Volume
OASIcs, Volume 147
26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)
Event
Editors
Publication Details
- published at: 2026-10-02
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-453-6
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Document
Complete Volume
OASIcs, Volume 147, ATMOS 2026, Complete Volume
Abstract
OASIcs, Volume 147, ATMOS 2026, Complete Volume
Cite as
26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 1-298, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@Proceedings{cacchiani_et_al:OASIcs.ATMOS.2026,
title = {{OASIcs, Volume 147, ATMOS 2026, Complete Volume}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {1--298},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026},
URN = {urn:nbn:de:0030-drops-280917},
doi = {10.4230/OASIcs.ATMOS.2026},
annote = {Keywords: OASIcs, Volume 147, ATMOS 2026, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{cacchiani_et_al:OASIcs.ATMOS.2026.0,
author = {Cacchiani, Valentina and Funke, Stefan},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {0:i--0:xii},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.0},
URN = {urn:nbn:de:0030-drops-280820},
doi = {10.4230/OASIcs.ATMOS.2026.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
Optimizing Last-Mile Deliveries at Amazon (Invited Talk)
Abstract
Amazon delivers tens of millions of shipments worldwide on a daily basis. Planning the last-mile routes that reach final customers requires solving combinatorial optimization problems at massive scale. While designing and engineering efficient algorithms is essential to address this challenge, it is far from sufficient. Drawing on practical examples, this talk argues that properly framing the problem, choosing the right metrics, and navigating real-world operational and organizational constraints are just as critical. In fact, they ultimately shape the algorithms themselves.
Cite as
Renato F. Werneck. Optimizing Last-Mile Deliveries at Amazon (Invited Talk). In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{werneck:OASIcs.ATMOS.2026.1,
author = {Werneck, Renato F.},
title = {{Optimizing Last-Mile Deliveries at Amazon}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {1:1--1:1},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.1},
URN = {urn:nbn:de:0030-drops-277976},
doi = {10.4230/OASIcs.ATMOS.2026.1},
annote = {Keywords: Vehicle Routing, Route Planning, Last-Mile Logistics, Algorithm Engineering}
}
Document
Passenger-Based Intermodal Connection Optimization with Elastic Demands
Abstract
A railway network can attract additional passengers by improving the quality of service. One way to do that is to establish new train connections by slight shifts in arrival and departure times. We propose a connection optimization model to find a shifting of a given aperiodic timetable that maximizes the passenger volume, in which the demand is elastic and forecast by an integrated discrete choice logit model. The resulting large-scale mixed-integer non-linear non-convex programming problems can be solved by tailor-made heuristics for the entire Italian railway network with its 2,000 stations and 10,000 daily train trips, uncovering substantial potentials for connectivity improvements and boosts in demand.
Cite as
Boris Grimm, Ralf Borndörfer, Andrea Fraioli, Paula Franke, Giovanni Luca Giacco, Federico Marinucci, and Tommaso Montino. Passenger-Based Intermodal Connection Optimization with Elastic Demands. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{grimm_et_al:OASIcs.ATMOS.2026.2,
author = {Grimm, Boris and Bornd\"{o}rfer, Ralf and Fraioli, Andrea and Franke, Paula and Giacco, Giovanni Luca and Marinucci, Federico and Montino, Tommaso},
title = {{Passenger-Based Intermodal Connection Optimization with Elastic Demands}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {2:1--2:18},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.2},
URN = {urn:nbn:de:0030-drops-277980},
doi = {10.4230/OASIcs.ATMOS.2026.2},
annote = {Keywords: Timetabling, Demand Elasticity, Discrete Choice, Mixed-Integer Nonlinear Programming, Heuristics}
}
Document
Time-Aware A* for Optimal Train Routing on Moving Block Systems
Abstract
Railway networks are operating at their capacity limits. Modern control systems allow for shorter train-following times on existing infrastructure, resulting in faster travel times and higher capacity. As new degrees of freedom emerge, developing effective and flexible algorithms becomes essential to incorporate these advancements into the planning process. Previously, a flexible method for generating provably optimal timetables using A* search has been proposed. However, in practice, the algorithm spends significant time exploring states that yield no new information. This work addresses this issue and shows that transforming the state space into a (directed) tree drastically reduces runtime and enhances scalability, particularly with respect to the number of trains. The implementation is available open-source as part of the Munich Train Control Toolkit on GitHub at https://github.com/cda-tum/mtct.
