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Subproblem Separation in Logic-Based Benders' Decomposition for the Vehicle Routing Problem with Local Congestion

Authors Aigerim Saken , Stephen J. Maher

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Author Details

Aigerim Saken
  • Department of Mathematics, University of Exeter, United Kingdom
Stephen J. Maher
  • Quantagonia GmbH, Bad Homburg, Germany


Computational experiments were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) and National Academic Infrastructure for Supercomputing in Sweden (NAISS).

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Aigerim Saken and Stephen J. Maher. Subproblem Separation in Logic-Based Benders' Decomposition for the Vehicle Routing Problem with Local Congestion. In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 16:1-16:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


Subproblem separation is a common strategy for the acceleration of the logic-based Benders' decomposition (LBBD). However, it has only been applied to problems with an inherently separable subproblem structure. This paper proposes a new method to separate the subproblem using the connected components algorithm. The subproblem separation is applied to the vehicle routing problem with local congestion (VRPLC). Accordingly, new Benders' cuts are derived for the new subproblem formulation. The computational experiments evaluate the effectiveness of subproblem separation for different methods applying new cuts. It is shown that subproblem separation significantly benefits the LBBD scheme.

Subject Classification

ACM Subject Classification
  • Theory of computation → Mathematical optimization
  • Applied computing → Transportation
  • logic-based Benders' decomposition
  • vehicle routing
  • subproblem separation
  • connected components


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