@misc{OrlowskiPioro2008, author = {Orlowski, Sebastian and Pi{\´o}ro, Michal}, title = {On the complexity of column generation in survivable network design with path-based survivability mechanisms}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11058}, number = {08-51}, year = {2008}, abstract = {This survey concerns optimization problems arising in the design of survivable communication networks. It turns out that such problems can be modeled in a natural way as non-compact linear programming formulations based on multicommodity flow network models. These non-compact formulations involve an exponential number of path flow variables, and therefore require column generation to be solved to optimality. We consider several path-based survivability mechanisms and present results, both known and new, on the complexity of the corresponding column generation problems (called the pricing problems). We discuss results for the case of the single link (or node) failures scenarios, and extend the considerations to multiple link failures. Further, we classify the design problems corresponding to different survivability mechanisms according to the structure of their pricing problem. Finally, we show that almost all encountered pricing problems are hard to solve for scenarios admitting multiple failures.}, language = {en} } @misc{Stephan2008, author = {Stephan, R{\"u}diger}, title = {Cardinality Constrained Combinatorial Optimization: Complexity and Polyhedra}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11026}, number = {08-48}, year = {2008}, abstract = {Given a combinatorial optimization problem and a subset \$N\$ of natural numbers, we obtain a cardinality constrained version of this problem by permitting only those feasible solutions whose cardinalities are elements of \$N\$. In this paper we briefly touch on questions that addresses common grounds and differences of the complexity of a combinatorial optimization problem and its cardinality constrained version. Afterwards we focus on polytopes associated with cardinality constrained combinatorial optimization problems. Given an integer programming formulation for a combinatorial optimization problem, by essentially adding Gr{\"o}tschel's cardinality forcing inequalities, we obtain an integer programming formulation for its cardinality restricted version. Since the cardinality forcing inequalities in their original form are mostly not facet defining for the associated polyhedra, we discuss possibilities to strengthen them.}, language = {en} } @misc{HillerVredeveld2008, author = {Hiller, Benjamin and Vredeveld, Tjark}, title = {On the optimality of Least Recently Used}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10928}, number = {08-39}, year = {2008}, abstract = {It is well known that competitive analysis yields too pessimistic results when applied to the paging problem and it also cannot make a distinction between many paging strategies. Many deterministic paging algorithms achieve the same competitive ratio, ranging from inefficient strategies as flush-when-full to the good performing least-recently-used (LRU). In this paper, we study this fundamental online problem from the viewpoint of stochastic dominance. We show that when sequences are drawn from distributions modelling locality of reference, LRU is stochastically better than any other online paging algorithm.}, language = {en} } @misc{BorndoerferHoang2008, author = {Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung}, title = {Fair Ticket Prices in Public Transport}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10999}, number = {08-46}, year = {2008}, abstract = {Ticket pricing in public transport usually takes a welfare or mnemonics maximization point of view. These approaches do not consider fairness in the sense that users of a shared infrastructure should pay for the costs that they generate. We propose an ansatz to determine fair ticket prices that combines concepts from cooperative game theory and integer programming. An application to pricing railway tickets for the intercity network of the Netherlands demonstrates that, in this sense, prices that are much fairer than standard ones can be computed in this way.}, language = {en} } @misc{BorndoerferMuraSchlechte2008, author = {Bornd{\"o}rfer, Ralf and Mura, Annette and Schlechte, Thomas}, title = {Vickrey Auctions for Railway Tracks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10855}, number = {08-34}, year = {2008}, abstract = {We consider an auction of slots to run trains through a railway network. In contrast to the classical setting for combinatorial auctions, there is not only competition for slots, but slots can mutually exclude each other, such that general conflict constraints on bids arise. This turns the winner determination problem associated with such an auction into a complex combinatorial optimization problem. It also raises a number of auction design questions, in particular, on incentive compatibilty. We propose a single-shot second price auction for railway slots, the Vickrey Track Auction (VTA). We show that this auction is incentive compatible, i.e., rational bidders are always motivated to bid their true valuation, and that it produces efficient allocations, even in the presence of constraints on allocations. These properties are, however, lost when rules on the submission of bids such as, e.g., lowest bids, are imposed. Our results carry over to generalized" Vickrey auctions with combinatorial constraints.}, language = {en} } @phdthesis{Stolle2000, author = {Stolle, Hermann}, title = {Mathematische Modellierung und L{\"o}sung von Optimierungsproblemen bei der Planung von Telefonnetzen}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:83-opus-1419}, year = {2000}, language = {de} } @phdthesis{Eisenblaetter2001, author = {Eisenbl{\"a}tter, Andreas}, title = {Frequency Assignment in GSM Networks: Models, Heuristics, and Lower Bounds}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10132}, year = {2001}, abstract = {Mobile cellular communcication is a key technology in today's information age. Despite the continuing improvements in equipment design, interference is and will remain a limiting factor for the use of radio communication. This Ph. D. thesis investigates how to prevent interference to the largest possible extent when assigning the available frequencies to the base stations of a GSM cellular network. The topic is addressed from two directions: first, new algorithms are presented to compute "good" frequency assignments fast; second, a novel approach, based on semidef inite programming, is employed to provide lower bounds for the amount of unavoidable interference. The new methods proposed for automatic frequency planning are compared in terms of running times and effectiveness in computational experiments, where the planning instances are taken from practice. For most of the heuristics the running time behavior is adequate for inter active planning; at the same time, they provide reasonable assignments from a practical point of view (compared to the currently best known, but substantially slower planning methods). In fact, several of these methods are successfully applied by the German GSM network operator E-Plus. The currently best lower bounds on the amount of unavoidable (co-channel) interference are obtained from solving semidefinite programs These programs arise as nonpolyhedral relaxation of a minimum /c-parti tion problem on complete graphs. The success of this approach is made plausible by revealing structural relations between the feasible set of the semidefinite program and a polytope associated with an integer linear programming formulation of the minimum ^-partition problem. Comparable relations are not known to hold for any polynomial time solvable polyhedral relaxation of the minimum ^-partition problem. The appli cation described is one of the first of semidefinite programming for large industrial problems in combinatorial optimization.