Cite as
Stefan Engels and Robert Wille. Time-Aware A* for Optimal Train Routing on Moving Block Systems. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{engels_et_al:OASIcs.ATMOS.2026.3,
author = {Engels, Stefan and Wille, Robert},
title = {{Time-Aware A* for Optimal Train Routing on Moving Block Systems}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {3:1--3:19},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.3},
URN = {urn:nbn:de:0030-drops-277992},
doi = {10.4230/OASIcs.ATMOS.2026.3},
annote = {Keywords: ETCS, European Train Control System, Train Routing, Moving Block, A*, Search Space Reduction, Munich Train Control Toolkit}
}
Document
Why Start Over: Incremental MaxSMT for Operational Railway Scheduling
Abstract
Railway timetables are planned periodically, but operational planners continuously need to deviate from this base: extra trains are added, or infrastructure changes are made, requiring local updates to the existing schedule. We study this process as a sequential extra train scheduling problem, in which requests arrive one at a time and must be routed and timed against the existing timetable while minimising deviation from it. Commonly, each admitted train is fixed before the next request arrives, and all accumulated solver knowledge is discarded between calls.
We propose an incremental MaxSAT framework over Integer Difference Logic (MaxSMT) that retains accumulated solver state across successive extra-train additions, rather than solving from scratch after each request. We evaluate the approach on the Rhätische Bahn network using different solving strategies and compare against a MIP baseline. Retained solver state substantially reduces solve time for successive additions, increasingly so as more extra trains are admitted, and is an order of magnitude faster than MIP given the same setup. Beyond solving time, we show that jointly re-optimising over all admitted extra trains yields better cumulative objective values, and that our approach achieves this while prioritising adjustments in the timetable region affected by the new request.
Cite as
Thomas Dubach, Florian Flükiger-Fuchs, and Bernardo Martin-Iradi. Why Start Over: Incremental MaxSMT for Operational Railway Scheduling. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{dubach_et_al:OASIcs.ATMOS.2026.4,
author = {Dubach, Thomas and Fl\"{u}kiger-Fuchs, Florian and Martin-Iradi, Bernardo},
title = {{Why Start Over: Incremental MaxSMT for Operational Railway Scheduling}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {4:1--4:19},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.4},
URN = {urn:nbn:de:0030-drops-278002},
doi = {10.4230/OASIcs.ATMOS.2026.4},
annote = {Keywords: MaxSAT, operational railway timetabling, incremental solving}
}
Document
Dispatching-Area Design
Abstract
Increasing traffic density and system interdependencies in railway networks can lead to imbalanced workload distribution among train dispatchers. Traditional dispatching-area design, often based on historical and geographical considerations, may no longer reflect current infrastructure complexity and coordination requirements, potentially affecting punctuality and operational robustness.
In this paper, we study the problem of partitioning a set of train stations into a predefined number of dispatching areas, formulated as a multi-objective mixed-integer programming problem. The objective is to minimize a weighted sum of inter-area interaction complexity and intra-area operational complexity. Inter-area complexity captures coordination needs through the number of trains crossing area boundaries, while intra-area complexity is modeled using station-related parameters, including track layout, traffic density, starting and ending services, and traffic heterogeneity (mix of passenger and freight traffic).
We apply the suggested approach to instances from the Malmö dispatching center in the southern part of the Swedish railway network, illustrating how an optimization-grounded sectorization framework can support structured and balanced redesign of dispatching areas. We evaluate the model’s robustness by through sensitivity analyses on objective weights, minimum area size, and the number of dispatching areas. These analyses provide insights into how different planning priorities influence the resulting sectorization.
