@misc{FischerGrimmKlugetal., 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}, 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{CheungGleixnerSteffy, author = {Cheung, Kevin K. H. and Gleixner, Ambros and Steffy, Daniel}, title = {Verifying Integer Programming Results}, issn = {1438-0064}, doi = {10.1007/978-3-319-59250-3_13}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61044}, abstract = {Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic errors, motivating the desire for a way to produce independently verifiable certificates of claimed results. Due to the complex nature of state-of-the-art MILP solution algorithms, the ideal form of such a certificate is not entirely clear. This paper proposes such a certificate format, illustrating its capabilities and structure through examples. The certificate format is designed with simplicity in mind and is composed of a list of statements that can be sequentially verified using a limited number of simple yet powerful inference rules. We present a supplementary verification tool for compressing and checking these certificates independently of how they were created. We report computational results on a selection of mixed-integer linear programming instances from the literature. To this end, we have extended the exact rational version of the MIP solver SCIP to produce such certificates.}, language = {en} } @misc{BorndoerferArslanElijazyferetal., author = {Bornd{\"o}rfer, Ralf and Arslan, Oytun and Elijazyfer, Ziena and G{\"u}ler, Hakan and Renken, Malte and Sahin, G{\"u}venc and Schlechte, Thomas}, title = {Line Planning on Path Networks with Application to the Istanbul Metrob{\"u}s}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60119}, abstract = {Bus rapid transit systems in developing and newly industrialized countries often consist of a trunk with a path topology. On this trunk, several overlapping lines are operated which provide direct connections. The demand varies heavily over the day, with morning and afternoon peaks typically in reverse directions. We propose an integer programming model for this problem, derive a structural property of line plans in the static (or single period) ``unimodal demand'' case, and consider approaches to the solution of the multi-period version that rely on clustering the demand into peak and off-peak service periods. An application to the Metrob{\"u}s system of Istanbul is discussed.}, language = {en} } @misc{BlancoBorndoerferHoangetal., author = {Blanco, Marco and Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung and Kaier, Anton and Schlechte, Thomas and Schlobach, Swen}, title = {The Shortest Path Problem with Crossing Costs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61240}, abstract = {We introduce the shortest path problem with crossing costs (SPPCC), a shortest path problem in a directed graph, in which the objective function is the sum of arc weights and crossing costs. The former are independently paid for each arc used by the path, the latter need to be paid every time the path intersects certain sets of arcs, which we call regions. The SPPCC generalizes not only the classical shortest path problem but also variants such as the resource constrained shortest path problem and the minimum label path problem. We use the SPPCC to model the flight trajectory optimization problem with overflight costs. In this paper, we provide a comprehensive analysis of the problem. In particular, we identify efficient exact and approximation algorithms for the cases that are most relevant in practice.}, language = {en} } @misc{SchwartzBorndoerferBartz, author = {Schwartz, Stephan and Bornd{\"o}rfer, Ralf and Bartz, Gerald}, title = {The Graph Segmentation Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60750}, abstract = {We investigate a graph theoretical problem arising in the automatic billing of a network toll. Given a network and a family of user paths, we study the graph segmentation problem (GSP) to cover parts of the user paths by a set of disjoint segments. The GSP is shown to be NP-hard but for special cases it can be solved in polynomial time. We also show that the marginal utility of a segment is bounded. Computational results for real-world instances show that in practice the problem is more amenable than the theoretic bounds suggest.}, language = {en} } @misc{BorndoerferGrimmReutheretal., author = {Bornd{\"o}rfer, Ralf and Grimm, Boris and Reuther, Markus and Schlechte, Thomas}, title = {Optimization of Handouts for Rolling Stock Rotations Visualization}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61430}, abstract = {A railway operator creates (rolling stock) rotations in order to have a precise master plan for the operation of a timetable by railway vehicles. A rotation is considered as a cycle that multiply traverses a set of operational days while covering trips of the timetable. As it is well known, the proper creation of rolling stock rotations by, e.g., optimization algorithms is challenging and still a topical research subject. Nevertheless, we study a completely different but strongly related question in this paper, i.e.: How to visualize a rotation? For this purpose, we introduce a basic handout concept, which directly leads to the visualization, i.e., handout of a rotation. In our industrial application at DB Fernverkehr AG, the handout is exactly as important as the rotation itself. Moreover, it turns out that also other European railway operators use exactly the same methodology (but not terminology). Since a rotation can have many handouts of different quality, we show how to compute optimal ones through an integer program (IP) by standard software. In addition, a construction as well as an improvement heuristic are presented. Our computational results show that the heuristics are a very reliable standalone approach to quickly find near-optimal and even optimal handouts. The efficiency of the heuristics is shown via a computational comparison to the IP approach.