04. Solution of the Train Platforming Problem

Caprara, Alberto; Galli, Laura; Toth, Paolo

doi:10.4230/OASIcs.ATMOS.2007.1174

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04. Solution of the Train Platforming Problem

Authors Alberto Caprara, Laura Galli, Paolo Toth

Part of: Volume: 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07) (ATMOS 2007)
Part of: Series: Open Access Series in Informatics (OASIcs)
Part of: Conference: Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2007-11-06

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Document Identifiers

DOI: 10.4230/OASIcs.ATMOS.2007.1174
URN: urn:nbn:de:0030-drops-11741

Subject Classification

Keywords

Train Platforming
Train Routing
Branch-and-Cut-and-Price
Quadratic Objective Function
Linearization

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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.

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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) https://doi.org/10.4230/OASIcs.ATMOS.2007.1174

Author Details

Alberto Caprara

Laura Galli

Paolo Toth

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