Cite as
Tomas Lidén, Christiane Schmidt, and Rabii Zahir. Dispatching-Area Design. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{liden_et_al:OASIcs.ATMOS.2026.5,
author = {Lid\'{e}n, Tomas and Schmidt, Christiane and Zahir, Rabii},
title = {{Dispatching-Area Design}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {5:1--5:17},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.5},
URN = {urn:nbn:de:0030-drops-278018},
doi = {10.4230/OASIcs.ATMOS.2026.5},
annote = {Keywords: Railway sectorization, Area design, Train dispatching}
}
Document
From Routes to Resources: A Model for Real-Time Train Dispatching with No-Wait Constraints
Abstract
Optimization for train dispatching promises to reduce delays. Yet scalable applications are challenging. We present an efficient MIP model, based on generalized disjunctive graphs, for the train dispatching problem with no-wait constraints. For each train, we model its possible movements with microscopic detail as a DAG of operations. We select one train path per DAG and associate it with reservation and release times for the exclusive infrastructure it uses, such that the resulting schedule is conflict-free. When the connecting velocity between consecutive operations is positive, no-wait constraints apply. Additionally, we give a procedure to transform realistic infrastructure constraints based on route exclusions into an equivalent representation on resources by means of edge clique covers and incorporation of overlap exclusions. This makes resource-based dispatching models applicable to real-life infrastructure. We embed the MIP into an iterative algorithm, which we evaluate on the DISPLIB benchmark set and on a real-life dataset from German dispatching regions that we publish together with this paper. We prove optimality for 70 of the 112 DISPLIB instances within short running times, and we find 27 new best known solutions within a 10-minute time limit.
Cite as
Luka Stärk, Ralf Borndörfer, and Niels Lindner. From Routes to Resources: A Model for Real-Time Train Dispatching with No-Wait Constraints. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{stark_et_al:OASIcs.ATMOS.2026.6,
author = {St\"{a}rk, Luka and Bornd\"{o}rfer, Ralf and Lindner, Niels},
title = {{From Routes to Resources: A Model for Real-Time Train Dispatching with No-Wait Constraints}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {6:1--6:20},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.6},
URN = {urn:nbn:de:0030-drops-278024},
doi = {10.4230/OASIcs.ATMOS.2026.6},
annote = {Keywords: Train Dispatching, No-Wait Constraints, Disjunctive Graph, Edge Clique Cover, Microscopic Railway Timetabling}
}
Document
Adaptive Metaheuristics for Multi-Objective Berth Allocation and Scheduling
Abstract
The Berth Allocation and Scheduling Problem (BASP) is a challenging combinatorial optimisation problem arising in container terminal operations, where decisions must balance conflicting goals including operational efficiency, economic cost, environmental impact, and infrastructure utilisation. This paper investigates the multi-objective discrete dynamic BASP with time windows and introduces a four-objective mixed-integer linear programming formulation that simultaneously captures vessel service efficiency, CO₂ emissions, operating cost, and berth workload balance.
To solve this computationally challenging problem, we develop and systematically evaluate adaptive multi-objective metaheuristic approaches. First, we adapt four evolutionary multi-objective algorithms through problem-specific variation operators and an adaptive operator selection mechanism. Second, we extend Adaptive Large Neighbourhood Search (ALNS) to the multi-objective BASP setting and propose two variants: SMOALNS, based on an external Pareto archive, and NSALNS, which integrates ALNS with NSGAII environmental selection.
Extensive computational experiments demonstrate that adaptive operator selection consistently improves evolutionary baselines and that the proposed multi-objective ALNS approaches achieve the best overall performance across benchmark instances. The results indicate that adaptive destroy-repair search mechanisms are particularly effective for highly constrained berth scheduling problems, providing high-quality approximations of the Pareto front for realistic port management scenarios.
