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  • 2020-2023  (17)
  • English  (17)
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  • English  (17)
  • 11
    Publication Date: 2022-03-30
    Description: We present an optimization model which is capable of routing and ordering trains on a microscopic level under a moving block regime. Based on a general timetabling definition (GTTP) that allows the plug in of arbitrarily detailed methods to compute running and headway times, we describe a layered graph approach using velocity expansion, and develop a mixed integer linear programming formulation. Finally, we present promising results for a German corridor scenario with mixed traffic, indicating that applying branch-and-cut to our model is able to solve reasonably sized instances with up to hundred trains to optimality.
    Language: English
    Type: article , doc-type:article
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  • 12
    Publication Date: 2022-03-14
    Description: The Periodic Event Scheduling Problem is a well-studied NP-hard problem with applications in public transportation to find good periodic timetables. Among the most powerful heuristics to solve the periodic timetabling problem is the modulo network simplex method. In this paper, we consider the more difficult version with integrated passenger routing and propose a refined integrated variant to solve this problem on real-world-based instances.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 13
    Publication Date: 2022-01-19
    Description: We present a new label-setting algorithm for the Multiobjective Shortest Path (MOSP) problem that computes the minimal complete set of efficient paths for a given instance. The size of the priority queue used in the algorithm is bounded by the number of nodes in the input graph and extracted labels are guaranteed to be efficient. These properties allow us to give a tight output-sensitive running time bound for the new algorithm that can almost be expressed in terms of the running time of Dijkstra's algorithm for the Shortest Path problem. Hence, we suggest to call the algorithm \emph{Multiobjective Dijkstra Algorithm} (MDA). The simplified label management in the MDA allows us to parallelize some subroutines. In our computational experiments, we compare the MDA and the classical label-setting MOSP algorithm by Martins', which we improved using new data structures and pruning techniques. On average, the MDA is $\times2$ to $\times9$ times faster on all used graph types. On some instances the speedup reaches an order of magnitude.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 14
    Publication Date: 2021-09-29
    Description: The Dynamic Multiobjective Shortest Path problem features multidimensional costs that can depend on several variables and not only on time; this setting is motivated by flight planning applications and the routing of electric vehicles. We give an exact algorithm for the FIFO case and derive from it an FPTAS for both, the static Multiobjective Shortest Path (MOSP) problems and, under mild assumptions, for the dynamic problem variant. The resulting FPTAS is computationally efficient and beats the known complexity bounds of other FPTAS for MOSP problems.
    Language: English
    Type: article , doc-type:article
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  • 15
    Publication Date: 2022-08-31
    Description: Balanced separators are node sets that split the graph into size bounded components. They find applications in different theoretical and practical problems. In this paper we discuss how to find a minimum set of balanced separators in node weighted graphs. Our contribution is a new and exact algorithm that solves Minimum Balanced Separators by a sequence of Hitting Set problems. The only other exact method appears to be a mixed-integer program (MIP) for the edge weighted case. We adapt this model to node weighted graphs and compare it to our approach on a set of instances, resembling transit networks. It shows that our algorithm is far superior on almost all test instances.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
    Format: application/pdf
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  • 16
    Publication Date: 2022-11-24
    Description: Finding connected subgraphs of maximum weight subject to additional constraints on the subgraphs is a common (sub)problem in many applications. In this paper, we study the Maximum Weight Connected Subgraph Problem with a given root node and a lower and upper capacity constraint on the chosen subgraph. In addition, the nodes of the input graph are colored blue and red, and the chosen subgraph is required to be balanced regarding its cumulated blue and red weight. This problem arises as an essential subproblem in district planning applications. We show that the problem is NP-hard and give an integer programming formulation. By exploiting the capacity and balancing condition, we develop a powerful reduction technique that is able to significantly shrink the problem size. In addition, we propose a method to strengthen the LP relaxation of our formulation by identifying conflict pairs, i.e., nodes that cannot be both part of a chosen subgraph. Our computational study confirms the positive impact of the new preprocessing technique and of the proposed conflict cuts.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 17
    Publication Date: 2022-12-01
    Description: We consider the line planning problem in public transport in the Parametric City, an idealized model that captures typical scenarios by a (small) number of parameters. The Parametric City is rotation symmetric, but optimal line plans are not always symmetric. This raises the question to quantify the symmetry gap between the best symmetric and the overall best solution. For our analysis, we formulate the line planning problem as a mixed integer linear program, that can be solved in polynomial time if the solutions are forced to be symmetric. The symmetry gap is provably small when a specific Parametric City parameter is fixed, and we give an approximation algorithm for line planning in the Parametric City in this case. While the symmetry gap can be arbitrarily large in general, we show that symmetric line plans are a good choice in most practical situations.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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