}, language = {en} } @misc{HennigSchwarz, author = {Hennig, Kai and Schwarz, Robert}, title = {Using Bilevel Optimization to find Severe Transport Situations in Gas Transmission Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61519}, abstract = {In the context of gas transmission in decoupled entry-exit systems, many approaches to determine the network capacity are based on the evaluation of realistic and severe transport situations. In this paper, we review the Reference Point Method, which is an algorithm used in practice to generate a set of scenarios using the so-called transport moment as a measure for severity. We introduce a new algorithm for finding severe transport situations that considers an actual routing of the flow through the network and is designed to handle issues arising from cyclic structures in a more dynamical manner. Further, in order to better approximate the physics of gas, an alternative, potential based flow formulation is proposed. The report concludes with a case study based on data from the benchmark library GasLib.}, language = {en} } @misc{LenzSchwarz, author = {Lenz, Ralf and Schwarz, Robert}, title = {Optimal Looping of Pipelines in Gas Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61564}, abstract = {In this paper, we compare several approaches for the problem of gas network expansions using loops, that is, to build new pipelines in parallel to existing ones. We present different model formulations for the problem of continuous loop expansions as well as discrete loop expansions. We then analyze problem properties, such as the structure and convexity of the underlying feasible regions. The paper concludes with a computational study comparing the continuous and the discrete formulations.}, language = {en} } @misc{BertholdHendelKoch, author = {Berthold, Timo and Hendel, Gregor and Koch, Thorsten}, title = {The Three Phases of MIP Solving}, issn = {1438-0064}, doi = {10.1080/10556788.2017.1392519}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61607}, abstract = {Modern MIP solvers employ dozens of auxiliary algorithmic components to support the branch-and-bound search in finding and improving primal solutions and in strengthening the dual bound. Typically, all components are tuned to minimize the average running time to prove optimality. In this article, we take a different look at the run of a MIP solver. We argue that the solution process consists of three different phases, namely achieving feasibility, improving the incumbent solution, and proving optimality. We first show that the entire solving process can be improved by adapting the search strategy with respect to the phase-specific aims using different control tunings. Afterwards, we provide criteria to predict the transition between the individual phases and evaluate the performance impact of altering the algorithmic behavior of the MIP solver SCIP at the predicted phase transition points.}, language = {en} } @misc{GleixnerBertholdMuelleretal., author = {Gleixner, Ambros and Berthold, Timo and M{\"u}ller, Benjamin and Weltge, Stefan}, title = {Three Enhancements for Optimization-Based Bound Tightening}, issn = {1438-0064}, doi = {10.1007/s10898-016-0450-4}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57803}, abstract = {Optimization-based bound tightening (OBBT) is one of the most effective procedures to reduce variable domains of nonconvex mixed-integer nonlinear programs (MINLPs). At the same time it is one of the most expensive bound tightening procedures, since it solves auxiliary linear programs (LPs)—up to twice the number of variables many. The main goal of this paper is to discuss algorithmic techniques for an efficient implementation of OBBT. Most state-of-the-art MINLP solvers apply some restricted version of OBBT and it seems to be common belief that OBBT is beneficial if only one is able to keep its computational cost under control. To this end, we introduce three techniques to increase the efficiency of OBBT: filtering strategies to reduce the number of solved LPs, ordering heuristics to exploit simplex warm starts, and the generation of Lagrangian variable bounds (LVBs). The propagation of LVBs during tree search is a fast approximation to OBBT without the need to solve auxiliary LPs. We conduct extensive computational experiments on MINLPLib2. Our results indicate that OBBT is most beneficial on hard instances, for which we observe a speedup of 17\% to 19\% on average. Most importantly, more instances can be solved when using OBBT.}, language = {en} }