Cite as
Konstantinos Karathanasis, Spyros Kontogiannis, Asterios Pegos, Vasileios Sofianos, and Christos Zaroliagis. Adaptive Metaheuristics for Multi-Objective Berth Allocation and Scheduling. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{karathanasis_et_al:OASIcs.ATMOS.2026.7,
author = {Karathanasis, Konstantinos and Kontogiannis, Spyros and Pegos, Asterios and Sofianos, Vasileios and Zaroliagis, Christos},
title = {{Adaptive Metaheuristics for Multi-Objective Berth Allocation and Scheduling}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {7:1--7:22},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.7},
URN = {urn:nbn:de:0030-drops-278031},
doi = {10.4230/OASIcs.ATMOS.2026.7},
annote = {Keywords: Berth Allocation and Scheduling, Multi-objective Optimization, Metaheuristics, Evolutionary Computation}
}
Document
Finding Maximum-Success Disjoint Paths
Abstract
Motivated by challenges occurring in disaster relief operations, we study the problem to find two edge-disjoint paths in a graph whose arcs are labeled with traversability probabilities that maximize the probability that (at least) one of the paths is traversable.
We show that this problem is NP-hard. To solve the problem, we propose to model it as a bi-objective problem, taking traversability probabilities of the two individual paths as objective functions. We show that an optimal solution to our problem is an extreme-supported solution of the so defined bi-objective problem and exploit this property to find optimal solutions. Furthermore, we present two approximation approaches, and compare the approaches experimentally with respect to runtime and solution quality.
Cite as
Aaron Neugebauer and Marie Schmidt. Finding Maximum-Success Disjoint Paths. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{neugebauer_et_al:OASIcs.ATMOS.2026.8,
author = {Neugebauer, Aaron and Schmidt, Marie},
title = {{Finding Maximum-Success Disjoint Paths}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {8:1--8:18},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.8},
URN = {urn:nbn:de:0030-drops-278048},
doi = {10.4230/OASIcs.ATMOS.2026.8},
annote = {Keywords: Route finding under uncertainty, Edge-disjoint paths, Optimization, Exact algorithms, Approximation algorithms, Vectorization}
}
Document
Scheduling Electric-Vehicle Charging Under Grid Capacity and Minimum Charge Rates
Abstract
Electric vehicle adoption is growing rapidly, and parking facilities face increasing pressure to expand their charging infrastructure. This paper studies the power allocation scheduling problem that arises when a parking facility with fixed grid-capacity limit must distribute power to connected electric vehicles, under given lower and upper bounds on the charge rate at any given time. We focus on the optimization goal of maximizing the number of vehicles that get charged a given target of power, with the secondary goal of providing as much power as possible. We show that the problem is NP-hard. We formulate the problem as a mixed-integer linear program (MILP) that establishes a theoretical upper bound on performance of any online algorithm, which is the main goal of the real-world problem. We design and compare a few online scheduling strategies against the offline bound, using a real-world instance of vehicles and testing across 6 to 40 chargers. We use MILP as an online strategy, classical earliest-deadline first greedy algorithm, and we also design data-driven approaches using machine learning techniques. Results show that the simplest static load balancing approach cannot compete with the best performing online approach, and that the real-world problem can benefit from dynamic load balancing strategies such as those designed and evaluated in this paper.
