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  • 2015-2019  (88)
  • 1990-1994  (4)
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  • 21
    Publication Date: 2020-08-05
    Description: PolySCIP is a new solver for multi-criteria integer and multi-criteria linear programs handling an arbitrary number of objectives. It is available as an official part of the non-commercial constraint integer programming framework SCIP. It utilizes a lifted weight space approach to compute the set of supported extreme non-dominated points and unbounded non-dominated rays, respectively. The algorithmic approach can be summarized as follows: At the beginning an arbitrary non-dominated point is computed (or it is determined that there is none) and a weight space polyhedron created. In every next iteration a vertex of the weight space polyhedron is selected whose entries give rise to a single-objective optimization problem via a combination of the original objectives. If the ptimization of this single-objective problem yields a new non-dominated point, the weight space polyhedron is updated. Otherwise another vertex of the weight space polyhedron is investigated. The algorithm finishes when all vertices of the weight space polyhedron have been investigated. The file format of PolySCIP is based on the widely used MPS format and allows a simple generation of multi-criteria models via an algebraic modelling language.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 22
    Publication Date: 2020-08-05
    Description: The task of periodic timetabling is to determine trip arrival and departure times in a public transport system such that travel and transfer times are minimized. This paper investigates periodic timetabling models with integrated passenger routing. We show that different routing models can have a huge influence on the quality of the entire system: Whatever metric is applied, the performance ratios of timetables w.r.t. different routing models can be arbitrarily large. Computations on a real-world instance for the city of Wuppertal substantiate the theoretical findings. These results indicate the existence of untapped optimization potentials that can be used to improve the efficiency of public transport systems by integrating passenger routing.
    Language: English
    Type: article , doc-type:article
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  • 23
    Publication Date: 2020-08-05
    Description: The rolling stock, i.e., railway vehicles, are one of the key ingredients of a running railway system. As it is well known, the offer of a railway company to their customers, i.e., the railway timetable, changes from time to time. Typical reasons for that are different timetables associated with different seasons, maintenance periods or holidays. Therefore, the regular lifetime of a timetable is split into (more or less) irregular periods where parts of the timetable are changed. In order to operate a railway timetable most railway companies set up sequences that define the operation of timetabled trips by a single physical railway vehicle called (rolling stock) rotations. Not surprisingly, the individual parts of a timetable also affect the rotations. More precisely, each of the parts brings up an acyclic rolling stock rotation problem with start and end conditions associated with the beginning and ending of the corresponding period. In this paper, we propose a propagation approach to deal with large planning horizons that are composed of many timetables with shorter individual lifetimes. The approach is based on an integer linear programming formulation that propagates rolling stock rotations through the irregular parts of the timetable while taking a large variety of operational requirements into account. This approach is implemented within the rolling stock rotation optimization framework ROTOR used by DB Fernverkehr AG, one of the leading railway operators in Europe. Computational results for real world scenarios are presented to evaluate the approach.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 24
    Publication Date: 2020-08-05
    Description: Wir stellen einen mathematischen Optimierungsansatz zur Berechnung von periodischen Taktfahrplänen vor, bei dem die Umsteigezeiten unter Berücksichtigung des Passagierverhaltens minimiert werden. Wir untersuchen damit den Einfluss wichtiger Systemparameter und Verhaltensmuster auf die Beförderungsqualität.
