Volume
OASIcs, Volume 123
24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)
Publication Details
- published at: 2024-10-07
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-350-8
Access Numbers
- Detailed Access Statistics available here
-
Total Document Accesses (updated on a weekly basis):
0PDF Downloads
Documents
No documents found matching your filter selection.
Document
Complete Volume
OASIcs, Volume 123, ATMOS 2024, Complete Volume
Abstract
OASIcs, Volume 123, ATMOS 2024, Complete Volume
Cite as
24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 1-316, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@Proceedings{bouman_et_al:OASIcs.ATMOS.2024,
title = {{OASIcs, Volume 123, ATMOS 2024, Complete Volume}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {1--316},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024},
URN = {urn:nbn:de:0030-drops-211873},
doi = {10.4230/OASIcs.ATMOS.2024},
annote = {Keywords: OASIcs, Volume 123, ATMOS 2024, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{bouman_et_al:OASIcs.ATMOS.2024.0,
author = {Bouman, Paul C. and Kontogiannis, Spyros C.},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {0:i--0:xii},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.0},
URN = {urn:nbn:de:0030-drops-211882},
doi = {10.4230/OASIcs.ATMOS.2024.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Landmark Hub Labeling: Improved Bounds and Faster Query Answering
Abstract
Hub Labeling (HL) is a state-of-the-art method for answering shortest-distance queries between node pairs in weighted graphs. It provides very fast query times but also requires considerable additional space to store the label information. Recently, a generalization of HL, called Landmark Hub Labeling (LHL), has been proposed, that conceptionally allows a storage of fewer label information without compromising the optimality of the query result. However, query answering with LHL was shown to be slower than with HL, both in theory and practice. Furthermore, it was not clear whether there are graphs with a substantial space reduction when using LHL instead of HL. In this paper, we describe a new way of storing label information of an LHL such that query times are significantly reduced and then asymptotically match those of HL. Thus, we alleviate the so far greatest shortcoming of LHL compared to HL. Moreover, we show that for the practically relevant hierarchical versions (HHL and HLHL), there are graphs in which the label size of an optimal HLHL is a factor of Θ(√ n) smaller than that of an optimal HHL. We establish further novel bounds between different labeling variants. Additionally, we provide a comparative experimental study between approximation algorithms for HL and LHL. We demonstrate that label sizes in an LHL are consistently smaller than those of HL across diverse benchmark graphs, including road networks.
Cite as
Justine Cauvi, Ruoying Li, and Sabine Storandt. Landmark Hub Labeling: Improved Bounds and Faster Query Answering. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 1:1-1:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{cauvi_et_al:OASIcs.ATMOS.2024.1,
author = {Cauvi, Justine and Li, Ruoying and Storandt, Sabine},
title = {{Landmark Hub Labeling: Improved Bounds and Faster Query Answering}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {1:1--1:17},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.1},
URN = {urn:nbn:de:0030-drops-211892},
doi = {10.4230/OASIcs.ATMOS.2024.1},
annote = {Keywords: Route Planning, Shortest Path, Hub Labeling}
}
Document
Indexing Graphs for Shortest Beer Path Queries
Abstract
A beer graph is an edge-weighted graph G = (V,E,ω) with beer vertices B ⊆ V. A beer path between two vertices s and t of a beer graph is a path that connects s and t and visits at least one vertex in B. The beer distance between two vertices is the weight of a shortest beer path, i.e. a beer path having minimum total weight. A graph indexing scheme is a two-phase method that constructs an index data structure by a one-time preprocessing of an input graph and then exploits it to compute (or accelerate the computation of) answers to queries on structures of the graph dataset. In the last decade, such indexing schemes have been designed to perform, effectively, many relevant types of queries, e.g. on reachability, and have gained significant popularity in essentially all data-intensive application domains where large number of queries have to be routinely answered (e.g. journey planners), since they have been shown, through many experimental studies, to offer extremely low query times at the price of limited preprocessing time and space overheads.
