approach is performed, identifying a number of enhancement techniques to further improve the solution runtimes.}, language = {en} } @misc{ConiglioGrimmKosteretal.2015, author = {Coniglio, Stefano and Grimm, Boris and Koster, Arie M.C.A. and Tieves, Martin and Werner, Axel}, title = {Optimal offline virtual network embedding with rent-at-bulk aspects}, arxiv = {http://arxiv.org/abs/1501.07887}, pages = {9}, year = {2015}, abstract = {Network virtualization techniques allow for the coexistence of many virtual networks (VNs) jointly sharing the resources of an underlying substrate network. The Virtual Network Embedding problem (VNE) arises when looking for the most profitable set of VNs to embed onto the substrate. In this paper, we address the offline version of the problem. We propose a Mixed-Integer Linear Programming formulation to solve it to optimality which accounts for acceptance and rejection of virtual network requests, allowing for both splittable and unsplittable (single path) routing schemes. Our formulation also considers a Rent-at-Bulk (RaB) model for the rental of substrate capacities where economies of scale apply. To better emphasize the importance of RaB, we also compare our method to a baseline one which only takes RaB into account a posteriori, once a solution to VNE, oblivious to RaB, has been found. Computational experiments show the viability of our approach, stressing the relevance of addressing RaB directly with an exact formulation.}, language = {en} } @inproceedings{SagnolHarman2015, author = {Sagnol, Guillaume and Harman, Radoslav}, title = {Optimal Designs for Steady-state Kalman filters}, volume = {122}, booktitle = {Stochastic Models, Statistics and Their Applications}, editor = {Steland, Ansgar and Rafajłowicz, Ewaryst and Szajowski, Krzysztof}, publisher = {Springer}, doi = {10.1007/978-3-319-13881-7_17}, pages = {149 -- 157}, year = {2015}, abstract = {We consider a stationary discrete-time linear process that can be observed by a finite number of sensors. The experimental design for the observations consists of an allocation of available resources to these sensors. We formalize the problem of selecting a design that maximizes the information matrix of the steady-state of the Kalman filter, with respect to a standard optimality criterion, such as \$D-\$ or \$A-\$optimality. This problem generalizes the optimal experimental design problem for a linear regression model with a finite design space and uncorrelated errors. Finally, we show that under natural assumptions, a steady-state optimal design can be computed by semidefinite programming.}, language = {en} } @inproceedings{HarmanSagnol2015, author = {Harman, Radoslav and Sagnol, Guillaume}, title = {Computing D-optimal experimental designs for estimating treatment contrasts under the presence of a nuisance time trend}, volume = {122}, booktitle = {Stochastic Models, Statistics and Their Applications}, editor = {Steland, Ansgar and Rafajłowicz, Ewaryst and Szajowski, Krzysztof}, publisher = {Springer}, doi = {10.1007/978-3-319-13881-7_10}, pages = {83 -- 91}, year = {2015}, abstract = {We prove a mathematical programming characterisation of approximate partial D-optimality under general linear constraints. We use this characterisation with a branch-and-bound method to compute a list of all exact D-optimal designs for estimating a pair of treatment contrasts in the presence of a nuisance time trend up to the size of 24 consecutive trials.}, language = {en} } @misc{Walther2014, type = {Master Thesis}, author = {Walther, Tom}, title = {A SCIP Constraint Handler for Piecewise Linear Functions}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49112}, year = {2014}, abstract = {In this thesis, we study different modelling approaches for piecewise linear functions, in particular with respect to their occurrence in mathematical optimization problems. Reviewing the quality of the classical MIP models from the literature, we will see that all but the disaggregated convex combination method yield both sharp and locally ideal formulations. In the main part, we will present an alternative approach for modelling constraints involving piecewise linear functions, based on ideas of constraint programming and using a convex hull relaxation. For the purpose of developing a branch-and-bound procedure specifically adapted to our constraint formulation within SCIP, all required components such as propagation, branching and separation will be discussed. In particular, we will focus on adapting well-known MIP strategies for the selection of branching variables to our type of piecewise linear constraints.