    Language: German
    Type: conferenceobject , doc-type:conferenceObject
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  • 25
    Publication Date: 2020-08-05
    Description: We consider railway timetables of our industrial partner DB Fernverkehr AG that operates the ICE high speed trains in the long-distance passenger railway network of Germany. Such a timetable covers a whole year with 364 days and, typically, includes more than 45,000 trips. A rolling stock rotation plan is not created for the whole timetable at once. Instead the timetable is divided into regular invariant sections and irregular deviations (e.g. for public holidays). A separate rotation plan with a weekly period can then be provided for each of the different sections of the timetable. We present an algorithmic approach to automatically recognize these sections. Together with the supplementing visualisation of the timetable this method has shown to be very relevant for our industrial partner.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 26
    Publication Date: 2020-08-05
    Description: The rolling stock, i.e., railway vehicles, are one of the key ingredients of a running railway system. As it is well known, the offer of a railway company to their customers, i.e., the railway timetable, changes from time to time. Typical reasons for that are different timetables associated with different seasons, maintenance periods or holidays. Therefore, the regular lifetime of a timetable is split into (more or less) irregular periods where parts of the timetable are changed. In order to operate a railway timetable most railway companies set up sequences that define the operation of timetabled trips by a single physical railway vehicle called (rolling stock) rotations. Not surprisingly, the individual parts of a timetable also affect the rotations. More precisely, each of the parts brings up an acyclic rolling stock rotation problem with start and end conditions associated with the beginning and ending of the corresponding period. In this paper, we propose a propagation approach to deal with large planning horizons that are composed of many timetables with shorter individual lifetimes. The approach is based on an integer linear programming formulation that propagates rolling stock rotations through the irregular parts of the timetable while taking a large variety of operational requirements into account. This approach is implemented within the rolling stock rotation optimization framework ROTOR used by DB Fernverkehr AG, one of the leading railway operators in Europe. Computational results for real world scenarios are presented to evaluate the approach.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
    Library Location Call Number Volume/Issue/Year Availability
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  • 27
    Publication Date: 2020-11-17
    Description: Real world routing problems, e.g., in the airline industry or in public and rail transit, can feature complex non-linear cost functions. An important case are costs for crossing regions, such as countries or fare zones. We introduce the shortest path problem with crossing costs (SPPCC) to address such situations; it generalizes the classical shortest path problem and variants such as the resource constrained shortest path problem and the minimum label path problem. Motivated by an application in flight trajectory optimization with overflight costs, we focus on the case in which the crossing costs of a region depend only on the nodes used to enter or exit it. We propose an exact Two-Layer-Dijkstra Algorithm as well as a novel cost-projection linearization technique that approximates crossing costs by shadow costs on individual arcs, thus reducing the SPPCC to a standard shortest path problem. We evaluate all algorithms’ performance on real-world flight trajectory optimization instances, obtaining very good à posteriori error bounds.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 28
    Publication Date: 2021-01-22
    Description: We study the problem of finding subpaths with high demand in a given network that is traversed by several users. The demand of a subpath is the number of users who completely cover this subpath during their trip. Especially with large instances, an efficient algorithm for computing all subpaths' demands is necessary. We introduce a path-graph to prevent multiple generations of the same subpath and give a recursive approach to compute the demands of all subpaths. Our runtime analysis shows, that the presented approach compares very well against the theoretical minimum runtime.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 29
    Publication Date: 2021-01-22
    Description: The problem of allocating operating rooms (OR) to surgical cases is a challenging task, involving both combinatorial aspects and uncertainty handling. We formulate this problem as a parallel machines scheduling problem, in which job durations follow a lognormal distribution, and a fixed assignment of jobs to machines must be computed. We propose a cutting-plane approach to solve the robust counterpart of this optimization problem. To this end, we develop an algorithm based on fixed-point iterations that identifies worst-case scenarios and generates cut inequalities. The main result of this article uses Hilbert's projective geometry to prove the convergence of this procedure under mild conditions. We also propose two exact solution methods for a similar problem, but with a polyhedral uncertainty set, for which only approximation approaches were known. Our model can be extended to balance the load over several planning periods in a rolling horizon. We present extensive numerical experiments for instances based on real data from a major hospital in Berlin. In particular, we find that: (i) our approach performs well compared to a previous model that ignored the distribution of case durations; (ii) compared to an alternative stochastic programming approach, robust optimization yields solutions that are more robust against uncertainty, at a small price in terms of average cost; (iii) the \emph{longest expected processing time first} (LEPT) heuristic performs well and efficiently protects against extreme scenarios, but only if a good prediction model for the durations is available. Finally, we draw a number of managerial implications from these observations.
    Language: English
    Type: article , doc-type:article
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  • 30
    Publication Date: 2020-08-05
    Description: Wir beschreiben die Optimierung des Nahverkehrsnetzes der Stadt Karlsruhe im Zusammmenhang mit den Baumaßnahmen der sogenannten Kombilösung.
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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