}, language = {en} } @phdthesis{Wessaely2000, author = {Wess{\"a}ly, Roland}, title = {Dimensioning Survivable Capacitated Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10158}, year = {2000}, abstract = {In der vorliegenden Dissertation untersuchen wir die Optimierung von ausfallsicheren Telekommunikationsnetzwerken. Wir pr{\"a}sentieren unterschiedliche gemischt-ganzzahlige Modelle f{\"u}r die diskrete Kapazit{\"a}tsttruktu,, sowie f{\"u}r die Sicherung des Netzes gegen den Ausfall einzelner Komponenten. Die Modelle wurden in einer Kooperation mit der E-Plus Mobilfunk GmbH verwendet. Die theoretischen Resultate wurden in Algorithmen umgesetzt und in das von uns entiickllte Netzwerksoptimierungswerkzeug Discnet (Dimensioning Survivable Capaiitated NETworks) integriert, welches seit mehreren Jahren in der Planung bei E-Plus eingesetzt wird. Wir betrachten das Transportnetzllanungsproblem eines Telekommunikationsanbieters. Dieses Problem setzt auf logischen Kommunikattonsanforerrungen zwischen den Standorten (Knoten) des zu planenden Netzes und potentiell inslallirrbaren Verbindungen (Kanten) zwischen derselben Knotenmenge auf. Ein Kapazit{\"a}tsmodell stellt die Information bereit, welche Kapazit{\"a}ten auf den potentiellen Kanten verf{\"u}gbar sind. Wir betrachten zwei Modelle. Entweder ist eine explizite Liste der verf{\"u}gbaren Kapazittten gegeben oder eine Menge von sogenannten Basiskapazit{\"a}ten, die auf jeder Kante indiviuelll kombiniert werden k{\"o}nnen. Die Basiskapazit{\"a}ten m{\"u}ßen paarweise ganzzahlige Vielfache voneinander sein. Man beachte, daß diese Eigenschaft von den internationalen Standards PDH und SDH erf{\"u}llt wiid. Ein Ausfallsicherheitsmodell stellt die Information bereit, wie das zu planende Netz gegen den Ausfall einzelner Netzkomponenten gesch{\"u}tzt werden soll. Wir betrachten sinnvolle Kombinationen der Modelle Diversification, Reservation und Path Restoration. Das erste Modell garantiert Ausfallsicherheit durch kommunikationsbedarfsabh{\"a}ngige Beschr{\"a}nkung des Prozentsatzes, der durch einzelne Netzkomponenten geroutet werden darf. Bei den beiden anderen Modelle k{\"o}nnen Kommunikationsbedarfe bei Ausfall einer Netzkomponente auf unterschiedliche Weise neu geroutet werden. Ziel der Planung ist eine ktstenminimlle Kapatit{\"a}tsentscheidung, die eine Routenllanung aller Kommunikationsbedarfe gem{\"a}ß den Ausfallsicherheitsanforderungen erm{\"o}glicht. Wir entwickeln ein Schnittebenenverfahren zur L{\"o}sung der betrachteten Optimiergngsrrobleme. Zu diesem Zweck untersuchen wir Polyeder, die mit den verschiedenen Problemen assoziiert sind. Wir pr{\"a}sentieren neue Klassen von Ungleichungen, entwickeln Separationsalgorithmen und Heuristiken. Mit dem Schnittebenenverfahren werden untere und obere Schranken f{\"u}r den Wert von Oitimall{\"o}sungen berechnet, und daher ist es m{\"o}glich, Qualit{\"a}tsgarantien f{\"u}r die berechneten L{\"o}ungen anzugeben. Parallel zur Beschreibung der implementierten Algorithmen pr{\"a}sentieren wir umfangreiche Tests mit praktisch relevanten Daten, die zu Problemen mit mehr als 2 Billionen Variablen f{\"u}hren.}, language = {en} } @phdthesis{Krumke2002, author = {Krumke, Sven}, title = {Online Optimization: Competitive Analysis and Beyond}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6925}, number = {02-25}, year = {2002}, abstract = {Traditional optimization techniques assume, in general, knowledge of all data of a problem instance. There are many cases in practice, however, where decisions have to be made before complete information about the data is available. In fact, it may be necessary to produce a part of the problem solution as soon as a new piece of information becomes known. This is called an \emph{online situation}, and an algorithm is termed \emph{online}, if it makes a decision (computes a partial solution) whenever a new piece of data requests an action. \emph{Competitive analysis} has become a standard yardstick to measure the quality of online algorithms. One compares the solution produced by an online algorithm to that of an optimal (clairvoyant) offline algorithm. An online algorithm is called \$c\$-competitive if on every input the solution it produces has cost'' at most \$c\$~times that of the optimal offline algorithm. This situation can be imagined as a game between an online player and a malicious adversary. Although competitive analysis is a worst-case analysis and henceforth pessimistic, it often allows important insights into the problem structure. One can obtain an idea about what kind of strategies are promising for real-world systems and why. On the other hand there are also cases where the offline adversary is simply too powerful and allows only trivial competitiveness results. This phenomenon is called hitting the triviality barrier''. We investigate several online problems by means of competitive analysis. We also introduce new concepts to overcome the weaknesses of the standard approach and to go beyond the triviality barrier.}, language = {en} } @misc{Kroeller2003, type = {Master Thesis}, author = {Kr{\"o}ller, Alexander}, title = {Network Optimization: Integration of Hardware Configuration and Capacity Dimensioning}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9952}, school = {Zuse Institute Berlin (ZIB)}, year = {2003}, language = {en} } @misc{Borndoerfer2003, author = {Bornd{\"o}rfer, Ralf}, title = {Combinatorial Packing Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7255}, number = {03-03}, year = {2003}, abstract = {This article investigates a certain class of combinatorial packing problems and some polyhedral relations between such problems and the set packing problem.}, language = {en} } @misc{Tuchscherer2003, type = {Master Thesis}, author = {Tuchscherer, Andreas}, title = {Dynamical Configuration of Transparent Optical Telecommunication Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10214}, school = {Zuse Institute Berlin (ZIB)}, year = {2003}, abstract = {All-optical telecommunication networks allow for switching connections by lightpaths which can pass several network links without any opto-electronic conversion. Upon arrival of a connection request, it must be decided online, i.e., without knowledge of future requests, if it is accepted and in that case on which lightpaths the connection is routed. This online problem with the goal of maximizing the total profit gained by accepted requests is called Dynamic Singleclass Call Admission Problem (DSCA). We present existing and new algorithms for the DSCA as well as their theoretical and practical evaluation.