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Documents authored by Toth, Paolo

Document
DOI: 10.4230/OASIcs.ATMOS.2012.1
A Fast Heuristic Algorithm for the Train Unit Assignment Problem

Authors: Valentina Cacchiani, Alberto Caprara, and Paolo Toth

Published in: OASIcs, Volume 25, 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2012)

Abstract
In this paper we study a railway optimization problem known as the Train Unit Assignment Problem. A train unit consists of a self-contained train with an engine and a set of wagons with passenger seats. Given a set of timetabled train trips, each with a required number of passenger seats, and a set of train units, each with a given number of available seats, the problem calls for the best assignment of the train units to the trips, possibly combining more than one train unit for a given trip, that fulfills the seat requests. We propose a heuristic algorithm based on the computation of a lower bound obtained by solving an Integer Linear Programming model that gives the optimal solution in a "peak period" of the day. The performance of the heuristic algorithm is computationally evaluated on real-world instances provided by a regional Italian Train Operator. The results are compared with those of existing methods from the literature, showing that the new method is able to obtain solutions of good quality in much shorter computing times.
Cite as

Valentina Cacchiani, Alberto Caprara, and Paolo Toth. A Fast Heuristic Algorithm for the Train Unit Assignment Problem. In 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 25, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{cacchiani_et_al:OASIcs.ATMOS.2012.1,
  author =	{Cacchiani, Valentina and Caprara, Alberto and Toth, Paolo},
  title =	{{A Fast Heuristic Algorithm for the Train Unit Assignment Problem}},
  booktitle =	{12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{1--9},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-45-3},
  ISSN =	{2190-6807},
  year =	{2012},
  volume =	{25},
  editor =	{Delling, Daniel and Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2012.1},
  URN =		{urn:nbn:de:0030-drops-36971},
  doi =		{10.4230/OASIcs.ATMOS.2012.1},
  annote =	{Keywords: Train Unit Assignment, Heuristic Algorithm, ILP model, Real-world instances}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2010.24
Robust Train Routing and Online Re-scheduling

Authors: Alberto Caprara, Laura Galli, Leo Kroon, Gábor Maróti, and Paolo Toth

Published in: OASIcs, Volume 14, 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10) (2010)

Abstract
Train Routing is a problem that arises in the early phase of the passenger railway planning process, usually several months before operating the trains. The main goal is to assign each train a stopping platform and the corresponding arrival/departure paths through a railway station. It is also called Train Platforming when referring to the platform assignment task. Railway stations often represent bottlenecks and train delays can easily disrupt the routing schedule. Thereby railway stations are responsible for a large part of the delay propagation in the whole network. In this research we present different models to compute robust routing schedules and we study their power in an online context together with different re-scheduling strategies. We also design a simulation framework and use it to evaluate and compare the effectiveness of the proposed robust models and re-scheduling algorithms using real-world data from Rete Ferroviaria Italiana, the main Italian Railway Infrastructure Manager.
Cite as

Alberto Caprara, Laura Galli, Leo Kroon, Gábor Maróti, and Paolo Toth. Robust Train Routing and Online Re-scheduling. In 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10). Open Access Series in Informatics (OASIcs), Volume 14, pp. 24-33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{caprara_et_al:OASIcs.ATMOS.2010.24,
  author =	{Caprara, Alberto and Galli, Laura and Kroon, Leo and Mar\'{o}ti, G\'{a}bor and Toth, Paolo},
  title =	{{Robust Train Routing and Online Re-scheduling}},
  booktitle =	{10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10)},
  pages =	{24--33},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-20-0},
  ISSN =	{2190-6807},
  year =	{2010},
  volume =	{14},
  editor =	{Erlebach, Thomas and L\"{u}bbecke, Marco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2010.24},
  URN =		{urn:nbn:de:0030-drops-27470},
  doi =		{10.4230/OASIcs.ATMOS.2010.24},
  annote =	{Keywords: Railway optimisation, Train platforming, Robust planning, Online re-scheduling, Simulation}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2007.1174
04. Solution of the Train Platforming Problem