In this paper, we showcase that an indexing scheme, to efficiently execute queries on beer distances or shortest beer paths for pairs of vertices of a beer graph, can be obtained by adapting the highway labeling, a recently introduced indexing method to accelerate the computation of classical shortest paths. We design a preprocessing algorithm to build a whl index, i.e. a weighted highway labeling of a beer graph, and show how it can be queried to compute beer distances and shortest beer paths. Through extensive experimentation on real networks, we empirically demonstrate its practical effectiveness and superiority, in terms of offered trade-off between preprocessing time, space overhead and query time, with respect to the state-of-the-art.
Cite as
David Coudert, Andrea D'Ascenzo, and Mattia D'Emidio. Indexing Graphs for Shortest Beer Path Queries. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{coudert_et_al:OASIcs.ATMOS.2024.2,
author = {Coudert, David and D'Ascenzo, Andrea and D'Emidio, Mattia},
title = {{Indexing Graphs for Shortest Beer Path Queries}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {2:1--2:18},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.2},
URN = {urn:nbn:de:0030-drops-211907},
doi = {10.4230/OASIcs.ATMOS.2024.2},
annote = {Keywords: Graph Algorithms, Indexing Schemes, Beer Distances, Algorithms Engineering}
}
Document
Pricing for the EVRPTW with Piecewise Linear Charging by a Bounding-Based Labeling Algorithm
Abstract
The elementary shortest path problem with resource constraints (ESPPRC) is a common problem that often arises as a pricing problem when solving vehicle routing problems with a column generation approach. One way of solving the ESPPRC is to use a labeling algorithm. In this paper, we focus on how different bounding strategies for labeling algorithms can be adapted and strengthened for the ESPPRC that arises from the Electric Vehicle Routing Problem with Time Windows and Piecewise Linear Recharging function (EVRPTW-PLR). We present a new completion bound method that takes charging times into account, and show how the completion bound can be combined with ng-routes. Computational experiments show that the new completion bound combined with ng-routes significantly improves the performance compared to a basic labeling algorithm.
Cite as
Jenny Enerbäck, Lukas Eveborn, and Elina Rönnberg. Pricing for the EVRPTW with Piecewise Linear Charging by a Bounding-Based Labeling Algorithm. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{enerback_et_al:OASIcs.ATMOS.2024.3,
author = {Enerb\"{a}ck, Jenny and Eveborn, Lukas and R\"{o}nnberg, Elina},
title = {{Pricing for the EVRPTW with Piecewise Linear Charging by a Bounding-Based Labeling Algorithm}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {3:1--3:18},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.3},
URN = {urn:nbn:de:0030-drops-211911},
doi = {10.4230/OASIcs.ATMOS.2024.3},
annote = {Keywords: ESPPRC, EVRP, Bounding, Labeling Algorithm}
}
Document
Periodic Event Scheduling with Flexible Infrastructure Assignment
Abstract
We present novel extensions of the Periodic Event Scheduling Problem (PESP) that integrate the assignment of activities to infrastructure elements. An application of this is railway timetabling, as station and platform capacities are limited and need to be taken into account. We show that an assignment of activities to platforms can always be made periodic, and that it can be beneficial to allow larger periods for the assignment than for the timetable. We present mixed-integer programming formulations for the general problem, as well as for the practically relevant case when multiple platforms can be considered equivalent, for which we present a bipartite matching approach. We finally test and compare these models on real-world instances.