}, language = {en} } @misc{Orlowski2003, type = {Master Thesis}, author = {Orlowski, Sebastian}, title = {Local and global restoration of node and link failures in telecommunication networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10008}, school = {Zuse Institute Berlin (ZIB)}, year = {2003}, abstract = {This diploma thesis deals with the restoration problem in telecommunication networks. The goal is to find a cost minimal capacity capacity assignment on the edges and nodes of a network such that given demands can be satisfied even in case of the failure of an edge or node in the network. Moreover, restrictions on the routing paths (like length restrictions) and hardware constraints have to be satisfied. A Mixed Integer Programming model is presented which takes into account restoration requirements as well as hardware constraints and which abstracts from a particular restoration protocol and failure situation. This abstraction provides new insight into the structure of the network restoration problem and shows that from a mathematical point of view, the commonly used restoration techniques Link Restoration, Path Restoration and Reservation are not as different as they seem to be from a practical point of view. In addition, our model allows (but is not limited to) optimizing working capacity, intended for normal use, and spare capacity, intended for rerouting purposes in case of a failure, in one step. Furthermore, our formulation of capacity cost allows taking into account the effects of discrete, non-linear cost structures which are common in practice. Up to our knowledge, no publication in the existing literature covers all these aspects, let alone in one model, although they are of major practical interest. The model has been implemented in a Branch and Cut framework. The theoretical background of the algorithmic procedure is presented in detail, including computational complexity investigations on the pricing problem. The abstraction from a particular restoration protocol turns out to be useful both from a theoretical and computational point of view. In fact, our investigations suggest a distinction into Local Restoration and Global Restoration rather than into Link Restoration,Path Restoration, Reservation and mixtures of these concepts. In addition to the theoretical aspects of the algorithmic procedure, some implementational details are briefly discussed. Our implementation has been tested on 14 real world instances, which is described in detail. One part of the computational results consists of a comparison of optimal network cost values using diffeent restoration mechanisms, applied to securing either all single node failures, all single edge failures or both. In addition, the effects of a discrete cost structure are investigated, which has rarely been considered yet in literature. Furthermore, the cost ifference between joint and successive working and spare capacity optimization is investigated. In the second part of the computational results, several heuristics for the network restoration problem are compared with respect to both solution quality and time. This diploma thesis deals with the restoration problem in telecommunication networks. The goal is to find a cost minimal capacity capacity assignment on the edges and nodes of a network such that given demands can be satisfied even in case of the failure of an edge or node in the network. Moreover, restrictions on the routing paths (like length restrictions) and hardware constraints have to be satisfied. A Mixed Integer Programming model is presented which takes into account restoration requirements as well as hardware constraints and which abstracts from a particular restoration protocol and failure situation. This abstraction provides new insight into the structure of the network restoration problem and shows that from a mathematical point of view, the commonly used restoration techniques Link Restoration, Path Restoration and Reservation are not as different as they seem to be from a practical point of view. In addition, our model allows (but is not limited to) optimizing working capacity, intended for normal use, and spare capacity, intended for rerouting purposes in case of a failure, in one step. Furthermore, our formulation of capacity cost allows taking into account the effects of discrete, non-linear cost structures which are common in practice. Up to our knowledge, no publication in the existing literature covers all these aspects, let alone in one model, although they are of major practical interest. The model has been implemented in a Branch and Cut framework. The theoretical background of the algorithmic procedure is presented in detail, including computational complexity investigations on the pricing problem. The abstraction from a particular restoration protocol turns out to be useful both from a theoretical and computational point of view. In fact, our investigations suggest a distinction into Local Restoration and Global Restoration rather than into Link Restoration, Path Restoration, Reservation and mixtures of these concepts. In addition to the theoretical aspects of the algorithmic procedure, some implementational details are briefly discussed. Our implementation has been tested on 14 real world instances, which is described in detail. One part of the computational results consists of a comparison of optimal network cost values using different restoration mechanisms, applied to securing either all single node failures, all single edge failures or both. In addition, the effects of a discrete cost structure are investigated, which has rarely been considered yet in literature. Furthermore, the cost difference between joint and successive working and spare capacity optimization is investigated. In the second part of the computational results, several heuristics for the network restoration problem are compared with respect to both solution quality and time.}, language = {en} } @misc{MarencoWagler2003, author = {Marenco, Javier and Wagler, Annegret}, title = {Chromatic Scheduling Polytopes coming from the Bandwidth Allocation Problem in Point-to-Multipoint Radio AccessSystems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7614}, number = {03-39}, year = {2003}, abstract = {Point-to-Multipoint systems are one kind of radio systems supplying wireless access to voice/data communication networks. Such systems have to be run using a certain frequency spectrum, which typically causes capacity problems. Hence it is, on the one hand, necessary to reuse frequencies but, on the other hand, no interference must be caused thereby. This leads to the bandwidth allocation problem, a special case of so-called chromatic scheduling problems. Both problems are NP-hard, and there exist no polynomial time approximation algorithms with a guaranteed quality. One kind of algorithms which turned out to be successful for many other combinatorial optimization problems uses cutting plane methods. In order to apply such methods, knowledge on the associated polytopes is required. The present paper contributes to this issue, exploring basic properties of chromatic scheduling polytopes and several classes of facet-defining inequalities.}, language = {en} } @misc{BorndoerferNeumannPfetsch2005, author = {Bornd{\"o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc}, title = {Optimal Fares for Public Transport}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8698}, number = {05-35}, year = {2005}, abstract = {The \emph{fare planning problem} for public transport is to design a system of fares that maximize the revenue. We introduce a nonlinear optimization model to approach this problem. It is based on a d iscrete choice logit model that expresses demand as a function of the fares. We illustrate our approach by computing and comparing two different fare systems for the intercity network of the Netherlands.}, language = {en} } @misc{GamrathKochRehfeldtetal.2014, author = {Gamrath, Gerald and Koch, Thorsten and Rehfeldt, Daniel and Shinano, Yuji}, title = {SCIP-Jack - A massively parallel STP solver}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-52293}, year = {2014}, abstract = {In this article we describe the impact from embedding a 15 year old model for solving the Steiner tree problem in graphs in a state-of-the-art MIP-Framework, making the result run in a massively parallel environment and extending the model to solve as many variants as possible. We end up with a high-perfomance solver that is capable of solving previously unsolved instances and, in contrast to its predecessor, is freely available for academic research.