Cite as
Bruna Cavalcanti Lauro, Matúš Mihalák, Filip Schlembach, and Evgueni Smirnov. Scheduling Electric-Vehicle Charging Under Grid Capacity and Minimum Charge Rates. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{cavalcantilauro_et_al:OASIcs.ATMOS.2026.9,
author = {Cavalcanti Lauro, Bruna and Mihal\'{a}k, Mat\'{u}\v{s} and Schlembach, Filip and Smirnov, Evgueni},
title = {{Scheduling Electric-Vehicle Charging Under Grid Capacity and Minimum Charge Rates}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {9:1--9:17},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.9},
URN = {urn:nbn:de:0030-drops-278059},
doi = {10.4230/OASIcs.ATMOS.2026.9},
annote = {Keywords: Electric-Vehicle Charging, Scheduling, Grid-Capacity Constraints, Charge-Rate Lower-Bounds}
}
Document
ASPaeroFlow: Decomposition Heuristics for Joint Air Traffic Flow & Capacity Management
Abstract
While mathematical models act as vital decision support systems for operational Air Traffic Flow and Capacity Management (ATFCM), existing approaches isolate Air Traffic Flow Management (ATFM) from Dynamic Airspace Configuration (DAC). This separation introduces an unresolved circular dependency between fixed-demand and fixed-capacity assumptions. Although joint optimization resolves this gap, the enlarged search space renders exact models computationally intractable for medium- to large-scale instances. To bridge this gap, we propose ASPaeroFlow: a heuristic for the joint ATFCM; it combines instance-space decomposition heuristics with a local exact approach using Answer Set Programming. We benchmark ASPaeroFlow from small to industry-sized instances and compare it with exact and alternative approaches. The results indicate that (1) the heuristic provides a computational middle ground between exact methods and operational baselines; (2) simultaneous optimization can outperform sequential optimization on joint ATFCM; and (3) an ablation study indicates that DAC has a larger impact on solution quality than flow measures.
Cite as
Alexander Beiser, Markus Hecher, Nysret Musliu, Georg Trausmuth, and Stefan Woltran. ASPaeroFlow: Decomposition Heuristics for Joint Air Traffic Flow & Capacity Management. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{beiser_et_al:OASIcs.ATMOS.2026.10,
author = {Beiser, Alexander and Hecher, Markus and Musliu, Nysret and Trausmuth, Georg and Woltran, Stefan},
title = {{ASPaeroFlow: Decomposition Heuristics for Joint Air Traffic Flow \& Capacity Management}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {10:1--10:20},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.10},
URN = {urn:nbn:de:0030-drops-278067},
doi = {10.4230/OASIcs.ATMOS.2026.10},
annote = {Keywords: Air Traffic Flow and Capacity Management, ATFCM, Answer Set Programming, Heuristics, Open Data}
}
Document
Integrated Line Planning and Strategic Ridepooling: Minimizing the Passengers' Travel Time
Abstract
Public transport systems increasingly combine fixed-line services with demand-responsive transportation such as ridepooling. In this paper, we present an integrated optimization model for line planning and strategic ridepooling that explicitly incorporates passenger routing into the planning process. Building on previous work on integrated line planning and strategic ridepooling as well as Change&Go networks, we develop a model for the integration of line planning and strategic ridepooling that minimizes the total travel time of all passengers while respecting a given budget. The resulting mixed-integer optimization model simultaneously determines line frequencies, ridepooling capacities, and passenger routes, capturing interactions between the two different transportation modes – one line-based mode and one mode without fixed lines and timetables – and still accounts for travel times, transfer times, and capacity decisions within a single optimization model. Focusing on an applicable model, we show how the data structure of an existing line planning model with integrated passenger routing in a Change&Go network can be improved, rendering the problem solvable for medium-sized instances. We consider the optimization model as a bi-criteria problem with the objective functions of travel time and operating cost, and compute pareto-optimal solutions with a budget constraint method. Our computational experiments on benchmark instances demonstrate the applicability of the model and show that integrating passenger routing into the strategic planning process yields multimodal transport systems that dominate solutions from approaches based on fixed routings.