}, language = {en} } @phdthesis{Cardonha2011, author = {Cardonha, Carlos}, title = {Applied Methods for the Vehicle Positioning Problem}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:83-opus-34211}, year = {2011}, abstract = {This dissertation is dedicated to the Vehicle Positioning Problem (VPP), a classical combinatorial optimization problem in public transport in which vehicles should be assigned to parking positions in a depot in such a way that shunting moves are minimized. We investigate several models and solution methods to solve the VPP and the VPPp, a multi-periodic extension of the problem which was not previously studied. In the first part of the thesis, the basic version of the problem is introduced and several formulations, theoretical properties, and concepts are investigated. In particular, we propose a mixed integer quadratic constrained formulation of the VPP whose QP relaxation produces the first known nontrivial lower bound on the number of shunting moves. The second part of our work describes two advanced solution methods. In the first approach, a set partitioning formulation is solved by a branch-and-price framework. We present efficient algorithms for the pricing problem and in order to improve the performance of the framework, we introduce heuristics and discuss strategies to reduce symmetry. The second approach consists of an iterative technique in which we try to optimize an ILP by solving some of its projections, which are smaller and therefore easier to compute. Both techniques are able to produce satisfactory solutions for large-scale instances of the VPPp. In the third part, advanced aspects of the problem are investigated. We propose and analyze several solution methods for the VPP+ and for the VPPp+, which are extended and more challenging versions of the VPP and of the VPPp, respectively. Finally, the role of uncertainty in the problem is discussed. In particular, we introduce a new criteria to evaluate the robustness of assignment plans, a formulation based on this concept, and a new online algorithm for the VPP.}, language = {en} } @misc{Warszawski2010, type = {Master Thesis}, author = {Warszawski, Maciej}, title = {Lagrange-Relaxierungen der Multi-Fluss-Formulierung f{\"u}r das Distance-Constrained-Vehicle-Routing-Problem und das Travelling-Salesman-Problem}, year = {2010}, language = {de} } @misc{Trillhaase2009, type = {Master Thesis}, author = {Trillhaase, Anja}, title = {Hierarchische Telekommunikationsnetze: ein {\"U}berblick zu Methoden der gemeinsamen Planung von Zugangs- und Kernnetzen}, year = {2009}, language = {de} } @misc{Klaehne2009, type = {Master Thesis}, author = {Kl{\"a}hne, Roman}, title = {Models for Survivable Multi-layer Network Reconfiguration}, year = {2009}, language = {en} } @misc{Spiegelberg2009, type = {Master Thesis}, author = {Spiegelberg, Ingo}, title = {Cardinality Constrained Polymatroids and LP Decoding}, year = {2009}, language = {en} } @misc{Schumann2009, type = {Master Thesis}, author = {Schumann, Christian}, title = {Multikriterielle Umlaufplanung im {\"O}PNV}, year = {2009}, language = {de} } @phdthesis{Koch2013, author = {Koch, Thorsten}, title = {Progress in computational integer programming}, year = {2013}, language = {en} } @misc{Erdogan2009, type = {Master Thesis}, author = {Erdogan, Cemil}, title = {Computing Prices for Track Allocations}, year = {2009}, language = {en} } @misc{Erol2009, type = {Master Thesis}, author = {Erol, Berkan}, title = {Models For The Train Timetabling Problem}, year = {2009}, language = {en} } @misc{Paetsch2009, type = {Master Thesis}, author = {Paetsch, Nils}, title = {Multiobjective Duty Scheduling}, year = {2009}, language = {en} } @misc{Dammer2010, type = {Master Thesis}, author = {Dammer, Ren{\´e}}, title = {Integrierte und robuste Planung von Flugzeugen und Personal im Luftverkehr}, year = {2010}, language = {de} } @masterthesis{Hansknecht2011, type = {Bachelor Thesis}, author = {Hansknecht, Christoph}, title = {Valid Cuts for Mixed-Integer Programming}, year = {2011}, language = {en} } @misc{Opel2011, type = {Master Thesis}, author = {Opel, Katharina}, title = {Experimente in der multikriteriellen linearen Optimierung}, year = {2011}, language = {de} } @misc{Meirich2010, type = {Master Thesis}, author = {Meirich, Robert}, title = {Polyedrische Untersuchungen eines Linienplanungsproblems}, year = {2010}, language = {de} } @misc{Schulz2010, type = {Master Thesis}, author = {Schulz, Christof}, title = {Eine parallele Variante des Netzwerksimplexalgorithmus}, year = {2010}, language = {de} }