}, language = {en} } @misc{BorndoerferReutherSchlechte2014, author = {Bornd{\"o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas}, title = {A Coarse-To-Fine Approach to the Railway Rolling Stock Rotation Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-51009}, year = {2014}, abstract = {We propose a new coarse-to-fine approach to solve certain linear programs by column generation. The problems that we address contain layers corresponding to different levels of detail, i.e., coarse layers as well as fine layers. These layers are utilized to design efficient pricing rules. In a nutshell, the method shifts the pricing of a fine linear program to a coarse counterpart. In this way, major decisions are taken in the coarse layer, while minor details are tackled within the fine layer. We elucidate our methodology by an application to a complex railway rolling stock rotation problem. We provide comprehensive computational results that demonstrate the benefit of this new technique for the solution of large scale problems.}, language = {en} } @misc{BetkerGamrathKosiankowskietal.2014, author = {Betker, Andreas and Gamrath, Inken and Kosiankowski, Dirk and Lange, Christoph and Lehmann, Heiko and Pfeuffer, Frank and Simon, Felix and Werner, Axel}, title = {Comprehensive Topology and Traffic Model of a Nation-wide Telecommunication Network}, issn = {1438-0064}, doi = {10.1364/JOCN.6.001038}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-52670}, year = {2014}, abstract = {As a basis for meaningful simulation and optimization efforts with regard to traffic engineering or energy consumption in telecommunication networks, suitable models are indispensable. This concerns not only realistic network topologies, but also models for the geographical distribution and the temporal dynamics of traffic, as well as the assumptions on network components and technology. This paper derives such a model from the practice of a large national carrier. Applying the network and traffic model, we demonstrate its use by presenting various optimization cases related to energy-efficient telecommunication. Here, we focus on load-adaptivity by employing sleep modes to the network hardware, where several constraints on the reconfigurability of the network over time are considered.}, language = {en} } @misc{BorndoerferKarbsteinMehrgardtetal.2014, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika and Mehrgardt, Julika and Reuther, Markus and Schlechte, Thomas}, title = {The Cycle Embedding Problem}, issn = {1438-0064}, doi = {10.1007/978-3-319-28697-6_65}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-52788}, year = {2014}, abstract = {Given two hypergraphs, representing a fine and a coarse "layer", and a cycle cover of the nodes of the coarse layer, the cycle embedding problem (CEP) asks for an embedding of the coarse cycles into the fine layer. The CEP is NP-hard for general hypergraphs, but it can be solved in polynomial time for graphs. We propose an integer rogramming formulation for the CEP that provides a complete escription of the CEP polytope for the graphical case. The CEP comes up in railway vehicle rotation scheduling. We present computational results for problem instances of DB Fernverkehr AG that justify a sequential coarse-first-fine-second planning approach.}, language = {en} } @article{HumpolaLehmannFuegenschuh2015, author = {Humpola, Jesco and Lehmann, Thomas and F{\"u}genschuh, Armin}, title = {A primal heuristic for optimizing the topology of gas networks based on dual information}, volume = {3}, journal = {EURO Journal on Computational Optimization}, number = {1}, doi = {10.1007/s13675-014-0029-0}, pages = {53 -- 78}, year = {2015}, abstract = {We present a novel heuristic to identify feasible solutions of a mixed-integer nonlinear programming problem arising in natural gas transportation: the selection of new pipelines to enhance the network's capacity to a desired level in a cost-efficient way. We solve this problem in a linear programming based branch-and-cut approach, where we deal with the nonlinearities by linear outer approximation and spatial branching. At certain nodes of the branching tree, we compute a KKT point of a nonlinear relaxation. Based on the information from the KKT point we alter some of the binary variables in a locally promising way exploiting our problem-specific structure. On a test set of real-world instances, we are able to increase the chance of identifying feasible solutions by some order of magnitude compared to standard MINLP heuristics that are already built in the general-purpose MINLP solver SCIP.}, language = {en} } @article{FroylandMaherWu2014, author = {Froyland, Gary and Maher, Stephen J. and Wu, Cheng-Lung}, title = {The recoverable robust tail assignment problem}, volume = {48}, journal = {Transportation Science}, number = {3}, doi = {10.1287/trsc.2013.0463}, pages = {351 -- 372}, year = {2014}, abstract = {Schedule disruptions are commonplace in the airline industry with many flight-delaying events occurring each day. Recently there has been a focus on introducing robustness into airline planning stages to reduce the effect of these disruptions. We propose a recoverable robustness technique as an alternative to robust optimisation to reduce the effect of disruptions and the cost of recovery. We formulate the recoverable robust tail assignment problem (RRTAP) as a stochastic program, solved using column generation in the master and subproblems of the Benders' decomposition. We implement a two-phase algorithm for the Benders' decomposition and identify pareto-optimal cuts. The RRTAP includes costs due to flight delays, cancellation, and passenger rerouting, and the recovery stage includes cancellation, delay, and swapping options. To highlight the benefits of simultaneously solving planning and recovery problems in the RRTAP we compare our tail assignment solution against current approaches from the literature. Using airline data we demonstrate that by developing a better tail assignment plan via the RRTAP framework, one can reduce recovery costs in the event of a disruption.}, language = {en} } @inproceedings{Reuther2014, author = {Reuther, Markus}, title = {Local Search for the Resource Constrained Assignment Problem}, volume = {42}, booktitle = {14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems}, doi = {10.4230/OASIcs.ATMOS.2014.62}, pages = {62 -- 78}, year = {2014}, abstract = {The resource constrained assignment problem (RCAP) is to find a minimal cost cycle partition in a directed graph such that a resource constraint is fulfilled. The RCAP has its roots in an application that deals with the covering of a railway timetable by rolling stock vehicles. Here, the resource constraint corresponds to maintenance constraints for rail vehicles. Moreover, the RCAP generalizes several variants of vehicle routing problems. We contribute a local search algorithm for this problem that is derived from an exact algorithm which is similar to the Hungarian method for the standard assignment problem. Our algorithm can be summarized as a k-OPT heuristic, exchanging k arcs of an alternating cycle of the incumbent solution in each improvement step. The alternating cycles are found by dual arguments from linear programming. We present computational results for instances from our railway application at Deutsche Bahn Fernverkehr AG as well as for instances of the vehicle routing problem from the literature.}, language = {en} } @article{BorndoerferHoang2014, author = {Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung}, title = {Fair ticket pricing in public transport as a constrained cost allocation game}, volume = {226}, journal = {Annals of Operations Research}, doi = {10.1007/s10479-014-1698-z}, pages = {51 -- 68}, year = {2014}, abstract = {Ticket pricing in public transport usually takes a welfare maximization point of view. Such an approach, however, does not consider fairness in the sense that users of a shared infrastructure should pay for the costs that they generate. We propose an ansatz to determine fair ticket prices that combines concepts from cooperative game theory and linear and integer programming. The ticket pricing problem is considered to be a constrained cost allocation game, which is a generalization of cost allocation games that allows to deal with constraints on output prices and on the formation of coalitions. An application to pricing railway tickets for the intercity network of the Netherlands is presented. The results demonstrate that the fairness of prices can be improved substantially in this way. A preliminary version of this paper appeared in the Proceedings of HPSC 2009 (Bornd{\"o}rfer and Hoang 2012). This journal article introduces better model and algorithms.