Cite as
Lena Dittrich, Sven Jäger, and Anita Schöbel. Integrated Line Planning and Strategic Ridepooling: Minimizing the Passengers' Travel Time. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{dittrich_et_al:OASIcs.ATMOS.2026.11,
author = {Dittrich, Lena and J\"{a}ger, Sven and Sch\"{o}bel, Anita},
title = {{Integrated Line Planning and Strategic Ridepooling: Minimizing the Passengers' Travel Time}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {11:1--11:18},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.11},
URN = {urn:nbn:de:0030-drops-278078},
doi = {10.4230/OASIcs.ATMOS.2026.11},
annote = {Keywords: Multi-modal planning, Line planning, Ridepooling, Integrated models}
}
Document
A Multimodal Framework for Transport Planning
Abstract
Planning high-quality public transport systems requires taking multiple modalities of transportation into account simultaneously. This includes public transport such as trains or buses, but also ridepooling, walking or biking. While planning of public transport lines and timetables has been studied extensively for unimodal systems, research on settings which include more than one modality is just at its beginning. In this paper, we categorize the modalities as line-based, ridepooling, and nonscheduled for which we develop a framework for multimodal planning. This can be applied for different line-based modalities, e.g., for planning bus and tram lines simultaneously, but also for modalities from different categories, e.g., for planning ridepooling together with bus lines while taking footpaths into account. Technically, we extend classic graph structures from unimodal public transport optimization to the multimodal case and show how established solution methods for the unimodal case carry over to the multimodal setting. In particular, we formulate multimodal line planning and periodic timetabling problems. We demonstrate the practical applicability of the framework through a case study on real-world data from Helsinki, Finland, considering five line-based modalities and walking. Our experiments show that incorporating multimodal aspects into the planning process consistently reduces average passenger travel time.
Cite as
Lena Dittrich, Michael Rihlmann, Philine Schiewe, and Anita Schöbel. A Multimodal Framework for Transport Planning. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{dittrich_et_al:OASIcs.ATMOS.2026.12,
author = {Dittrich, Lena and Rihlmann, Michael and Schiewe, Philine and Sch\"{o}bel, Anita},
title = {{A Multimodal Framework for Transport Planning}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {12:1--12:20},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.12},
URN = {urn:nbn:de:0030-drops-278084},
doi = {10.4230/OASIcs.ATMOS.2026.12},
annote = {Keywords: multimodal planning, line planning, timetabling}
}
Document
Exploiting Treewidth to Solve the Pricing Problem in Column Generation for Non-Pool-Based Line Planning
Abstract
The line planning problem (LPP) involves determining a set of lines (routes for vehicles to travel on) for a transportation network that meet travel demands while minimizing both travel time and the line operation costs. Unfortunately, this problem is NP-hard. Recently, Heinrich et al. [Irene Heinrich et al., 2023] proposed using treewidth to solve (a variant of) this problem; however, the sizes of networks and values of treewidth for which it is practical are limited.
We propose a different way of exploiting bounded treewidth in solving the LPP. We combine a column generation approach due to Borndörfer et al. [Ralf Borndörfer et al., 2007] with dynamic programming on tree decompositions to solve the pricing problem, which entails solving the NP-hard longest path problem.
We show that this approach is feasible. We are able to apply our approach to graphs with both more vertices and higher treewidth (up to 9) than Heinrich et al. We experimentally evaluate our approach using artificial benchmarks (connected concentric ring graphs) and two practical examples, the Munich train/subway network and the Japanese railroad system.
Cite as
Markus Niebisch and Tom C. van der Zanden. Exploiting Treewidth to Solve the Pricing Problem in Column Generation for Non-Pool-Based Line Planning. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{niebisch_et_al:OASIcs.ATMOS.2026.13,
author = {Niebisch, Markus and van der Zanden, Tom C.},
title = {{Exploiting Treewidth to Solve the Pricing Problem in Column Generation for Non-Pool-Based Line Planning}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {13:1--13:20},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.13},
URN = {urn:nbn:de:0030-drops-278093},
doi = {10.4230/OASIcs.ATMOS.2026.13},
annote = {Keywords: line planning, public transport, treewidth, integer programming, fixed parameter tractability, column generation}
}
Document
Algorithmics for Safe Bicycle Network Design with Bounded Detours in Rural Areas
Abstract
We introduce the Safe Bicycle Network with Bounded Detours (SBNBD) problem, a network-design problem motivated by the upgrade of rural road networks for bicycle traffic. Given an undirected graph whose edges have length and are classified as safe or unsafe with unsafe edges carrying upgrade costs, a set of terminal pairs, an upgrade budget, and a detour factor α, the task is to upgrade unsafe edges so that every terminal pair is connected by a safe path whose length is at most α times its shortest-path distance in the original network.