Cite as
Enrico Bortoletto, Rolf Nelson van Lieshout, Berenike Masing, and Niels Lindner. Periodic Event Scheduling with Flexible Infrastructure Assignment. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{bortoletto_et_al:OASIcs.ATMOS.2024.4,
author = {Bortoletto, Enrico and van Lieshout, Rolf Nelson and Masing, Berenike and Lindner, Niels},
title = {{Periodic Event Scheduling with Flexible Infrastructure Assignment}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {4:1--4:18},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.4},
URN = {urn:nbn:de:0030-drops-211929},
doi = {10.4230/OASIcs.ATMOS.2024.4},
annote = {Keywords: Periodic Event Scheduling, Periodic Timetabling, Railway Timetabling, Matchings, Infrastructure Assignments, Platform Assignments, Station Capacities}
}
Document
Balanced Assignments of Periodic Tasks
Abstract
This work deals with a problem of assigning periodic tasks to employees in such a way that each employee performs each task with the same frequency in the long term. The motivation comes from a collaboration with the main French railway company, the SNCF. An almost complete solution is provided under the form of a necessary and sufficient condition that can be checked in polynomial time. A complementary discussion about possible extensions is also proposed.
Cite as
Héloïse Gachet and Frédéric Meunier. Balanced Assignments of Periodic Tasks. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 5:1-5:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{gachet_et_al:OASIcs.ATMOS.2024.5,
author = {Gachet, H\'{e}lo\"{i}se and Meunier, Fr\'{e}d\'{e}ric},
title = {{Balanced Assignments of Periodic Tasks}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {5:1--5:12},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.5},
URN = {urn:nbn:de:0030-drops-211938},
doi = {10.4230/OASIcs.ATMOS.2024.5},
annote = {Keywords: Fair schedule, Eulerian digraph, Markov chain, interval graph}
}
Document
Two-Stage Weekly Shift Scheduling for Train Dispatchers
Abstract
We consider the problem of creating weekly shift schedules for train dispatchers, which conform to a variety of operational constraints, in particular, several work and rest time restrictions. We create the schedules in a two-stage process. First, using a previously presented IP model, we create a set of feasible daily shifts, which takes care of minimum-rest and shift-length requirements, taskload bounds, and combinability of dispatching areas. We then formulate an IP model to combine these daily shifts into weekly schedules, enforcing that each daily shift is covered by some dispatcher every day of the week, while ensuring that the weekly schedules comply with various restrictions on working hours from a union agreement. With this approach, we aim to identify "good" sets of daily shifts for the longer schedules. We run experiments for real-world sized input and consider different distributions of the daily shifts w.r.t. shift length and ratio of night shifts. Daily shifts with shift-length variability, relatively few long shifts, and a low ratio of night shifts generally yield better weekly schedules. The runtime for the second stage with the best daily-shift pattern is below three hours, which - together with the runtime for stage 1 of ca. 2 hours per run - can be feasible for real-world use.
Cite as
Tomas Lidén, Christiane Schmidt, and Rabii Zahir. Two-Stage Weekly Shift Scheduling for Train Dispatchers. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{liden_et_al:OASIcs.ATMOS.2024.6,
author = {Lid\'{e}n, Tomas and Schmidt, Christiane and Zahir, Rabii},
title = {{Two-Stage Weekly Shift Scheduling for Train Dispatchers}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {6:1--6:16},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.6},
URN = {urn:nbn:de:0030-drops-211944},
doi = {10.4230/OASIcs.ATMOS.2024.6},
annote = {Keywords: shift scheduling, IP, train dispatcher shift scheduling}
}
Document
Improved Algorithms for the Capacitated Team Orienteering Problem
Abstract
We study the Capacitated Team Orienteering Problem, where a fleet of vehicles with capacities have to meet customers with known demands and prizes for a single commodity.
The objective is to maximize the total prize and to assign a sequence of customers to each vehicle while keeping the total distance traveled within a given budget and such that the total demand served by each vehicle does not exceed its capacity.
The problem has been widely studied both from a theoretical and a practical point of view. The contribution of this paper is twofold: (1) We advance the theoretical knowledge on the problem by providing new approximation algorithms that achieve, under some natural assumption, improved approximation ratios compared to the current best algorithms; (2) We propose four efficient heuristics that outperform the current state-of-the-art practical methods in the sense that they compute solutions that collect nearly the same prize in a significantly smaller running time. We also experimentally test the scalability of the new heuristics, showing that their running time increases approximately linearly with the size of the input, allowing us to process large graphs which were not possible to analyze before.