Authors: Alberto Caprara, Laura Galli, and Paolo Toth

Published in: OASIcs, Volume 7, 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07) (2007)

Abstract
In this paper we study a general formulation of the train platforming problem, which contains as special cases all the versions previously considered in the literature as well as a case study from the Italian Infrastructure manager that we addressed. In particular, motivated by our case study, we consider a general quadratic objective function, and propose a new way to linearize it by using a small number of new variables along with a set of constraints that can be separated efficiently by solving an appropriate linear program. The resulting integer linear programming formulation has a continuous relaxation that leads to strong bounds on the optimal value. For the instances in our case study, we show that a simple diving heuristic based on this relaxation produces solutions that are much better than those produced by a simple heuristic currently in use, and that often turn out to be (nearly-) optimal.
Cite as

Alberto Caprara, Laura Galli, and Paolo Toth. 04. Solution of the Train Platforming Problem. In 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07). Open Access Series in Informatics (OASIcs), Volume 7, pp. 49-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{caprara_et_al:OASIcs.ATMOS.2007.1174,
  author =	{Caprara, Alberto and Galli, Laura and Toth, Paolo},
  title =	{{04. Solution of the Train Platforming Problem}},
  booktitle =	{7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07)},
  pages =	{49--61},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-04-0},
  ISSN =	{2190-6807},
  year =	{2007},
  volume =	{7},
  editor =	{Ahuja, Ravindra K. and Liebchen, Christian and Mesa, Juan A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2007.1174},
  URN =		{urn:nbn:de:0030-drops-11741},
  doi =		{10.4230/OASIcs.ATMOS.2007.1174},
  annote =	{Keywords: Train Platforming, Train Routing, Branch-and-Cut-and-Price, Quadratic Objective Function, Linearization}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2007.1172
06. Solving a Real-World Train Unit Assignment Problem

Authors: Valentina Cacchiani, Alberto Caprara, and Paolo Toth

Published in: OASIcs, Volume 7, 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07) (2007)

Abstract
INVALID Windows-1252: We face a real-world train unit assignment problem for an operator running trains in a regional area. Given a set of timetabled train trips, each with a required number of passenger seats, and a set of train units, each with a given number of available seats, the problem calls for an assignment of the train units to trips, possibly combining more than one train unit for a given trip, that fulfills the seat requests. With respect to analogous case studies previously faced in the literature, ours is characterized by the fairly large number of distinct train unit types available (in addition to the fairly large number of trips to be covered). As a result, although there is a wide margin of improvement over the solution used by the practitioners (as our results show), even only finding a solution of the same value is challenging in practice. We present a successful approach, based on an ILP formulation in which the seat requirement constraints are stated in a “strong” form, derived from the description of the convex hull of the variant of the knapsack polytope arising when the sum of the variables is restricted not to exceed two, illustrating computational results on our case study.
Cite as

Valentina Cacchiani, Alberto Caprara, and Paolo Toth. 06. Solving a Real-World Train Unit Assignment Problem. In 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07). Open Access Series in Informatics (OASIcs), Volume 7, pp. 79-95, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

Copy BibTex To Clipboard

@InProceedings{cacchiani_et_al:OASIcs.ATMOS.2007.1172,
  author =	{Cacchiani, Valentina and Caprara, Alberto and Toth, Paolo},
  title =	{{06. Solving a Real-World Train Unit Assignment Problem}},
  booktitle =	{7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07)},
  pages =	{79--95},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-04-0},
  ISSN =	{2190-6807},
  year =	{2007},
  volume =	{7},
  editor =	{Ahuja, Ravindra K. and Liebchen, Christian and Mesa, Juan A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2007.1172},
  URN =		{urn:nbn:de:0030-drops-11726},
  doi =		{10.4230/OASIcs.ATMOS.2007.1172},
  annote =	{Keywords: }
}
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