}, language = {en} } @inproceedings{MatuschkeBleyMueller2013, author = {Matuschke, Jannik and Bley, Andreas and M{\"u}ller, Benjamin}, title = {Approximation Algorithms for Facility Location with Capacitated and Length-Bounded Tree Connections}, volume = {Algorithms -- ESA 2013}, editor = {Bodlaender, Hans L. and Italiano, Giuseppe F.}, publisher = {Springer}, doi = {10.1007/978-3-642-40450-4_60}, pages = {707 -- 718}, year = {2013}, abstract = {We consider a generalization of the uncapacitated facility location problem that occurs in planning of optical access networks in telecommunications. Clients are connected to open facilities via depth-bounded trees. The total demand of clients served by a tree must not exceed a given tree capacity. We investigate a framework for combining facility location algorithms with a tree-based clustering approach and derive approximation algorithms for several variants of the problem, using techniques for approximating shallow-light Steiner trees via layer graphs, simultaneous approximation of shortest paths and minimum spanning trees, and greedy coverings.}, language = {en} } @misc{WernerAurzadaBleyetal.2014, author = {Werner, Axel and Aurzada, Frank and Bley, Andreas and Eisenbl{\"a}tter, Andreas and Geerdes, Hans-Florian and Guillemard, Mijail and Kutyniok, Gitta and Philipp, Friedrich and Raack, Christian and Scheutzow, Michael}, title = {Mathematics for telecommunications}, volume = {1}, journal = {MATHEON - Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, edition = {EMS Series in Industrial and Applied Mathematics}, publisher = {European Mathematical Society}, doi = {10.4171/137}, pages = {75 -- 89}, year = {2014}, language = {en} } @misc{Hoppmann2014, type = {Master Thesis}, author = {Hoppmann, Heide}, title = {A Configuration Model for the Line Planning Problem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-51610}, pages = {108}, year = {2014}, abstract = {In this thesis we present a novel extended formulation for the line planning problem that is based on what we call "configurations" of lines and frequencies. Configurations are combinatorial building blocks of primal solutions; they rule out the "capacity numerics" and make the problem purely combinatorial. The concept of configurations can also be adapted to other capacitated network design problems. The configuration model is strong in the sense that it implies several facet-defining inequalities for the standard model: set cover, symmetric band, multicover, and MIR inequalities. These theoretical findings can be confirmed in computations, however, the enormous number of configurations can blow up the formulation for large instances. We propose a mixed model that enriches the standard model by a judiciously chosen subset of configurations that provide a good compromise between model strength and size. Computational results for large-scale line planning problems are presented.}, language = {en} } @misc{Schweiger2014, author = {Schweiger, Jonas}, title = {Gas network extension planning for multiple demand scenarios}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-51030}, year = {2014}, abstract = {Today's gas markets demand more flexibility from the network operators which in turn have to invest into their network infrastructure. As these investments are very cost-intensive and long-living, network extensions should not only focus on one bottleneck scenario, but should increase the flexibility to fulfill different demand scenarios. We formulate a model for the network extension problem for multiple demand scenarios and propose a scenario decomposition. We solve MINLP single-scenario sub-problems and obtain valid bounds even without solving them to optimality. Heuristics prove capable of improving the initial solutions substantially. Results of computational experiments are presented.}, language = {en} } @misc{BeckenbachBorndoerfer2014, author = {Beckenbach, Isabel and Bornd{\"o}rfer, Ralf}, title = {An Approximation Result for Matchings in Partitioned Hypergraphs}, doi = {10.1007/978-3-319-28697-6_5}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-51083}, year = {2014}, abstract = {We investigate the matching and perfect matching polytopes of hypergraphs having a special structure, which we call partitioned hypergraphs. We show that the integrality gap of the standard LP-relaxation is at most \$2\sqrt{d}\$ for partitioned hypergraphs with parts of size \$\leq d\$. Furthermore, we show that this bound cannot be improved to \$\mathcal{O}(d^{0.5-\epsilon})\$.}, language = {en} } @article{MaherDesaulniersSoumis2014, author = {Maher, Stephen J. and Desaulniers, Guy and Soumis, Francois}, title = {Recoverable robust single day aircraft maintenance routing problem}, volume = {51}, journal = {Computers \& Operations Research}, doi = {10.1016/j.cor.2014.03.007}, pages = {130 -- 145}, year = {2014}, abstract = {Aircraft maintenance planning is of critical importance to the safe and efficient operations of an airline. It is common to solve the aircraft routing and maintenance planning problems many months in advance, with the solution spanning multiple days. An unfortunate consequence of this approach is the possible infeasibility of the maintenance plan due to frequent perturbations occurring in operations. There is an emerging concept that focuses on the generation of aircraft routes for a single day to ensure maintenance coverage that night, alleviating the effects of schedule perturbations from preceding days. In this paper, we present a novel approach to ensure that a sufficient number of aircraft routes are provided each day so maintenance critical aircraft receive maintenance that night. By penalising the under supply of routes terminating at maintenance stations from each overnight airport, we construct a single day routing to provide the best possible maintenance plan. This single day aircraft maintenance routing problem (SDAMRP) is further protected from disruptions by applying the recoverable robustness framework. To efficiently solve the recoverable robust SDAMRP acceleration techniques, such as identifying Pareto-optimal cuts and a trust region approach, have been applied. The SDAMRP is evaluated against a set of flight schedules and the results demonstrate a significantly improved aircraft maintenance plan. Further, the results demonstrate the magnitude of recoverability improvement that is achieved by employing recoverable robustness to the SDAMRP.}, language = {en} } @article{Maher2015, author = {Maher, Stephen J.