Cite as
Gianlorenzo D'Angelo, Mattia D'Emidio, Esmaeil Delfaraz, and Gabriele Di Stefano. Improved Algorithms for the Capacitated Team Orienteering Problem. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{dangelo_et_al:OASIcs.ATMOS.2024.7,
author = {D'Angelo, Gianlorenzo and D'Emidio, Mattia and Delfaraz, Esmaeil and Di Stefano, Gabriele},
title = {{Improved Algorithms for the Capacitated Team Orienteering Problem}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {7:1--7:17},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.7},
URN = {urn:nbn:de:0030-drops-211957},
doi = {10.4230/OASIcs.ATMOS.2024.7},
annote = {Keywords: Vehicle Routing, Approximation algorithms, Algorithm Engineering}
}
Document
Short Paper
New Bounds on the Performance of SBP for the Dial-a-Ride Problem with Revenues (Short Paper)
Abstract
We revisit the Segmented Best Path (sbp) algorithm for online DARP in an offline setting with revenues and a time limit. The goal is to find a subset of the inputted ride requests that can be served within the time limit while maximizing the total revenue earned. sbp divides the time into segments and greedily chooses the highest-revenue path of requests to serve within each time segment. We show that sbp’s performance has an upper bound of 5. Further, while sbp is a tight 4-approximation in the uniform-revenue case, we find that with non-uniform revenues, the approximation ratio of sbp has a lower bound strictly greater than 4; in particular, we provide a lower bound of (√e + 1)/(√e - 1) ≈ 4.08299, which we show can be generalized to instances with ratio greater than 4.278.
Cite as
Barbara M. Anthony, Christine Chung, Ananya Das, and David Yuen. New Bounds on the Performance of SBP for the Dial-a-Ride Problem with Revenues (Short Paper). In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 8:1-8:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{anthony_et_al:OASIcs.ATMOS.2024.8,
author = {Anthony, Barbara M. and Chung, Christine and Das, Ananya and Yuen, David},
title = {{New Bounds on the Performance of SBP for the Dial-a-Ride Problem with Revenues}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {8:1--8:6},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.8},
URN = {urn:nbn:de:0030-drops-211964},
doi = {10.4230/OASIcs.ATMOS.2024.8},
annote = {Keywords: Dial-a-Ride problems, Lower bounds, Vehicle routing}
}
Document
Online Vehicle Routing with Pickups and Deliveries Under Time-Dependent Travel-Time Constraints
Abstract
The Vehicle Routing Problem with pickups, deliveries and spatiotemporal service constraints (VRP_PDSTC) is a quite challenging algorithmic problem that can be dealt with in either an offline or an online fashion. In this work, we focus on a generalization, called VRP_PDSTCtd, in which the travel-time metric is time-dependent: the traversal-time per road segment (represented as a directed arc) is determined by some function of the departure-time from its tail towards its head. Time-dependence makes things much more complicated, even for the simpler problem of computing earliest-arrival-time paths which is a crucial subroutine to be solved (numerous times) by VRP_PDSTCtd schedulers. We propose two online schedulers of requests to workers, one which is a time-dependent variant of the classical Plain-Insertion heuristic, and an extension of it trying to digest some sort of forecasts for future demands for service. We enrich these two online schedulers with two additional heuristics, one targeting for distance-balanced assignments of work loads to the workers and another that makes local-search-improvements to the produced solutions. We conduct a careful experimental evaluation of the proposed algorithms on a real-world instance, with or without these heuristics, and compare their quality with human-curated assignments provided by professional experts (human operators at actual pickup-and-delivery control centers), and also with feasible solutions constructed from a relaxed MILP formulation of VRP_PDSTCtd, which is also introduced in this paper. Our findings are quite encouraging, demonstrating that the proposed algorithms produce solutions which (i) are significant improvements over the human-curated assignments, and (ii) have overall quality pretty close to that of the (extremely time-consuming) solutions provided by an exact solver for the MILP formulation.
