TY - CHAP A1 - Schewe, Lars A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Pfetsch, Marc T1 - Mathematical optimization for evaluating gas network capacities T2 - Evaluating Gas Network Capacities Y1 - 2015 SN - 9781611973686 SP - 87 EP - 102 PB - Society for Industrial and Applied Mathematics ER - TY - CHAP A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Lehmann, Thomas A1 - Lenz, Ralf A1 - Morsi, Antonio A1 - Pfetsch, Marc A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Willert, Bernhard T1 - Computational results for validation of nominations T2 - Evaluating Gas Network Capacities N2 - 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. Y1 - 2015 SN - 9781611973686 VL - SIAM-MOS series on Optimization ER - TY - BOOK A1 - Koch, Thorsten A1 - Hiller, Benjamin A1 - Pfetsch, Marc A1 - Schewe, Lars T1 - Evaluating Gas Network Capacities Y1 - 2015 SN - 978-1-611973-68-6 PB - SIAM ER - TY - GEN A1 - Harks, Tobias A1 - Heinz, Stefan A1 - Pfetsch, Marc A1 - Vredeveld, Tjark T1 - Online Multicommodity Routing with Time Windows N2 - We consider a multicommodity routing problem, where demands are released \emph{online} and have to be routed in a network during specified time windows. The objective is to minimize a time and load dependent convex cost function of the aggregate arc flow. First, we study the fractional routing variant. We present two online algorithms, called Seq and Seq$^2$. Our first main result states that, for cost functions defined by polynomial price functions with nonnegative coefficients and maximum degree~$d$, the competitive ratio of Seq and Seq$^2$ is at most $(d+1)^{d+1}$, which is tight. We also present lower bounds of $(0.265\,(d+1))^{d+1}$ for any online algorithm. In the case of a network with two nodes and parallel arcs, we prove a lower bound of $(2-\frac{1}{2} \sqrt{3})$ on the competitive ratio for Seq and Seq$^2$, even for affine linear price functions. Furthermore, we study resource augmentation, where the online algorithm has to route less demand than the offline adversary. Second, we consider unsplittable routings. For this setting, we present two online algorithms, called U-Seq and U-Seq$^2$. We prove that for polynomial price functions with nonnegative coefficients and maximum degree~$d$, the competitive ratio of U-Seq and U-Seq$^2$ is bounded by $O{1.77^d\,d^{d+1}}$. We present lower bounds of $(0.5307\,(d+1))^{d+1}$ for any online algorithm and $(d+1)^{d+1}$ for our algorithms. Third, we consider a special case of our framework: online load balancing in the $\ell_p$-norm. For the fractional and unsplittable variant of this problem, we show that our online algorithms are $p$ and $O{p}$ competitive, respectively. Such results where previously known only for scheduling jobs on restricted (un)related parallel machines. T3 - ZIB-Report - 07-22 KW - Online Optimization KW - Routing KW - Telecommunications Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9654 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc A1 - Vigerske, Stefan T1 - Large Neighborhood Search beyond MIP N2 - Large neighborhood search (LNS) heuristics are an important component of modern branch-and-cut algorithms for solving mixed-integer linear programs (MIPs). Most of these LNS heuristics use the LP relaxation as the basis for their search, which is a reasonable choice in case of MIPs. However, for more general problem classes, the LP relaxation alone may not contain enough information about the original problem to find feasible solutions with these heuristics, e.g., if the problem is nonlinear or not all constraints are present in the current relaxation. In this paper, we discuss a generic way to extend LNS heuristics that have been developed for MIP to constraint integer programming (CIP), which is a generalization of MIP in the direction of constraint programming (CP). We present computational results of LNS heuristics for three problem classes: mixed-integer quadratically constrained programs, nonlinear pseudo-Boolean optimization instances, and resource-constrained project scheduling problems. Therefore, we have implemented extended versions of the following LNS heuristics in the constraint integer programming framework SCIP: Local Branching, RINS, RENS, Crossover, and DINS. Our results indicate that a generic generalization of LNS heuristics to CIP considerably improves the success rate of these heuristics. T3 - ZIB-Report - 11-21 KW - Large Neighborhood Search KW - Primal Heuristic KW - MIP KW - MIQCP KW - Pseudo-Boolean Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12989 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc ED - Fleischmann, Bernhard ED - Borgwardt, Karl ED - Klein, Robert ED - Tuma, Axel T1 - The Line Connectivity Problem T2 - Operations Research Proceedings 2008 Y1 - 2009 UR - http://opus.kobv.de/zib/volltexte/2008/1117/ SP - 557 EP - 562 PB - Springer-Verlag ER - TY - CHAP A1 - Torres, Luis Miguel A1 - Torres, Ramiro A1 - Borndörfer, Ralf A1 - Pfetsch, Marc ED - Fischetti, Matteo ED - Widmayer, Peter T1 - Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System T2 - ATMOS 2008 - 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems Y1 - 2008 UR - http://drops.dagstuhl.de/opus/volltexte/2008/1580 PB - Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany CY - Dagstuhl, Germany ER - TY - CHAP A1 - Pfetsch, Marc A1 - Borndörfer, Ralf ED - Haasis, Hans-Dietrich T1 - Routing in Line Planning for Public Transportation T2 - Operations Research Proceedings 2005 Y1 - 2006 UR - http://opus.kobv.de/zib/volltexte/2005/870/ SP - 405 EP - 410 PB - Springer-Verlag ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - Angebotsplanung im öffentlichen Nahverkehr T2 - HEUREKA’08 Y1 - 2008 UR - http://opus.kobv.de/zib/volltexte/2008/1084/ PB - FGSV Verlag ER - TY - CHAP A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc ED - Kullmann, Oliver T1 - Nonlinear pseudo-Boolean optimization T2 - Theory and Applications of Satisfiability Testing – SAT 2009 Y1 - 2009 VL - 5584 SP - 441 EP - 446 PB - Springer ER - TY - CHAP A1 - Berthold, Timo A1 - Pfetsch, Marc ED - Fleischmann, Bernhard ED - Borgwardt, Karl ED - Klein, Robert ED - Tuma, Axel T1 - Detecting Orbitopal Symmetries T2 - Operations Research Proceedings 2008 Y1 - 2009 SP - 433 EP - 438 PB - Springer-Verlag ER - TY - GEN A1 - Pfetsch, Marc A1 - Fügenschuh, Armin A1 - Geißler, Björn A1 - Geißler, Nina A1 - Gollmer, Ralf A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Martin, Alexander A1 - Morsi, Antonio A1 - Rövekamp, Jessica A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Steinbach, Marc A1 - Vigerske, Stefan A1 - Willert, Bernhard T1 - Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions N2 - In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult mixed-integer non-convex nonlinear feasibility problem. The first phase consists of four distinct algorithms facilitating mixed-integer linear, mixed-integer nonlinear, reduced nonlinear, and complementarity constrained methods to compute possible settings for the discrete decisions. The second phase employs a precise continuous nonlinear programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances whose size is significantly larger than networks that have appeared in the literature previously. T3 - ZIB-Report - 12-41 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16531 SN - 1438-0064 ER - TY - JOUR A1 - Schmidt, Martin A1 - Assmann, Denis A1 - Burlacu, Robert A1 - Humpola, Jesco A1 - Joormann, Imke A1 - Kanelakis, Nikolaos A1 - Koch, Thorsten A1 - Oucherif, Djamal A1 - Pfetsch, Marc A1 - Schewe, Lars A1 - Schwarz, Robert A1 - Sirvent, Matthias T1 - GasLib – A Library of Gas Network Instances JF - Data Y1 - 2017 U6 - https://doi.org/10.3390/data2040040 VL - 2 IS - 4 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc T1 - Nonlinear pseudo-Boolean optimization: relaxation or propagation? N2 - Pseudo-Boolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudo-Boolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branch-and-cut-and-propagate framework, resulting in an efficient nonlinear pseudo-Boolean solver. T3 - ZIB-Report - 09-11 KW - Pseudo-Boolean KW - constraint integer programming KW - linear relaxation KW - separation algorithm KW - domain propagation Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11232 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - The Steiner Connectivity Problem N2 - The Steiner connectivity problem is a generalization of the Steiner tree problem. It consists in finding a minimum cost set of simple paths to connect a subset of nodes in an undirected graph. We show that polyhedral and algorithmic results on the Steiner tree problem carry over to the Steiner connectivity problem, namely, the Steiner cut and the Steiner partition inequalities, as well as the associated polynomial time separation algorithms, can be generalized. Similar to the Steiner tree case, a directed formulation, which is stronger than the natural undirected one, plays a central role. T3 - ZIB-Report - 09-07 KW - Steiner Tree KW - Partition Inequalities KW - Paths KW - Connectivity KW - Generalization Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11171 SN - 1438-0064 ER - TY - GEN A1 - Torres, Luis Miguel A1 - Torres, Ramiro A1 - Borndörfer, Ralf A1 - Pfetsch, Marc T1 - Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System (Extended Abstract) N2 - Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated. T3 - ZIB-Report - 08-53 KW - line planning KW - computational complexity KW - public transport KW - integer programming Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11076 SN - 1438-0064 ER - TY - GEN A1 - Torres, Luis Miguel A1 - Torres, Ramiro A1 - Borndörfer, Ralf A1 - Pfetsch, Marc T1 - On the Line Planning Problem in Tree Networks N2 - We introduce an optimization model for the line planning problem in a public transportation system that aims at minimizing operational costs while ensuring a given level of quality of service in terms of available transport capacity. We discuss the computational complexity of the model for tree network topologies and line structures that arise in a real-world application at the Trolebus Integrated System in Quito. Computational results for this system are reported. T3 - ZIB-Report - 08-52 KW - line planning KW - computational complexity KW - public transport optimization Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11069 SN - 1438-0064 ER - TY - GEN A1 - Torres, Luis Miguel A1 - Torres, Ramiro A1 - Borndörfer, Ralf A1 - Pfetsch, Marc T1 - Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System N2 - Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated. T3 - ZIB-Report - 08-35 KW - line planning KW - computational complexity KW - public transport KW - integer programming Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10869 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - Optimal Fares for Public Transport N2 - 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. T3 - ZIB-Report - 05-35 KW - fare planning KW - demand function KW - discrete choice model Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8698 ER - TY - GEN A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Pfetsch, Marc ED - Jünger, Michael ED - Reinelt, Gerhard T1 - Progress in Academic Computational Integer Programming T2 - Facets of Combinatorial Optimization Y1 - 2013 U6 - https://doi.org/10.1007/978-3-642-38189-8_19 SP - 483 EP - 506 PB - Springer ER -