}, title = {Solving the integrated airline recovery problem using column-and-row generation}, volume = {50}, journal = {Transportation Science}, number = {1}, doi = {10.1287/trsc.2014.0552}, pages = {216 -- 239}, year = {2015}, abstract = {Airline recovery presents very large and difficult problems requiring high quality solutions within very short time limits. To improve computational performance, the complete airline recovery problem is generally formulated as a series of sequential stages. While the sequential approach greatly simplifies the complete recovery problem, there is no guarantee of global optimality or solution quality. To address this, there has been increasing interest in the development of efficient solution techniques to solve an integrated recovery problem. In this paper, an integrated airline recovery problem is proposed by integrating the schedule, crew and aircraft recovery stages. To achieve short runtimes and high quality solutions, this problem is solved using column-and-row generation. Column-and-row generation achieves an improvement in solution runtimes by reducing the problem size and thereby achieving a faster execution of each LP solve. Further, the results demonstrate that a good upper bound achieved early in the solution process, indicating an improved solution quality with the early termination of the algorithm. This paper also details the integration of the row generation procedure with branch-and-price, which is used to achieve integral optimal solutions. The benefits of applying column-and-row generation to solve the integrated recovery problem are demonstrated with a comparison to a standard column generation technique.}, language = {en} } @inproceedings{BorndoerferMehrgardtReutheretal.2014, author = {Bornd{\"o}rfer, Ralf and Mehrgardt, Julika and Reuther, Markus and Schlechte, Thomas and Waas, Kerstin}, title = {Re-Optimization of Rolling Stock Rotations}, edition = {Operations Research Proceedings 2013}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-07001-8_8}, pages = {49 -- 55}, year = {2014}, abstract = {The Rolling Stock Rotation Problem is to schedule rail vehicles in order to cover timetabled trips by a cost optimal set of vehicle rotations. The problem integrates several facets of railway optimization, such as vehicle composition, maintenance constraints, and regularity aspects. In industrial applications existing vehicle rotations often have to be re-optimized to deal with timetable changes or construction sites. We present an integrated modeling and algorithmic approach to this task as well as computational results for industrial problem instances of DB Fernverkehr AG.}, language = {en} } @inproceedings{BlancoSchlechte2014, author = {Blanco, Marco and Schlechte, Thomas}, title = {Analysis of Micro-Macro Transformations of Railway Networks}, booktitle = {Operations Research Proceedings 2013}, doi = {10.1007/978-3-319-07001-8_6}, pages = {37 -- 42}, year = {2014}, abstract = {A common technique in the solution of large or complex optimization problems is the use of micro-macro transformations. In this paper, we carry out a theoretical analysis of such transformations for the track allocation problem in railway networks. We prove that the cumulative rounding technique of Schlechte et al. satisfies two of three natural optimality criteria and that this performance cannot be improved. We also show that under extreme circumstances, this technique can perform inconveniently by underestimating the global optimal value.}, language = {en} } @inproceedings{HeismannBorndoerfer2014, author = {Heismann, Olga and Bornd{\"o}rfer, Ralf}, title = {A Generalization of Odd Set Inequalities for the Set Packing Problem}, booktitle = {Operations Research Proceedings 2013}, doi = {10.1007/978-3-319-07001-8_26}, pages = {193 -- 199}, year = {2014}, abstract = {The set packing problem, sometimes also called the stable set problem, is a well-known NP-hard problem in combinatorial optimization with a wide range of applications and an interesting polyhedral structure, that has been the subject of intensive study. We contribute to this field by showing how, employing cliques, odd set inequalities for the matching problem can be generalized to valid inequalities for the set packing polytope with a clear combinatorial meaning.}, language = {en} } @misc{KochMartinPfetsch2013, author = {Koch, Thorsten and Martin, Alexander and Pfetsch, Marc}, title = {Progress in Academic Computational Integer Programming}, journal = {Facets of Combinatorial Optimization}, editor = {J{\"u}nger, Michael and Reinelt, Gerhard}, publisher = {Springer}, doi = {10.1007/978-3-642-38189-8_19}, pages = {483 -- 506}, year = {2013}, language = {en} } @misc{GroetschelBorndoerfer2014, author = {Gr{\"o}tschel, Martin and Bornd{\"o}rfer, Ralf}, title = {Mathematik im Verkehr}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-50287}, year = {2014}, abstract = {Nach einem kurzen Abriss {\"u}ber die Bedeutung des Verkehrssektors als eine wichtige Schl{\"u}sseltechnologie im gesamten Verlauf der Menschheitsgeschichte skizzieren wir die Rolle der Mathematik f{\"u}r Verkehr und Transport. Wir spekulieren dann {\"u}ber zuk{\"u}nftige Entwicklungen, insbesondere im Bereich des {\"o}ffentlichen Personenverkehrs, und begr{\"u}nden, dass die in diesem Bereich anstehenden Herausforderungen nur mit dem Einsatz mathematischer Methoden angemessen bew{\"a}ltigt werden k{\"o}nnen. Die demographischen Prozesse, die in verschiedenen Teilen der Welt unterschiedlich verlaufen, wie z.B. {\"U}beralterung in Europa oder dynamische Trends zu Megast{\"a}dten in Entwicklungsl{\"a}ndern, sich {\"a}ndernde Lebens- und Produktionsverh{\"a}ltnisse, stark wachsender Bedarf nach Mobilit{\"a}t und enormes Anwachsen der Komplexit{\"a}t der Verkehrsplanung und -durchf{\"u}hrung, machen einen verst{\"a}rkten Zugriff auf mathematische Modellierung, Simulation und Optimierung notwendig. Diese Entwicklung stellt sowohl große Herausforderungen an die Mathematik, wo vielfach noch keine geeigneten Methoden vorhanden sind, als auch an die Praktiker im Bereich von Verkehr und Transport, die sich mit neuen Planungs- und Steuerungstechnologien befassen und diese effizient einsetzen m{\"u}ssen. Hier wird intensive Kooperation zwischen vielen beteiligten Akteuren gefragt sein.}, language = {de} } @misc{ArnoldBertholdHeinzetal.2014, author = {Arnold, Thomas and Berthold, Timo and Heinz, Stefan and Vigerske, Stefan and Henrion, Ren{\´e} and Gr{\"o}tschel, Martin and Koch, Thorsten and Tischendorf, Caren and R{\"o}misch, Werner}, title = {A Jack of all Trades? Solving stochastic mixed-integer nonlinear constraint programs}, issn = {1438-0064}, doi = {10.4171/137}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49947}, year = {2014}, abstract = {Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby assigning a central role in energy politics to the transportation and distribution of gas. These newly imposed political requirements influenced the technical processes of gas transport in such a way that the complex task of planning and operating gas networks has become even more intricate. Mathematically, the combination of discrete decisions on the configuration of a gas transport network, the nonlinear equations describing the physics of gas, and the uncertainty in demand and supply yield large-scale and highly complex stochastic mixed-integer nonlinear optimization problems. The Matheon project "Optimization of Gas Transport" takes the key role of making available the necessary core technology to solve the mathematical optimization problems which model the topology planning and the operation of gas networks. An important aspect of the academic impact is the free availability of our framework. As a result of several years of research and development, it is now possible to download a complete state-of-the-art framework for mixed-integer linear and nonlinear programming in source code at http://scip.zib.de}, language = {en} } @misc{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}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-50270}, year = {2014}, abstract = {Wir stellen einen mathematischen Optimierungsansatz zur integrierten Dienst- und Dienstreihenfolgeplanung im {\"o}ffentlichen Nahverkehr vor, mit dem sich bei konstanten Personalkosten die Fahrerzufriedenheit deutlich steigern l{\"a}sst.