Cite as
Spyros Kontogiannis, Andreas Paraskevopoulos, and Christos Zaroliagis. Online Vehicle Routing with Pickups and Deliveries Under Time-Dependent Travel-Time Constraints. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{kontogiannis_et_al:OASIcs.ATMOS.2024.9,
author = {Kontogiannis, Spyros and Paraskevopoulos, Andreas and Zaroliagis, Christos},
title = {{Online Vehicle Routing with Pickups and Deliveries Under Time-Dependent Travel-Time Constraints}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {9:1--9:20},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.9},
URN = {urn:nbn:de:0030-drops-211972},
doi = {10.4230/OASIcs.ATMOS.2024.9},
annote = {Keywords: transport optimization heuristics, vehicle routing with pickups and deliveries, time-dependent travel-times}
}
Document
Periodic Timetabling: Travel Time vs. Regenerative Energy
Abstract
While it is important to provide attractive public transportation to the passengers allowing short travel times, it should also be a major concern to reduce the amount of energy used by the public transport system. Electrical trains can regenerate energy when braking, which can be used by a nearby accelerating train. Therefore, apart from the minimization of travel times, the maximization of brake-traction overlaps of nearby trains is an important objective in periodic timetabling. Recently, this has been studied in a model allowing small modifications of a nominal timetable. We investigate the problem of finding periodic timetables that are globally good in both objective functions. We show that the general problem is NP-hard, even restricted to a single transfer station and if only travel time is to be minimized, and give an algorithm with an additive error bound for maximizing the brake-traction overlap on this small network. Moreover, we identify special cases in which the problem is solvable in polynomial time. Finally, we demonstrate the trade-off between the two objective functions in an experimental study.
Cite as
Sven Jäger, Sarah Roth, and Anita Schöbel. Periodic Timetabling: Travel Time vs. Regenerative Energy. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{jager_et_al:OASIcs.ATMOS.2024.10,
author = {J\"{a}ger, Sven and Roth, Sarah and Sch\"{o}bel, Anita},
title = {{Periodic Timetabling: Travel Time vs. Regenerative Energy}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {10:1--10:20},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.10},
URN = {urn:nbn:de:0030-drops-211983},
doi = {10.4230/OASIcs.ATMOS.2024.10},
annote = {Keywords: periodic timetabling, regenerative braking}
}
Document
Solving the Electric Bus Scheduling Problem by an Integrated Flow and Set Partitioning Approach
Abstract
Attractive and cost-efficient public transport requires solving computationally difficult optimization problems from network design to crew rostering. While great progress has been made in many areas, new requirements to handle increasingly complex constraints are constantly coming up. One such challenge is a new type of resource constraints that are used to deal with the state-of-charge of battery-electric vehicles, which have limited driving ranges and need to be recharged in-service.
Resource constrained vehicle scheduling problems can classically be modelled in terms of either a resource constrained (multi-commodity) flow problem or in terms of a path-based set partition problem. We demonstrate how a novel integrated version of both formulations can be leveraged to solve resource constrained vehicle scheduling with replenishment in general and the electric bus scheduling problem in particular by Lagrangian relaxation and the proximal bundle method.