We study the computational complexity of SBNBD from a parameterized perspective. We prove strong NP-hardness even on highly restricted graph classes, including planar graphs of treewidth two, graphs with feedback vertex set number one, and graphs of maximum degree three. We complement these lower bounds with polynomial-time algorithms for trees and graphs of maximum degree two. For parameterized complexity, we show fixed-parameter tractability for the number of unsafe edges and prove matching lower bounds under SETH, a polynomial-kernel lower bound, and W-hardness for natural parameters. Our main positive structural result is an algorithm that maps any instance to an equivalent instance with O(fes+p) vertices and edges, where fes is the feedback edge number and p is the number of terminal pairs; this yields fixed-parameter tractability for the combined parameter fes+p.
Finally, we construct and evaluate exact ILP-based algorithms on road networks derived from OpenStreetMap data for small German municipalities and their surrounding rural regions. The experiments show that these networks have small treewidth upper bounds and moderate feedback edge structure. We introduce a preprocessing routine based on the reduction algorithm for the parameter fes+p and a heuristic cut generation based on tree decompositions. Both improve exact solving performance, in particular for harder instances. Our results for different detour-factor bounds show that a moderate increase in α can substantially reduce the total length of the upgraded network, revealing practical trade-offs between upgrade budget and the maximum allowed relative detour. Our results indicate that structural graph parameters provide a useful algorithmic lens for safe bicycle-network design in rural areas.
Cite as
Till Fluschnik. Algorithmics for Safe Bicycle Network Design with Bounded Detours in Rural Areas. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 14:1-14:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{fluschnik:OASIcs.ATMOS.2026.14,
author = {Fluschnik, Till},
title = {{Algorithmics for Safe Bicycle Network Design with Bounded Detours in Rural Areas}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {14:1--14:22},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.14},
URN = {urn:nbn:de:0030-drops-278106},
doi = {10.4230/OASIcs.ATMOS.2026.14},
annote = {Keywords: Parameterized Algorithms, NP-hardness, Pairwise weighted spanners, Preprocessing, Integer linear programming, Cut generation}
}
Document
Large Scale Middle Mile Network Design Through Efficient Local Search
Abstract
E-commerce competition has intensified in recent years, further raising the delivery speed and cost efficiency standards that companies must meet. The middle mile network that connects fulfillment centers to local distribution centers plays a decisive role in achieving these standards. In this paper, we study the Middle Mile Network Design Problem, which determines optimal network investments that balance the trade-off between fastest delivery speed and minimal operational costs. The problem requires computing truck schedules, shipment routes, and parcel flows through intermediate facilities subject to complex capacity constraints. Two key challenges make this problem computationally hard to solve for standard exact and heuristic approaches: (i) the use of complex black-box evaluations to predict operational outcomes, and (ii) problem instances involving over 200,000 commodities that must be solved within hours for operational planning. We propose a metaheuristic based on variable neighborhood search with specialized local search operators alongside lazy neighborhood evaluation that enable efficient exploration of the high-dimensional solution space. Our algorithm achieves up to 7.6% solution improvement over an incumbent heuristic while reducing runtime by up to 44%.