}, language = {de} } @misc{HeismannBorndoerfer2014, author = {Heismann, Olga and Bornd{\"o}rfer, Ralf}, title = {A Generalization of Odd Set Inequalities for the Set Packing Problem}, issn = {1438-0064}, doi = {10.1007/978-3-319-07001-8_26}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-51010}, year = {2014}, abstract = {The set packing problem, sometimes also called the stable set problem, is a well-known NP-hard problem in combinatorial optimization with a wide range of applications and an interesting polyhedral structure, that has been the subject of intensive study. We contribute to this field by showing how, employing cliques, odd set inequalities for the matching problem can be generalized to valid inequalities for the set packing polytope with a clear combinatorial meaning.}, language = {en} } @phdthesis{Heismann2014, author = {Heismann, Olga}, title = {The Hypergraph Assignment Problem}, year = {2014}, abstract = {This thesis deals with the hypergraph assignment problem (HAP), a set partitioning problem in a special type of hypergraph. The HAP generalizes the assignment problem from bipartite graphs to what we call bipartite hypergraphs, and is motivated by applications in railway vehicle rotation planning. The main contributions of this thesis concern complexity, polyhedral results, analyses of random instances, and primal methods for the HAP. We prove that the HAP is NP-hard and APX-hard even for small hyperedge sizes and hypergraphs with a special partitioned structure. We also study the complexity of the set packing and covering relaxations of the HAP, and present for certain cases polynomial exact or approximation algorithms. A complete linear description is known for the assignment problem. We therefore also study the HAP polytope. There, we have a huge number of facet-defining inequalities already for a very small problem size. We describe a method for dividing the inequalities into equivalence classes without resorting to a normal form. Within each class, facets are related by certain symmetries and it is sufficient to list one representative of each class to give a complete picture of the structural properties of the polytope. We propose the algorithm "HUHFA" for the classification that is applicable not only to the HAP but combinatorial optimization problems involving symmetries in general. In the largest possible HAP instance for which we could calculate the complete linear description, we have 14049 facets, which can be divided into 30 symmetry classes. We can combinatorially interpret 16 of these classes. This is possible by employing cliques to generalize the odd set inequalities for the matching problem. The resulting inequalities are valid for the polytope associated with the set packing problem in arbitrary hypergraphs and have a clear combinatorial meaning. An analysis of random instances provides a better insight into the structure of hyperassignments. Previous work has extensively analyzed random instances for the assignment problem theoretically and practically. As a generalization of these results for the HAP, we prove bounds on the expected value of a minimum cost hyperassignment that uses half of the maximum possible number of hyperedges that are not edges. In a certain complete partitioned hypergraph G2,2n with i. i. d. exponential random variables with mean 1 as hyperedge costs it lies between 0.3718 and 1.8310 if the vertex number tends to infinity. Finally, we develop an exact combinatorial solution algorithm for the HAP that combines three methods: A very large-scale neighborhood search, the composite columns method for the set partitioning problem, and the network simplex algorithm.}, language = {en} } @misc{ArnoldBertholdHeinzetal.2014, author = {Arnold, Thomas and Berthold, Timo and Heinz, Stefan and Vigerske, Stefan and Henrion, Ren{\´e} and Gr{\"o}tschel, Martin and Koch, Thorsten and Tischendorf, Caren and R{\"o}misch, Werner}, title = {A Jack of all Trades? Solving stochastic mixed-integer nonlinear constraint programs}, volume = {1}, journal = {MATHEON - Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, doi = {10.4171/137}, pages = {135 -- 146}, year = {2014}, abstract = {Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby assigning a central role in energy politics to the transportation and distribution of gas. These newly imposed political requirements influenced the technical processes of gas transport in such a way that the complex task of planning and operating gas networks has become even more intricate. Mathematically, the combination of discrete decisions on the configuration of a gas transport network, the nonlinear equations describing the physics of gas, and the uncertainty in demand and supply yield large-scale and highly complex stochastic mixed-integer nonlinear optimization problems. The Matheon project "Optimization of Gas Transport" takes the key role of making available the necessary core technology to solve the mathematical optimization problems which model the topology planning and the operation of gas networks. An important aspect of the academic impact is the free availability of our framework. As a result of several years of research and development, it is now possible to download a complete state-of-the-art framework for mixed-integer linear and nonlinear programming in source code at http://scip.zib.de}, language = {en} } @article{CookKochSteffyetal.2013, author = {Cook, William and Koch, Thorsten and Steffy, Daniel and Wolter, Kati}, title = {A hybrid branch-and-bound approach for exact rational mixed-integer programming}, volume = {5}, journal = {Mathematical Programming Computation}, number = {3}, doi = {10.1007/s12532-013-0055-6}, pages = {305 -- 344}, year = {2013}, abstract = {We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. This allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric implementation of LP-based branch-and-bound, using numerically-safe methods for all binding computations in the search tree. Computing provably accurate solutions by dynamically choosing the fastest of several safe dual bounding methods depending on the structure of the instance, our exact solver is only moderately slower than an inexact floating-point branch-and-bound solver. The software is incorporated into the SCIP optimization framework, using the exact LP solver QSopt_ex and the GMP arithmetic library. Computational results are presented for a suite of test instances taken from the MIPLIB and Mittelmann libraries and for a new collection of numerically difficult instances.}, language = {en} } @inproceedings{SchlosserWernerSchlenketal.2014, author = {Schlosser, Michael and Werner, Axel and Schlenk, Ralph and Jungel, Tobias and Lange, Christoph}, title = {Demonstrating energy-efficiency improvements in load-adaptive dynamic multilayer optical networks}, volume = {248}, booktitle = {Tagungsband Photonische Netze}, publisher = {VDE-Verlag}, pages = {42 -- 46}, year = {2014}, abstract = {The discussion about sustainability and climate change as well as the energy cost perspective of network operators gives increasing attention to the energy efficiency of telecommunication networks. A promising way to improve the energy efficiency of such networks is the load-adaptive operation in which the network capacity is adjusted to the actual timevarying traffic transport needs. In this paper the concept of load-adaptive operation in the core network is explained, with the respective underlying optical network and the associated mathematical optimization. Within the DESI project a demonstrator has been realized with a commercially available WDM/OTN system. As results, concrete proven power and energy savings and the projected savings for a nationwide multilayer core network are reported.