Cite as
Ralf Borndörfer, Andreas Löbel, Fabian Löbel, and Steffen Weider. Solving the Electric Bus Scheduling Problem by an Integrated Flow and Set Partitioning Approach. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{borndorfer_et_al:OASIcs.ATMOS.2024.11,
author = {Bornd\"{o}rfer, Ralf and L\"{o}bel, Andreas and L\"{o}bel, Fabian and Weider, Steffen},
title = {{Solving the Electric Bus Scheduling Problem by an Integrated Flow and Set Partitioning Approach}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {11:1--11:16},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.11},
URN = {urn:nbn:de:0030-drops-211992},
doi = {10.4230/OASIcs.ATMOS.2024.11},
annote = {Keywords: Electric Bus Scheduling, Electric Vehicle Scheduling, Non-linear Charging, Multi-commodity Flow, Set Partition, Lagrangian Relaxation, Proximal Bundle Method}
}
Document
Short Paper
Towards an Optimization Pipeline for the Design of Train Control Systems with Hybrid Train Detection (Short Paper)
Abstract
Increasing the capacity of our railway infrastructure will become more and more essential in coping with the need for sustainable transportation. This can be achieved by intelligently implementing train control systems on specific railway networks. Methods that automate and optimize parts of this planning process are of great interest. For control systems based on hybrid train detection, such optimization tasks simultaneously involve routing and block layout generation. These tasks are already complex on their own; hence, a joint consideration often becomes infeasible. This work-in-progress paper proposes an idea to tackle the corresponding complexity. To this end, we present a pipeline that allows to sequentially handle corresponding optimization tasks in a less complex fashion while generating results that remain (close to) optimal. Results from an initial case study showcase that this approach is, indeed, promising. A prototypical implementation is included in the open-source Munich Train Control Toolkit available at https://github.com/cda-tum/mtct.
Cite as
Stefan Engels and Robert Wille. Towards an Optimization Pipeline for the Design of Train Control Systems with Hybrid Train Detection (Short Paper). In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 12:1-12:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{engels_et_al:OASIcs.ATMOS.2024.12,
author = {Engels, Stefan and Wille, Robert},
title = {{Towards an Optimization Pipeline for the Design of Train Control Systems with Hybrid Train Detection}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {12:1--12:6},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.12},
URN = {urn:nbn:de:0030-drops-212002},
doi = {10.4230/OASIcs.ATMOS.2024.12},
annote = {Keywords: ETCS, MILP, Design Automation, Hybrid Train Detection}
}
Document
A Bayesian Rolling Horizon Approach for Rolling Stock Rotation Planning with Predictive Maintenance
Abstract
We consider the rolling stock rotation planning problem with predictive maintenance (RSRP-PdM), where a timetable given by a set of trips must be operated by a fleet of vehicles. Here, the health states of the vehicles are assumed to be random variables, and their maintenance schedule should be planned based on their predicted failure probabilities. Utilizing the Bayesian update step of the Kalman filter, we develop a rolling horizon approach for RSRP-PdM, in which the predicted health state distributions are updated as new data become available. This approach reduces the uncertainty of the health states and thus improves the decision-making basis for maintenance planning. To solve the instances, we employ a local neighborhood search, which is a modification of a heuristic for RSRP-PdM, and demonstrate its effectiveness. Using this solution algorithm, the presented approach is compared with the results of common maintenance strategies on test instances derived from real-world timetables. The obtained results show the benefits of the rolling horizon approach.
Cite as
Felix Prause and Ralf Borndörfer. A Bayesian Rolling Horizon Approach for Rolling Stock Rotation Planning with Predictive Maintenance. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{prause_et_al:OASIcs.ATMOS.2024.13,
author = {Prause, Felix and Bornd\"{o}rfer, Ralf},
title = {{A Bayesian Rolling Horizon Approach for Rolling Stock Rotation Planning with Predictive Maintenance}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {13:1--13:19},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.13},
URN = {urn:nbn:de:0030-drops-212013},
doi = {10.4230/OASIcs.ATMOS.2024.13},
annote = {Keywords: Rolling stock rotation planning, Predictive maintenance, Rolling horizon approach, Bayesian inference, Local neighborhood search}
}
Document
The Line-Based Dial-a-Ride Problem
Abstract
On-demand ridepooling systems offer flexible services pooling multiple passengers into one vehicle, complementing traditional bus services. We propose a transportation system combining the spatial aspects of a fixed sequence of bus stops with the temporal flexibility of ridepooling. In the line-based Dial-a-Ride problem (liDARP), vehicles adhere to a fixed, ordered sequence of stops in their routes, with the possibility of taking shortcuts and turning if they are empty. We propose three MILP formulations for the liDARP with a multi-objective function balancing environmental aspects with customer satisfaction, comparing them on a real-world bus line. Our experiments show that the formulation based on an Event-Based graph is the fastest, solving instances with up to 50 requests in under one second. Compared to the classical DARP, the liDARP is computationally faster, with minimal increases in total distance driven and average ride times.