Cite as
Carlo S. Sartori, Jian Shen, Anastasia Kireeva, Mattia Neroni, and Philipp Loick. Large Scale Middle Mile Network Design Through Efficient Local Search. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{sartori_et_al:OASIcs.ATMOS.2026.15,
author = {Sartori, Carlo S. and Shen, Jian and Kireeva, Anastasia and Neroni, Mattia and Loick, Philipp},
title = {{Large Scale Middle Mile Network Design Through Efficient Local Search}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {15:1--15:18},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.15},
URN = {urn:nbn:de:0030-drops-278110},
doi = {10.4230/OASIcs.ATMOS.2026.15},
annote = {Keywords: Network design, Middle mile logistics, Black-box evaluation, Local search, Variable Neighborhood Search}
}
Document
Short Paper
Computing the Cost of Stability in Periodic Microscopic Railway Timetabling via Logic-Based Benders Decomposition (Short Paper)
Abstract
Periodic railway timetables require stability in operation, but the cost of increasing stability in terms of total travel time remains unclear. We study this cost of stability in microscopic periodic timetabling using the realisable cycle time as a stability measure. To implement stability, we compress the timetable to a shorter realisable cycle time that remains feasible at the microscopic level, and then rescale it back to the nominal period used in regular operation. The difference between this nominal period and the realisable cycle time becomes the time supplement available for absorbing delays. We formulate an optimization problem that jointly considers realisable cycle time and total travel time, and solve it with Logic-Based Benders Decomposition. The master problem optimizes commercial timing variables, while the subproblem verifies microscopic feasibility with routing, periodicity, and resource-conflict constraints. Infeasible subproblems yield activity cuts that constrain the master. Experiments on two Swiss railway case studies show that the proposed decomposition substantially improves computational performance on the larger instance and reveals nonlinear cost-of-stability frontiers with topology-dependent infeasible cycle-time regions and exceptionally high marginal costs at certain stability levels.
Cite as
Tongcheng Ouyang, Florian Flükiger-Fuchs, Bernardo Martin-Iradi, and Francesco Corman. Computing the Cost of Stability in Periodic Microscopic Railway Timetabling via Logic-Based Benders Decomposition (Short Paper). In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 16:1-16:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{ouyang_et_al:OASIcs.ATMOS.2026.16,
author = {Ouyang, Tongcheng and Fl\"{u}kiger-Fuchs, Florian and Martin-Iradi, Bernardo and Corman, Francesco},
title = {{Computing the Cost of Stability in Periodic Microscopic Railway Timetabling via Logic-Based Benders Decomposition}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {16:1--16:6},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.16},
URN = {urn:nbn:de:0030-drops-278128},
doi = {10.4230/OASIcs.ATMOS.2026.16},
annote = {Keywords: Railway timetabling, periodic stability, microscopic timetabling, logic-based Benders decomposition}
}
Document
Short Paper
Integrated Location-Routing-Scheduling for Multi-Trip Mobile Parcel Lockers with Time Windows (Short Paper)
Abstract
Mobile parcel lockers can reposition delivery capacity during the day, but this flexibility requires decisions that are tightly linked: where lockers stop, which customers are assigned to each stop, how lockers move, and when service takes place. We introduce the multi-trip mobile parcel locker problem with time windows (MT-MPLP-TW), which integrates locker deployment, customer assignment, parking selection, routing, scheduling, parking capacity, walking limits, and depot replenishment. We present a compact mixed-integer programming formulation and a logic-based Benders decomposition (LBBD) that separates route-and-assignment decisions from detailed time-expanded certification. Computational results on generated instances and on the single-trip mobile parcel locker benchmark show that the compact formulation is effective on small and medium instances, while LBBD gives stronger performance on larger and more constrained cases.
Cite as
Salma Essouaied, Leandro C. Coelho, Christophe Wilbaut, and Raca Todosijević. Integrated Location-Routing-Scheduling for Multi-Trip Mobile Parcel Lockers with Time Windows (Short Paper). In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 17:1-17:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{essouaied_et_al:OASIcs.ATMOS.2026.17,
author = {Essouaied, Salma and Coelho, Leandro C. and Wilbaut, Christophe and Todosijevi\'{c}, Raca},
title = {{Integrated Location-Routing-Scheduling for Multi-Trip Mobile Parcel Lockers with Time Windows}},
booktitle = {26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026)},
pages = {17:1--17:6},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-453-6},
ISSN = {2190-6807},
year = {2026},
volume = {147},
editor = {Cacchiani, Valentina and Funke, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2026.17},
URN = {urn:nbn:de:0030-drops-278132},
doi = {10.4230/OASIcs.ATMOS.2026.17},
annote = {Keywords: Mobile parcel lockers, City logistics, Routing and scheduling, Mixed-integer programming, Logic-based Benders decomposition}
}