}, language = {en} } @book{OPUS4-5024, title = {MATHEON - Mathematics for Key Technologies}, volume = {1}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, isbn = {978-3-03719-137-8}, doi = {10.4171/137}, year = {2014}, language = {en} } @misc{Schienle2016, type = {Master Thesis}, author = {Schienle, Adam}, title = {Shortest Paths on Airway Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64047}, pages = {66}, year = {2016}, language = {en} } @misc{RalphsShinanoBertholdetal.2016, author = {Ralphs, Ted and Shinano, Yuji and Berthold, Timo and Koch, Thorsten}, title = {Parallel Solvers for Mixed Integer Linear Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62239}, year = {2016}, abstract = {In this article, we introduce parallel mixed integer linear programming (MILP) solvers. MILP solving algorithms have been improved tremendously in the last two decades. Currently, commercial MILP solvers are known as a strong optimization tool. Parallel MILP solver development has started in 1990s. However, since the improvements of solving algorithms have much impact to solve MILP problems than application of parallel computing, there were not many visible successes. With the spread of multi-core CPUs, current state-of-the-art MILP solvers have parallel implementations and researches to apply parallelism in the solving algorithm also getting popular. We summarize current existing parallel MILP solver architectures.}, language = {en} } @misc{HillerWalther2018, author = {Hiller, Benjamin and Walther, Tom}, title = {Modelling compressor stations in gas networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-67443}, year = {2018}, abstract = {Gas networks are an important application area for optimization. When considering long-range transmission, compressor stations play a crucial role in these applications. The purpose of this report is to collect and systematize the models used for compressor stations in the literature. The emphasis is on recent work on simple yet accurate polyhedral models that may replace more simplified traditional models without increasing model complexity. The report also describes an extension of the compressor station data available in GasLib (http://gaslib.zib.de/) with the parameters of these models.}, language = {en} } @misc{BorndoerferOmontSagnoletal.2012, author = {Bornd{\"o}rfer, Ralf and Omont, Bertrand and Sagnol, Guillaume and Swarat, Elmar}, title = {A Stackelberg game to optimize the distribution of controls in transportation networks}, issn = {1438-0064}, doi = {10.1007/978-3-642-35582-0_17}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14995}, year = {2012}, abstract = {We propose a game theoretic model for the spatial distribution of inspectors on a transportation network. The problem is to spread out the controls so as to enforce the payment of a transit toll. We formulate a linear program to find the control distribution which maximizes the expected toll revenue, and a mixed integer program for the problem of minimizing the number of evaders. Furthermore, we show that the problem of finding an optimal mixed strategy for a coalition of \$N\$ inspectors can be solved efficiently by a column generation procedure. Finally, we give experimental results from an application to the truck toll on German motorways.}, language = {en} } @misc{BorndoerferSagnolSchwartz2015, author = {Bornd{\"o}rfer, Ralf and Sagnol, Guillaume and Schwartz, Stephan}, title = {An Extended Network Interdiction Problem for Optimal Toll Control}, issn = {1438-0064}, doi = {10.1016/j.endm.2016.03.040}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-55405}, year = {2015}, 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} } @inproceedings{WitzigBertholdHeinz2017, author = {Witzig, Jakob and Berthold, Timo and Heinz, Stefan}, title = {Experiments with Conflict Analysis in Mixed Integer Programming}, volume = {10335}, booktitle = {Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2017}, publisher = {Springer}, doi = {10.1007/978-3-319-59776-8_17}, pages = {211 -- 222}, year = {2017}, abstract = {The analysis of infeasible subproblems plays an import role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications obtained by domain propagation that led to infeasibility. The result of the analysis is one or more sets of contradicting variable bounds from which so-called conflict constraints can be generated. This concept has its origin in solving satisfiability problems and is similarly used in constraint programming. The second concept is to analyze infeasible linear programming (LP) relaxations. The dual LP solution provides a set of multipliers that can be used to generate a single new globally valid linear constraint. The main contribution of this short paper is an empirical evaluation of two ways to combine both approaches. Experiments are carried out on general MIP instances from standard public test sets such as Miplib2010; the presented algorithms have been implemented within the non-commercial MIP solver SCIP. Moreover, we present a pool-based approach to manage conflicts which addresses the way a MIP solver traverses the search tree better than aging strategies known from SAT solving.}, language = {en} } @article{BorndoerferBuwayaSagnoletal.2015, author = {Bornd{\"o}rfer, Ralf and Buwaya, Julia and Sagnol, Guillaume and Swarat, Elmar}, title = {Network spot-checking games: Theory and application to toll enforcing in transportation networks}, volume = {65}, journal = {Networks}, publisher = {Wiley Periodicals, Inc.}, doi = {10.1002/net.21596}, pages = {312 -- 328}, year = {2015}, 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. In an SC game, the pure strategies of network users correspond to paths in a graph, and the pure strategies of the inspectors are subset of arcs to be controlled. 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 (SSE) is more relevant for this problem and we give a mixed integer programming (MIP) formulation for this problem. We show that the computation of such an equilibrium is NP-hard. More generally, we prove that it is NP-hard to compute a SSE in a polymatrix game, even if the game is pairwise zero-sum. Then, we give some bounds on the price of spite, which measures how the payoff of the inspector degrades when committing to a Nash equilibrium. Finally, we report computational experiments on instances constructed from real data, for an application to the enforcement of a truck toll in Germany. These numerical results show the efficiency of the proposed methods, as well as the quality of the bounds derived in this article.}, language = {en} } @article{VigerskeGleixner2018, author = {Vigerske, Stefan and Gleixner, Ambros}, title = {SCIP: Global Optimization of Mixed-Integer Nonlinear Programs in a Branch-and-Cut Framework}, volume = {33}, journal = {Optimization Methods \& Software}, number = {3}, doi = {10.1080/10556788.2017.1335312}, pages = {563 -- 593}, year = {2018}, abstract = {This paper describes the extensions that were added to the constraint integer programming framework SCIP in order to enable it to solve convex and nonconvex mixed-integer nonlinear programs (MINLPs) to global optimality. SCIP implements a spatial branch-and-bound algorithm based on a linear outer-approximation, which is computed by convex over- and underestimation of nonconvex functions. An expression graph representation of nonlinear constraints allows for bound tightening, structure analysis, and reformulation. Primal heuristics are employed throughout the solving process to find feasible solutions early. We provide insights into the performance impact of individual MINLP solver components via a detailed computational study over a large and heterogeneous test set.}, language = {en} } @inproceedings{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}, volume = {8768}, booktitle = {7th International Symposium on Algorithmic Game Theory (SAGT'2014)}, editor = {Lavi, Ron}, publisher = {Springer}, isbn = {978-3-662-44802-1}, doi = {10.1007/978-3-662-44803-8}, pages = {293}, 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} }