Cite as
Kendra Reiter, Marie Schmidt, and Michael Stiglmayr. The Line-Based Dial-a-Ride Problem. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{reiter_et_al:OASIcs.ATMOS.2024.14,
author = {Reiter, Kendra and Schmidt, Marie and Stiglmayr, Michael},
title = {{The Line-Based Dial-a-Ride Problem}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {14:1--14:20},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.14},
URN = {urn:nbn:de:0030-drops-212024},
doi = {10.4230/OASIcs.ATMOS.2024.14},
annote = {Keywords: DARP, ridepooling, liDARP, public transport, on-demand}
}
Document
A Bi-Objective Optimization Model for Fare Structure Design in Public Transport
Abstract
Fare planning in public transport is important from the view of passengers as well as of operators. In this paper, we propose a bi-objective model that maximizes the revenue as well as the number of attracted passengers. The potential demand per origin-destination pair is divided into demand groups that have their own willingness how much to pay for using public transport, i.e., a demand group is only attracted as public transport passengers if the fare does not exceed their willingness to pay. We study the bi-objective problem for flat and distance tariffs and develop specialized algorithms to compute the Pareto front in quasilinear or cubic time, respectively. Through computational experiments on structured data sets we evaluate the running time of the developed algorithms in practice and analyze the number of non-dominated points and their respective efficient solutions.
Cite as
Philine Schiewe, Anita Schöbel, and Reena Urban. A Bi-Objective Optimization Model for Fare Structure Design in Public Transport. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{schiewe_et_al:OASIcs.ATMOS.2024.15,
author = {Schiewe, Philine and Sch\"{o}bel, Anita and Urban, Reena},
title = {{A Bi-Objective Optimization Model for Fare Structure Design in Public Transport}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {15:1--15:19},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.15},
URN = {urn:nbn:de:0030-drops-212034},
doi = {10.4230/OASIcs.ATMOS.2024.15},
annote = {Keywords: Public transport, fare structure design, modeling, bi-objective, algorithm}
}
Document
Modeling Subway Networks and Passenger Flows
Abstract
Simulation of urban rail networks provides useful information to optimize traffic management strategies w.r.t. goals such as satisfaction of passenger demands, adherence to schedules or energy saving. Many network models are too precise for the analysis needs, and do not exploit concurrency. This results in an explosion in the size of models, and long simulation times. This paper presents an extension of Petri nets that handles trajectories of trains, passenger flows, and scenarios for passenger arrivals. We then define a fast event-based simulation scheme. We test our model on a real case study, the Metro of Montreal, and show that full days of train operations with passengers can be simulated in a few seconds, allowing analysis of quantitative properties.
Cite as
Antoine Thébault, Loïc Hélouët, and Kenza Saiah. Modeling Subway Networks and Passenger Flows. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{thebault_et_al:OASIcs.ATMOS.2024.16,
author = {Th\'{e}bault, Antoine and H\'{e}lou\"{e}t, Lo\"{i}c and Saiah, Kenza},
title = {{Modeling Subway Networks and Passenger Flows}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {16:1--16:20},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.16},
URN = {urn:nbn:de:0030-drops-212046},
doi = {10.4230/OASIcs.ATMOS.2024.16},
annote = {Keywords: Subways, Passenger Flows, Modelization, Petri-Nets, Trajectory-Nets}
}
Document
Computing User Equilibria for Schedule-Based Transit Networks with Hard Vehicle Capacities
Abstract
Modelling passenger assignments in public transport networks is a fundamental task for city planners, especially when deliberating network infrastructure decisions. A key aspect of a realistic model for passenger assignments is to integrate selfish routing behaviour of passengers on the one hand, and the limited vehicle capacities on the other hand. We formulate a side-constrained user equilibrium model in a schedule-based time-expanded transit network, where passengers are modelled via a continuum of non-atomic agents that want to travel with a fixed start time from a user-specific origin to a destination. An agent’s route may comprise several rides along given lines, each using vehicles with hard loading capacities. We give a characterization of (side-constrained) user equilibria via a quasi-variational inequality and prove their existence by generalizing a well-known existence result of Bernstein and Smith (Transp. Sci., 1994). We further derive a polynomial time algorithm for single-commodity instances and an exact finite time algorithm for the multi-commodity case. Based on our quasi-variational characterization, we finally devise a fast heuristic computing user equilibria, which is tested on real-world instances based on data gained from the Hamburg S-Bahn system and the Swiss long-distance train network. It turns out that w.r.t. the total travel time, the computed user-equilibria are quite efficient compared to a system optimum, which neglects equilibrium constraints and only minimizes total travel time.
Cite as
Tobias Harks, Sven Jäger, Michael Markl, and Philine Schiewe. Computing User Equilibria for Schedule-Based Transit Networks with Hard Vehicle Capacities. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{harks_et_al:OASIcs.ATMOS.2024.17,
author = {Harks, Tobias and J\"{a}ger, Sven and Markl, Michael and Schiewe, Philine},
title = {{Computing User Equilibria for Schedule-Based Transit Networks with Hard Vehicle Capacities}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {17:1--17:17},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.17},
URN = {urn:nbn:de:0030-drops-212054},
doi = {10.4230/OASIcs.ATMOS.2024.17},
annote = {Keywords: traffic assignment, side-constrained equilibrium, public transportation}
}
Document
Dynamic Traffic Assignment for Public Transport with Vehicle Capacities
Abstract
Traffic assignment is a core component of many urban transport planning tools. It is used to determine how traffic is distributed over a transportation network. We study the task of computing traffic assignments for public transport: Given a public transit network, a timetable, vehicle capacities and a demand (i.e. a list of passengers, each with an associated origin, destination, and departure time), the goal is to predict the resulting passenger flow and the corresponding load of each vehicle. Microscopic stochastic simulation of individual passengers is a standard, but computationally expensive approach. Briem et al. (2017) have shown that a clever adaptation of the Connection Scan Algorithm (CSA) can lead to highly efficient traffic assignment algorithms, but ignores vehicle capacities, resulting in overcrowded vehicles. Taking their work as a starting point, we here propose a new and extended model that guarantees capacity-feasible assignments and incorporates dynamic network congestion effects such as crowded vehicles, denied boarding, and dwell time delays. Moreover, we also incorporate learning and adaptation of individual passengers based on their experience with the network. Applications include studying the evolution of perceived travel times as a result of adaptation, the impact of an increase in capacity, or network effects due to changes in the timetable such as the addition or the removal of a service or a whole line. The proposed framework has been experimentally evaluated with public transport networks of Göttingen and Stuttgart (Germany). The simulation proves to be highly efficient. On a standard PC the computation of a traffic assignment takes just a few seconds per simulation day.
Cite as
Julian Patzner and Matthias Müller-Hannemann. Dynamic Traffic Assignment for Public Transport with Vehicle Capacities. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
Copy BibTex To Clipboard
@InProceedings{patzner_et_al:OASIcs.ATMOS.2024.18,
author = {Patzner, Julian and M\"{u}ller-Hannemann, Matthias},
title = {{Dynamic Traffic Assignment for Public Transport with Vehicle Capacities}},
booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
pages = {18:1--18:20},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-350-8},
ISSN = {2190-6807},
year = {2024},
volume = {123},
editor = {Bouman, Paul C. and Kontogiannis, Spyros C.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.18},
URN = {urn:nbn:de:0030-drops-212064},
doi = {10.4230/OASIcs.ATMOS.2024.18},
annote = {Keywords: Public transport, traffic assignment, vehicle capacities, crowding, stochastic simulation, learning}
}